Homework 3: Regression Model Selection and Regularization
Yu Zhang
4/28/2020
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# Q1. Perform all necessary cleaning and transformation of the data to make it useful for regression modeling. Hint: It might be easier just to set some variables up as factors rather than to create indicator variables across the board.
setwd("/Users/Fisher/Desktop/BANA 288 Predictive Analytics/HW3 Regression Model Selection and Regularization")
dbike <- read.csv("hw3_hour.csv")
dim(dbike)## [1] 17379 15str(dbike)## 'data.frame': 17379 obs. of 15 variables:
## $ obs : int 1 2 3 4 5 6 7 8 9 10 ...
## $ dteday : Factor w/ 731 levels "1/1/2011","1/1/2012",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ season : int 1 1 1 1 1 1 1 1 1 1 ...
## $ yr : int 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth : int 1 1 1 1 1 1 1 1 1 1 ...
## $ hr : int 0 1 2 3 4 5 6 7 8 9 ...
## $ holiday : int 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday : int 6 6 6 6 6 6 6 6 6 6 ...
## $ workday : int 0 0 0 0 0 0 0 0 0 0 ...
## $ weathersit: int 1 1 1 1 1 2 1 1 1 1 ...
## $ temp : num 0.24 0.22 0.22 0.24 0.24 0.24 0.22 0.2 0.24 0.32 ...
## $ atemp : num 0.288 0.273 0.273 0.288 0.288 ...
## $ hum : num 0.81 0.8 0.8 0.75 0.75 0.75 0.8 0.86 0.75 0.76 ...
## $ windspeed : num 0 0 0 0 0 0.0896 0 0 0 0 ...
## $ cnt : int 16 40 32 13 1 1 2 3 8 14 ...head(dbike)## obs dteday season yr mnth hr holiday wkday workday weathersit temp atemp
## 1 1 1/1/2011 1 0 1 0 0 6 0 1 0.24 0.2879
## 2 2 1/1/2011 1 0 1 1 0 6 0 1 0.22 0.2727
## 3 3 1/1/2011 1 0 1 2 0 6 0 1 0.22 0.2727
## 4 4 1/1/2011 1 0 1 3 0 6 0 1 0.24 0.2879
## 5 5 1/1/2011 1 0 1 4 0 6 0 1 0.24 0.2879
## 6 6 1/1/2011 1 0 1 5 0 6 0 2 0.24 0.2576
## hum windspeed cnt
## 1 0.81 0.0000 16
## 2 0.80 0.0000 40
## 3 0.80 0.0000 32
## 4 0.75 0.0000 13
## 5 0.75 0.0000 1
## 6 0.75 0.0896 1dbike1 <- dbike
dbike1$wkday <- as.factor(dbike1$wkday)
dbike1$season <- as.factor(dbike1$season)
dbike1$mnth <- as.factor(dbike1$mnth)
dbike1$weathersit <- as.factor(dbike1$weathersit)
#dbike1$yr <- as.factor(dbike1$yr)
#dbike1$holiday <- as.factor(dbike1$holiday)
#dbike1$workday <- as.factor(dbike1$workday)
dbike1 <- mutate(dbike1,
daytime = ifelse(dbike1$hr %in% c(7,8,9,10,11,12,13,14,15,16,17,18), 1, 0))
#dbike1$daytime <- as.factor(dbike1$daytime)
dbike1 <- dbike1 %>%
cbind(acm.disjonctif(dbike1[c("season","mnth","wkday","weathersit")])) %>%
ungroup()
str(dbike1)## 'data.frame': 17379 obs. of 43 variables:
## $ obs : int 1 2 3 4 5 6 7 8 9 10 ...
## $ dteday : Factor w/ 731 levels "1/1/2011","1/1/2012",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ season : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...
## $ yr : int 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth : Factor w/ 12 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ hr : int 0 1 2 3 4 5 6 7 8 9 ...
## $ holiday : int 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday : Factor w/ 7 levels "0","1","2","3",..: 7 7 7 7 7 7 7 7 7 7 ...
## $ workday : int 0 0 0 0 0 0 0 0 0 0 ...
## $ weathersit : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 2 1 1 1 1 ...
## $ temp : num 0.24 0.22 0.22 0.24 0.24 0.24 0.22 0.2 0.24 0.32 ...
## $ atemp : num 0.288 0.273 0.273 0.288 0.288 ...
## $ hum : num 0.81 0.8 0.8 0.75 0.75 0.75 0.8 0.86 0.75 0.76 ...
## $ windspeed : num 0 0 0 0 0 0.0896 0 0 0 0 ...
## $ cnt : int 16 40 32 13 1 1 2 3 8 14 ...
## $ daytime : num 0 0 0 0 0 0 0 1 1 1 ...
## $ season.1 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ season.2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ season.3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ season.4 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.1 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ mnth.2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.4 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.5 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.6 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.7 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.8 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.9 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.10 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.11 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.12 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.0 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.4 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.5 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.6 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ weathersit.1: num 1 1 1 1 1 0 1 1 1 1 ...
## $ weathersit.2: num 0 0 0 0 0 1 0 0 0 0 ...
## $ weathersit.3: num 0 0 0 0 0 0 0 0 0 0 ...
## $ weathersit.4: num 0 0 0 0 0 0 0 0 0 0 ...dbike2 <- dbike1 %>%
select(-obs, -hr, -dteday, -season.4, -mnth.12, -weathersit.4, -season, -mnth, -wkday, -weathersit)
str(dbike2)## 'data.frame': 17379 obs. of 33 variables:
## $ yr : int 0 0 0 0 0 0 0 0 0 0 ...
## $ holiday : int 0 0 0 0 0 0 0 0 0 0 ...
## $ workday : int 0 0 0 0 0 0 0 0 0 0 ...
## $ temp : num 0.24 0.22 0.22 0.24 0.24 0.24 0.22 0.2 0.24 0.32 ...
## $ atemp : num 0.288 0.273 0.273 0.288 0.288 ...
## $ hum : num 0.81 0.8 0.8 0.75 0.75 0.75 0.8 0.86 0.75 0.76 ...
## $ windspeed : num 0 0 0 0 0 0.0896 0 0 0 0 ...
## $ cnt : int 16 40 32 13 1 1 2 3 8 14 ...
## $ daytime : num 0 0 0 0 0 0 0 1 1 1 ...
## $ season.1 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ season.2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ season.3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.1 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ mnth.2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.4 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.5 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.6 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.7 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.8 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.9 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.10 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.11 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.0 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.4 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.5 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.6 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ weathersit.1: num 1 1 1 1 1 0 1 1 1 1 ...
## $ weathersit.2: num 0 0 0 0 0 1 0 0 0 0 ...
## $ weathersit.3: num 0 0 0 0 0 0 0 0 0 0 ...# season <- as.data.frame(dummy(dbike2$season))
# mnth <- as.data.frame(dummy(dbike2$mnth))
# wkday <- as.data.frame(dummy(dbike2$wkday))
# weathersit <- as.data.frame(dummy(dbike2$weathersit))
#
# dbike2 <- as.data.frame(cbind(dbike2, season, mnth, wkday, weathersit))
# names(dbike2$weathersit)1) <- "Clear"
# names(dbike2$weathersit)2) <- "Mist"
# names(dbike2$weathersit)3) <- "Light"
# names(dbike2$weathersit)4) <- "Heavy"
#
# names(dbike2$wkday)[1] <- "Mon"
# names(dbike2$wkday)[2] <- "Tue"
# names(dbike2$wkday)[3] <- "Wed"
# names(dbike2$wkday)[4] <- "Thur"
# names(dbike2$wkday)[5] <- "Fri"
# names(dbike2$wkday)[6] <- "Sat"
# names(dbike2$wkday)[7] <- "Sun"
#
# names(dbike2$mnth)[1] <- "Jan"
# names(dbike2$mnth)[2] <- "Feb"
# names(dbike2$mnth)[3] <- "Mar"
# names(dbike2$mnth)[4] <- "Apr"
# names(dbike2$mnth)[5] <- "May"
# names(dbike2$mnth)[6] <- "June"
# names(dbike2$mnth)[7] <- "July"
# names(dbike2$mnth)[8] <- "Aug"
# names(dbike2$mnth)[9] <- "Sep"
# names(dbike2$mnth)[10] <- "Oct"
# names(dbike2$mnth)[11] <- "Nov"
# names(dbike2$mnth)[12] <- "Dec"
#
# names(dbike2$season)[1] <- "winter"
# names(dbike2$season)[2] <- "spring"
# names(dbike2$season)[3] <- "summer"
# names(dbike2$season)[4] <- "fall"
#
# dbike2 <- dbike2 %>%
# select(-c("season", "mnth", "wkday", "weathersit"))
#
# str(dbike2)# Q2. Are there any variables with a curvilinear relationship with the response? If so, add squared versions of these variables to the data set. In addition, pick one situation in this data where an interaction term might be useful, that is, where adding an interaction variable might make sense. Explain, in your own words why this is the case. Add the corresponding interaction variable to the data set.
dbike2 %>%
gather(temp, atemp, hum, windspeed, key = "var", value = "value") %>%
ggplot(aes(x = value, y = cnt)) +
geom_point() +
stat_smooth() +
facet_wrap(~ var, scales = "free") +
theme_bw()## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
# temp
reg_temp1 <- lm(cnt ~ temp, data = dbike2)
summary(reg_temp1)##
## Call:
## lm(formula = cnt ~ temp, data = dbike2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -291.37 -110.23 -32.86 76.77 744.76
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.0356 3.4827 -0.01 0.992
## temp 381.2949 6.5344 58.35 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 165.9 on 17377 degrees of freedom
## Multiple R-squared: 0.1638, Adjusted R-squared: 0.1638
## F-statistic: 3405 on 1 and 17377 DF, p-value: < 2.2e-16reg_temp2 <- lm(cnt ~ temp + I(temp^2), data = dbike2)
summary(reg_temp2)##
## Call:
## lm(formula = cnt ~ temp + I(temp^2), data = dbike2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -294.13 -109.58 -33.54 77.07 747.08
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.270 7.735 1.716 0.0862 .
## temp 318.192 33.398 9.527 <2e-16 ***
## I(temp^2) 63.559 32.990 1.927 0.0540 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 165.9 on 17376 degrees of freedom
## Multiple R-squared: 0.164, Adjusted R-squared: 0.1639
## F-statistic: 1705 on 2 and 17376 DF, p-value: < 2.2e-16# atemp
reg_atemp1 <- lm(cnt ~ atemp, data = dbike2)
summary(reg_atemp1)##
## Call:
## lm(formula = cnt ~ atemp, data = dbike2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -314.55 -110.95 -33.25 77.70 743.29
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11.876 3.711 -3.20 0.00137 **
## atemp 423.180 7.335 57.69 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 166.2 on 17377 degrees of freedom
## Multiple R-squared: 0.1607, Adjusted R-squared: 0.1607
## F-statistic: 3328 on 1 and 17377 DF, p-value: < 2.2e-16reg_atemp2 <- lm(cnt ~ atemp + I(atemp^2), data = dbike2)
summary(reg_atemp2)##
## Call:
## lm(formula = cnt ~ atemp + I(atemp^2), data = dbike2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -334.55 -110.12 -34.07 77.86 746.02
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.251 8.414 0.743 0.4575
## atemp 333.616 38.026 8.773 <2e-16 ***
## I(atemp^2) 95.687 39.863 2.400 0.0164 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 166.2 on 17376 degrees of freedom
## Multiple R-squared: 0.161, Adjusted R-squared: 0.1609
## F-statistic: 1667 on 2 and 17376 DF, p-value: < 2.2e-16# hum
reg_hum1 <- lm(cnt ~ hum, data = dbike2)
summary(reg_hum1)##
## Call:
## lm(formula = cnt ~ hum, data = dbike2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -378.88 -118.90 -44.12 78.73 747.91
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 379.88 4.43 85.76 <2e-16 ***
## hum -303.59 6.75 -44.98 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 171.7 on 17377 degrees of freedom
## Multiple R-squared: 0.1043, Adjusted R-squared: 0.1042
## F-statistic: 2023 on 1 and 17377 DF, p-value: < 2.2e-16reg_hum2 <- lm(cnt ~ hum + I(hum^2), data = dbike2)
summary(reg_hum2)##
## Call:
## lm(formula = cnt ~ hum + I(hum^2), data = dbike2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -326.21 -119.64 -42.93 78.43 744.26
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 327.21 11.97 27.338 < 2e-16 ***
## hum -114.08 40.57 -2.812 0.00493 **
## I(hum^2) -153.70 32.45 -4.737 2.19e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 171.6 on 17376 degrees of freedom
## Multiple R-squared: 0.1054, Adjusted R-squared: 0.1053
## F-statistic: 1024 on 2 and 17376 DF, p-value: < 2.2e-16# windspeed
reg_windspeed1 <- lm(cnt ~ windspeed, data = dbike2)
summary(reg_windspeed1)##
## Call:
## lm(formula = cnt ~ windspeed, data = dbike2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -265.47 -146.00 -48.75 90.25 806.81
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 163.185 2.532 64.46 <2e-16 ***
## windspeed 138.233 11.198 12.34 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 180.6 on 17377 degrees of freedom
## Multiple R-squared: 0.008693, Adjusted R-squared: 0.008635
## F-statistic: 152.4 on 1 and 17377 DF, p-value: < 2.2e-16reg_windspeed2 <- lm(cnt ~ windspeed + I(windspeed^2), data = dbike2)
summary(reg_windspeed2)##
## Call:
## lm(formula = cnt ~ windspeed + I(windspeed^2), data = dbike2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -211.00 -141.48 -47.84 90.24 823.24
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 146.755 3.285 44.668 < 2e-16 ***
## windspeed 352.541 29.579 11.918 < 2e-16 ***
## I(windspeed^2) -475.690 60.787 -7.826 5.34e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 180.3 on 17376 degrees of freedom
## Multiple R-squared: 0.01217, Adjusted R-squared: 0.01206
## F-statistic: 107.1 on 2 and 17376 DF, p-value: < 2.2e-16It seems the accuracy of each model were improved by adding squared versions of these variables to the data set.
attach(dbike2)
dbike3 <- dbike2 %>%
mutate(temp2 = temp^2,
atemp2 = atemp^2,
hum2 = hum^2,
windspeed2 = windspeed^2)# Season and temprature will be a set of interactive terms but since we set season as a factor, we could consider use the daytime variable we created. The humidity is also determined by temperature more or less.
cor(dbike3$temp, as.numeric(dbike1$season))## [1] 0.3120252cor(dbike3$temp, as.numeric(dbike1$daytime))## [1] 0.1393702cor(dbike3$temp, dbike1$hum)## [1] -0.06988139dbike3 <- dbike3 %>%
mutate(temp_dif_s = temp * as.numeric(dbike1$season))
str(dbike3)## 'data.frame': 17379 obs. of 38 variables:
## $ yr : int 0 0 0 0 0 0 0 0 0 0 ...
## $ holiday : int 0 0 0 0 0 0 0 0 0 0 ...
## $ workday : int 0 0 0 0 0 0 0 0 0 0 ...
## $ temp : num 0.24 0.22 0.22 0.24 0.24 0.24 0.22 0.2 0.24 0.32 ...
## $ atemp : num 0.288 0.273 0.273 0.288 0.288 ...
## $ hum : num 0.81 0.8 0.8 0.75 0.75 0.75 0.8 0.86 0.75 0.76 ...
## $ windspeed : num 0 0 0 0 0 0.0896 0 0 0 0 ...
## $ cnt : int 16 40 32 13 1 1 2 3 8 14 ...
## $ daytime : num 0 0 0 0 0 0 0 1 1 1 ...
## $ season.1 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ season.2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ season.3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.1 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ mnth.2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.4 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.5 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.6 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.7 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.8 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.9 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.10 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth.11 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.0 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.4 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.5 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ wkday.6 : num 1 1 1 1 1 1 1 1 1 1 ...
## $ weathersit.1: num 1 1 1 1 1 0 1 1 1 1 ...
## $ weathersit.2: num 0 0 0 0 0 1 0 0 0 0 ...
## $ weathersit.3: num 0 0 0 0 0 0 0 0 0 0 ...
## $ temp2 : num 0.0576 0.0484 0.0484 0.0576 0.0576 ...
## $ atemp2 : num 0.0829 0.0744 0.0744 0.0829 0.0829 ...
## $ hum2 : num 0.656 0.64 0.64 0.562 0.562 ...
## $ windspeed2 : num 0 0 0 0 0 ...
## $ temp_dif_s : num 0.24 0.22 0.22 0.24 0.24 0.24 0.22 0.2 0.24 0.32 ...# Q3. Use your own student identification number as a seed in the homework. Randomly select approximately 50% of the rows for a training data set and include the rest of the data in a test data set. Run the “all-variables-in” regression model on the training data. What is the fit for this model?
set.seed(49204366)
split = sample.split(dbike3$cnt, SplitRatio = 0.5)
training_set = subset(dbike3, split == TRUE)
test_set = subset(dbike3, split == FALSE)
as.numeric(dbike1$season)## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [37] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [73] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [109] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [145] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [181] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [217] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [253] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [289] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [325] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [361] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [397] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [433] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [469] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [505] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [541] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [577] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [613] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [649] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [685] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [721] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [757] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [793] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [829] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [865] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [901] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [937] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [973] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1009] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1045] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1081] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1117] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1153] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1189] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1225] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1261] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1405] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1441] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1477] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1513] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1549] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1585] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1621] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1657] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1693] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1729] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1765] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1801] 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1837] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1873] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1909] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1945] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1981] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2017] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2053] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2089] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2125] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2161] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2197] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2233] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2269] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2305] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2341] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2377] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2413] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2449] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2485] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2521] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2557] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2593] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2629] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2665] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2701] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2737] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2773] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2809] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2845] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2881] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2917] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2953] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2989] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3025] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3061] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3097] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3133] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3169] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3205] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3241] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3277] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3313] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3349] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3385] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3421] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3457] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3493] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3529] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3565] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3601] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3637] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3673] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3709] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3745] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3781] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3817] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3853] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3889] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3925] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3961] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3997] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4033] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4069] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4105] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4141] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4177] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4213] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4249] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4285] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4321] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4357] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4393] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4429] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4465] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4501] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4537] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4573] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4609] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4645] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4681] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4717] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4753] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4789] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4825] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4861] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4897] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4933] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4969] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5005] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5041] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5077] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5113] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5149] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5185] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5221] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5257] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5293] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5329] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5365] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5401] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5437] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5473] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5509] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5545] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5581] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5617] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5653] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5689] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5725] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5761] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5797] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5833] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5869] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5905] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5941] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [5977] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [6013] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [6049] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [6085] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [6121] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [6157] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [6193] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [6229] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6265] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6301] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6337] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6373] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6409] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6445] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6481] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6517] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6553] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6589] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6625] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6661] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6697] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6733] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6769] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6805] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6841] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6877] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6913] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6949] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [6985] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7021] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7057] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7093] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7129] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7165] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7201] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7237] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7273] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7309] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7345] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7381] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7417] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7453] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7489] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7525] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7561] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7597] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7633] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7669] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7705] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7741] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7777] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7813] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7849] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7885] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7921] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7957] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [7993] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [8029] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [8065] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [8101] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [8137] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [8173] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [8209] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [8245] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [8281] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [8317] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [8353] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 1 1 1
## [8389] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8425] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8461] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8497] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8533] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8569] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8605] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8641] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8677] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8713] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8749] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8785] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8821] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8857] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8893] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8929] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8965] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9001] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9073] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9109] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9145] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9181] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9217] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9253] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9289] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9325] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9361] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9397] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9433] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9469] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9505] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9541] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9577] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9613] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9649] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9685] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9721] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9757] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9793] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9829] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9865] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9901] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9937] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9973] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10009] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10045] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10081] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10117] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10153] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10189] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10225] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10261] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10405] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10441] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10477] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10513] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10549] 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10585] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10621] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10657] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10693] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10729] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10765] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10801] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10837] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10873] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10909] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10945] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [10981] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11017] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11053] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11089] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11125] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11161] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11197] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11233] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11269] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11305] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11341] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11377] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11413] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11449] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11485] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11521] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11557] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11593] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11629] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11665] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11701] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11737] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11773] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11809] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11845] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11881] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11917] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11953] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [11989] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12025] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12061] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12097] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12133] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12169] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12205] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12241] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12277] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12313] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12349] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12385] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12421] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12457] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12493] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12529] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12565] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12601] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12637] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12673] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12709] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [12745] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [12781] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [12817] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [12853] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [12889] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [12925] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [12961] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [12997] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13033] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13069] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13105] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13141] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13177] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13213] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13249] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13285] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13321] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13357] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13393] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13429] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13465] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13501] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13537] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13573] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13609] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13645] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13681] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13717] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13753] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13789] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13825] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13861] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13897] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13933] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [13969] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14005] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14041] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14077] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14113] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14149] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14185] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14221] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14257] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14293] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14329] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14365] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14401] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14437] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14473] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14509] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14545] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14581] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14617] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14653] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14689] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14725] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14761] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14797] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14833] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14869] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14905] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14941] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [14977] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [15013] 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15049] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15085] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15121] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15157] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15193] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15229] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15265] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15301] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15337] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15373] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15409] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15445] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15481] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15517] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15553] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15589] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15625] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15661] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15697] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15733] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15769] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15805] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15841] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15877] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15913] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15949] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [15985] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16021] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16057] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16093] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16129] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16165] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16201] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16237] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16273] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16309] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16345] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16381] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16417] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16453] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16489] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16525] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16561] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16597] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16633] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16669] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16705] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16741] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16777] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16813] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16849] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16885] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16921] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16957] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [16993] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [17029] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [17065] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [17101] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17137] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17173] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17209] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17245] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17281] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17317] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17353] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1reg_all <- lm(cnt ~., data = training_set)
summary(reg_all)##
## Call:
## lm(formula = cnt ~ ., data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -370.28 -95.52 -18.24 67.08 554.31
##
## Coefficients: (2 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -50.7105 98.4908 -0.515 0.606653
## yr 85.3105 2.9207 29.209 < 2e-16 ***
## holiday -31.4690 10.3739 -3.033 0.002425 **
## workday 2.3295 5.4261 0.429 0.667714
## temp -556.5099 165.4196 -3.364 0.000771 ***
## atemp 955.4759 182.1552 5.245 1.60e-07 ***
## hum 9.0753 49.6999 0.183 0.855114
## windspeed 137.6221 32.7976 4.196 2.74e-05 ***
## daytime 153.3723 3.1789 48.247 < 2e-16 ***
## season.1 -38.9183 17.6817 -2.201 0.027758 *
## season.2 -5.1309 16.1315 -0.318 0.750440
## season.3 -29.1217 11.0201 -2.643 0.008242 **
## mnth.1 2.7472 9.6136 0.286 0.775070
## mnth.2 -1.7816 9.3738 -0.190 0.849264
## mnth.3 5.7176 9.2602 0.617 0.536963
## mnth.4 -19.3828 11.9705 -1.619 0.105439
## mnth.5 -3.1724 12.4593 -0.255 0.799021
## mnth.6 -34.0348 12.2780 -2.772 0.005583 **
## mnth.7 -61.8605 13.5969 -4.550 5.45e-06 ***
## mnth.8 -31.8491 13.1901 -2.415 0.015772 *
## mnth.9 20.0113 11.2186 1.784 0.074498 .
## mnth.10 13.4208 8.6626 1.549 0.121351
## mnth.11 -7.2005 7.8064 -0.922 0.356355
## wkday.0 -12.8076 5.3643 -2.388 0.016982 *
## wkday.1 -3.0135 5.5348 -0.544 0.586134
## wkday.2 -8.4617 5.4268 -1.559 0.118973
## wkday.3 -2.2435 5.4523 -0.411 0.680727
## wkday.4 -1.4723 5.4374 -0.271 0.786579
## wkday.5 NA NA NA NA
## wkday.6 NA NA NA NA
## weathersit.1 7.9381 95.2555 0.083 0.933587
## weathersit.2 0.2877 95.2301 0.003 0.997590
## weathersit.3 -21.3883 95.2855 -0.224 0.822401
## temp2 674.6153 147.0899 4.586 4.57e-06 ***
## atemp2 -789.5091 177.5443 -4.447 8.82e-06 ***
## hum2 -143.5744 39.6283 -3.623 0.000293 ***
## windspeed2 -253.2290 65.6772 -3.856 0.000116 ***
## temp_dif_s 19.9128 13.3219 1.495 0.135018
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 134.3 on 8722 degrees of freedom
## Multiple R-squared: 0.4918, Adjusted R-squared: 0.4897
## F-statistic: 241.1 on 35 and 8722 DF, p-value: < 2.2e-16The R-squared is 0.4918 means that 49.18% of the training cases were explained by this linear model.
# Q4. Using the training data set from question 3, perform best subsets regression to pick a “good” model. What model was selected here and why?
regfit.full <- regsubsets(cnt~., dbike3, nvmax = 38, method = "exhaustive")## Warning in leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax, force.in =
## force.in, : 2 linear dependencies found## Reordering variables and trying again:summary(regfit.full)## Subset selection object
## Call: regsubsets.formula(cnt ~ ., dbike3, nvmax = 38, method = "exhaustive")
## 37 Variables (and intercept)
## Forced in Forced out
## yr FALSE FALSE
## holiday FALSE FALSE
## workday FALSE FALSE
## temp FALSE FALSE
## atemp FALSE FALSE
## hum FALSE FALSE
## windspeed FALSE FALSE
## daytime FALSE FALSE
## season.1 FALSE FALSE
## season.2 FALSE FALSE
## season.3 FALSE FALSE
## mnth.1 FALSE FALSE
## mnth.2 FALSE FALSE
## mnth.3 FALSE FALSE
## mnth.4 FALSE FALSE
## mnth.5 FALSE FALSE
## mnth.6 FALSE FALSE
## mnth.7 FALSE FALSE
## mnth.8 FALSE FALSE
## mnth.9 FALSE FALSE
## mnth.10 FALSE FALSE
## mnth.11 FALSE FALSE
## wkday.0 FALSE FALSE
## wkday.1 FALSE FALSE
## wkday.2 FALSE FALSE
## wkday.3 FALSE FALSE
## wkday.4 FALSE FALSE
## weathersit.1 FALSE FALSE
## weathersit.2 FALSE FALSE
## weathersit.3 FALSE FALSE
## temp2 FALSE FALSE
## atemp2 FALSE FALSE
## hum2 FALSE FALSE
## windspeed2 FALSE FALSE
## temp_dif_s FALSE FALSE
## wkday.5 FALSE FALSE
## wkday.6 FALSE FALSE
## 1 subsets of each size up to 35
## Selection Algorithm: exhaustive
## yr holiday workday temp atemp hum windspeed daytime season.1
## 1 ( 1 ) " " " " " " " " " " " " " " "*" " "
## 2 ( 1 ) " " " " " " "*" " " " " " " "*" " "
## 3 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 4 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 5 ( 1 ) "*" " " " " " " "*" " " " " "*" "*"
## 6 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 7 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 8 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 9 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 10 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 11 ( 1 ) "*" "*" " " " " "*" " " " " "*" " "
## 12 ( 1 ) "*" "*" " " "*" " " " " " " "*" "*"
## 13 ( 1 ) "*" "*" " " "*" " " " " "*" "*" " "
## 14 ( 1 ) "*" "*" " " "*" " " " " "*" "*" " "
## 15 ( 1 ) "*" "*" " " "*" " " " " "*" "*" "*"
## 16 ( 1 ) "*" "*" " " "*" " " " " "*" "*" "*"
## 17 ( 1 ) "*" "*" " " " " "*" " " "*" "*" " "
## 18 ( 1 ) "*" "*" " " " " "*" " " "*" "*" "*"
## 19 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 20 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 21 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 22 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 23 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 24 ( 1 ) "*" "*" "*" "*" "*" " " "*" "*" "*"
## 25 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 26 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 27 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 28 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 29 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 30 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 31 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 32 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 33 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 34 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 35 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## season.2 season.3 mnth.1 mnth.2 mnth.3 mnth.4 mnth.5 mnth.6 mnth.7
## 1 ( 1 ) " " " " " " " " " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " " " " " " " " " "
## 6 ( 1 ) " " "*" " " " " " " " " " " " " " "
## 7 ( 1 ) " " "*" " " " " " " " " " " " " "*"
## 8 ( 1 ) " " "*" " " " " " " " " " " " " "*"
## 9 ( 1 ) " " "*" " " " " " " " " " " " " "*"
## 10 ( 1 ) "*" " " " " " " " " " " " " "*" "*"
## 11 ( 1 ) "*" " " " " " " " " " " " " "*" "*"
## 12 ( 1 ) " " "*" " " " " " " " " " " "*" "*"
## 13 ( 1 ) " " "*" " " " " " " " " " " "*" "*"
## 14 ( 1 ) " " "*" " " " " " " " " " " "*" "*"
## 15 ( 1 ) " " "*" " " " " " " " " " " "*" "*"
## 16 ( 1 ) " " "*" " " " " " " " " " " "*" "*"
## 17 ( 1 ) " " "*" " " " " " " " " " " "*" "*"
## 18 ( 1 ) " " "*" " " " " " " " " " " "*" "*"
## 19 ( 1 ) " " "*" " " " " " " " " " " "*" "*"
## 20 ( 1 ) " " "*" " " " " " " "*" " " "*" "*"
## 21 ( 1 ) " " "*" " " " " " " "*" "*" "*" "*"
## 22 ( 1 ) " " "*" " " " " " " "*" "*" "*" "*"
## 23 ( 1 ) " " "*" " " " " " " "*" "*" "*" "*"
## 24 ( 1 ) " " "*" " " " " " " "*" "*" "*" "*"
## 25 ( 1 ) " " "*" " " " " " " "*" "*" "*" "*"
## 26 ( 1 ) " " "*" " " " " " " "*" "*" "*" "*"
## 27 ( 1 ) "*" "*" " " " " " " "*" "*" "*" "*"
## 28 ( 1 ) "*" "*" " " " " " " "*" "*" "*" "*"
## 29 ( 1 ) " " "*" "*" " " "*" "*" "*" "*" "*"
## 30 ( 1 ) " " "*" "*" "*" "*" "*" "*" "*" "*"
## 31 ( 1 ) " " "*" "*" "*" "*" "*" "*" "*" "*"
## 32 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 33 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 34 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 35 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## mnth.8 mnth.9 mnth.10 mnth.11 wkday.0 wkday.1 wkday.2 wkday.3 wkday.4
## 1 ( 1 ) " " " " " " " " " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " " " " " " " " " "
## 6 ( 1 ) " " " " " " " " " " " " " " " " " "
## 7 ( 1 ) " " " " " " " " " " " " " " " " " "
## 8 ( 1 ) " " " " " " " " " " " " " " " " " "
## 9 ( 1 ) " " "*" " " " " " " " " " " " " " "
## 10 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 11 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 12 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 13 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 14 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 15 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 16 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 17 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 18 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 19 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 20 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 21 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 22 ( 1 ) "*" " " " " "*" "*" " " " " " " " "
## 23 ( 1 ) "*" " " " " "*" "*" " " " " " " " "
## 24 ( 1 ) "*" " " " " "*" " " " " " " " " " "
## 25 ( 1 ) "*" " " " " "*" " " " " " " " " " "
## 26 ( 1 ) "*" " " " " "*" "*" " " " " "*" " "
## 27 ( 1 ) "*" " " " " "*" "*" " " " " "*" " "
## 28 ( 1 ) "*" "*" " " "*" "*" " " " " "*" " "
## 29 ( 1 ) "*" "*" " " "*" "*" " " " " "*" " "
## 30 ( 1 ) "*" "*" " " "*" "*" " " " " "*" " "
## 31 ( 1 ) "*" "*" " " "*" "*" " " " " "*" "*"
## 32 ( 1 ) "*" "*" " " "*" "*" " " " " "*" "*"
## 33 ( 1 ) "*" "*" " " "*" " " " " " " "*" "*"
## 34 ( 1 ) "*" "*" " " "*" " " "*" " " "*" "*"
## 35 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## wkday.5 wkday.6 weathersit.1 weathersit.2 weathersit.3 temp2 atemp2
## 1 ( 1 ) " " " " " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " " " " " "
## 6 ( 1 ) " " " " " " " " " " " " " "
## 7 ( 1 ) " " " " " " " " " " " " " "
## 8 ( 1 ) " " " " " " " " "*" " " " "
## 9 ( 1 ) " " " " " " " " "*" " " " "
## 10 ( 1 ) " " " " " " " " "*" " " " "
## 11 ( 1 ) " " " " " " " " "*" " " " "
## 12 ( 1 ) " " " " " " " " "*" " " " "
## 13 ( 1 ) " " " " " " " " "*" " " " "
## 14 ( 1 ) " " " " " " "*" "*" " " " "
## 15 ( 1 ) " " " " " " "*" "*" " " " "
## 16 ( 1 ) " " " " " " "*" "*" " " " "
## 17 ( 1 ) " " " " " " "*" "*" "*" "*"
## 18 ( 1 ) " " " " " " "*" "*" "*" "*"
## 19 ( 1 ) " " " " " " "*" "*" "*" "*"
## 20 ( 1 ) " " " " " " "*" "*" "*" "*"
## 21 ( 1 ) " " " " " " "*" "*" "*" "*"
## 22 ( 1 ) " " " " " " "*" "*" "*" "*"
## 23 ( 1 ) "*" " " " " "*" "*" "*" "*"
## 24 ( 1 ) "*" "*" " " "*" "*" "*" "*"
## 25 ( 1 ) "*" "*" " " "*" "*" "*" "*"
## 26 ( 1 ) "*" " " " " "*" "*" "*" "*"
## 27 ( 1 ) "*" " " " " "*" "*" "*" "*"
## 28 ( 1 ) "*" " " " " "*" "*" "*" "*"
## 29 ( 1 ) "*" " " " " "*" "*" "*" "*"
## 30 ( 1 ) "*" " " " " "*" "*" "*" "*"
## 31 ( 1 ) "*" " " " " "*" "*" "*" "*"
## 32 ( 1 ) "*" " " " " "*" "*" "*" "*"
## 33 ( 1 ) "*" "*" "*" "*" "*" "*" "*"
## 34 ( 1 ) "*" "*" "*" "*" "*" "*" "*"
## 35 ( 1 ) " " " " "*" "*" "*" "*" "*"
## hum2 windspeed2 temp_dif_s
## 1 ( 1 ) " " " " " "
## 2 ( 1 ) " " " " " "
## 3 ( 1 ) " " " " " "
## 4 ( 1 ) "*" " " " "
## 5 ( 1 ) "*" " " " "
## 6 ( 1 ) "*" " " "*"
## 7 ( 1 ) "*" " " "*"
## 8 ( 1 ) "*" " " "*"
## 9 ( 1 ) "*" " " "*"
## 10 ( 1 ) "*" " " "*"
## 11 ( 1 ) "*" " " "*"
## 12 ( 1 ) "*" " " "*"
## 13 ( 1 ) "*" "*" "*"
## 14 ( 1 ) "*" "*" "*"
## 15 ( 1 ) "*" "*" "*"
## 16 ( 1 ) "*" "*" "*"
## 17 ( 1 ) "*" "*" "*"
## 18 ( 1 ) "*" "*" "*"
## 19 ( 1 ) "*" "*" "*"
## 20 ( 1 ) "*" "*" "*"
## 21 ( 1 ) "*" "*" "*"
## 22 ( 1 ) "*" "*" "*"
## 23 ( 1 ) "*" "*" "*"
## 24 ( 1 ) "*" "*" "*"
## 25 ( 1 ) "*" "*" "*"
## 26 ( 1 ) "*" "*" "*"
## 27 ( 1 ) "*" "*" "*"
## 28 ( 1 ) "*" "*" "*"
## 29 ( 1 ) "*" "*" "*"
## 30 ( 1 ) "*" "*" "*"
## 31 ( 1 ) "*" "*" "*"
## 32 ( 1 ) "*" "*" "*"
## 33 ( 1 ) "*" "*" "*"
## 34 ( 1 ) "*" "*" "*"
## 35 ( 1 ) "*" "*" "*"summary(regfit.full)$which## (Intercept) yr holiday workday temp atemp hum windspeed daytime
## 1 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 2 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE
## 3 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 4 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 5 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 6 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 7 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 8 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 9 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 10 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 11 TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE
## 12 TRUE TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE
## 13 TRUE TRUE TRUE FALSE TRUE FALSE FALSE TRUE TRUE
## 14 TRUE TRUE TRUE FALSE TRUE FALSE FALSE TRUE TRUE
## 15 TRUE TRUE TRUE FALSE TRUE FALSE FALSE TRUE TRUE
## 16 TRUE TRUE TRUE FALSE TRUE FALSE FALSE TRUE TRUE
## 17 TRUE TRUE TRUE FALSE FALSE TRUE FALSE TRUE TRUE
## 18 TRUE TRUE TRUE FALSE FALSE TRUE FALSE TRUE TRUE
## 19 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 20 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 21 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 22 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 23 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 24 TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 25 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 26 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 27 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 28 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 29 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 30 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 31 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 32 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 33 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 34 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 35 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## season.1 season.2 season.3 mnth.1 mnth.2 mnth.3 mnth.4 mnth.5 mnth.6 mnth.7
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 3 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 4 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 5 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 6 FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 7 FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 8 FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 9 FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 10 FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 11 FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 12 TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 13 FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 14 FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 15 TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 16 TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 17 FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 18 TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 19 TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 20 TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 21 TRUE FALSE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 22 TRUE FALSE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 23 TRUE FALSE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 24 TRUE FALSE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 25 TRUE FALSE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 26 TRUE FALSE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 27 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 28 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 29 TRUE FALSE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 30 TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 31 TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 32 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 33 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 34 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 35 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## mnth.8 mnth.9 mnth.10 mnth.11 wkday.0 wkday.1 wkday.2 wkday.3 wkday.4
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 3 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 4 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 5 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 6 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 7 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 8 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 9 FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 10 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 11 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 12 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 13 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 14 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 15 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 16 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 17 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 18 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 19 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 20 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 21 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 22 TRUE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE
## 23 TRUE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE
## 24 TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## 25 TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## 26 TRUE FALSE FALSE TRUE TRUE FALSE FALSE TRUE FALSE
## 27 TRUE FALSE FALSE TRUE TRUE FALSE FALSE TRUE FALSE
## 28 TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE FALSE
## 29 TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE FALSE
## 30 TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE FALSE
## 31 TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE TRUE
## 32 TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE TRUE
## 33 TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE TRUE
## 34 TRUE TRUE FALSE TRUE FALSE TRUE FALSE TRUE TRUE
## 35 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## wkday.5 wkday.6 weathersit.1 weathersit.2 weathersit.3 temp2 atemp2 hum2
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 3 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 4 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 5 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 6 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 7 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 8 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 9 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 10 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 11 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 12 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 13 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 14 FALSE FALSE FALSE TRUE TRUE FALSE FALSE TRUE
## 15 FALSE FALSE FALSE TRUE TRUE FALSE FALSE TRUE
## 16 FALSE FALSE FALSE TRUE TRUE FALSE FALSE TRUE
## 17 FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 18 FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 19 FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 20 FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 21 FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 22 FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 23 TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 24 TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 25 TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 26 TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 27 TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 28 TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 29 TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 30 TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 31 TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 32 TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 33 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 34 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 35 FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## windspeed2 temp_dif_s
## 1 FALSE FALSE
## 2 FALSE FALSE
## 3 FALSE FALSE
## 4 FALSE FALSE
## 5 FALSE FALSE
## 6 FALSE TRUE
## 7 FALSE TRUE
## 8 FALSE TRUE
## 9 FALSE TRUE
## 10 FALSE TRUE
## 11 FALSE TRUE
## 12 FALSE TRUE
## 13 TRUE TRUE
## 14 TRUE TRUE
## 15 TRUE TRUE
## 16 TRUE TRUE
## 17 TRUE TRUE
## 18 TRUE TRUE
## 19 TRUE TRUE
## 20 TRUE TRUE
## 21 TRUE TRUE
## 22 TRUE TRUE
## 23 TRUE TRUE
## 24 TRUE TRUE
## 25 TRUE TRUE
## 26 TRUE TRUE
## 27 TRUE TRUE
## 28 TRUE TRUE
## 29 TRUE TRUE
## 30 TRUE TRUE
## 31 TRUE TRUE
## 32 TRUE TRUE
## 33 TRUE TRUE
## 34 TRUE TRUE
## 35 TRUE TRUEsummary(regfit.full)$rsq## [1] 0.2571076 0.3709439 0.4281075 0.4546976 0.4647773 0.4719204 0.4754116
## [8] 0.4774123 0.4788067 0.4799354 0.4808037 0.4814501 0.4823230 0.4829841
## [15] 0.4835621 0.4840786 0.4844385 0.4849411 0.4853609 0.4856316 0.4858562
## [22] 0.4861199 0.4861962 0.4862903 0.4863327 0.4863507 0.4863672 0.4863749
## [29] 0.4863866 0.4864017 0.4864043 0.4864045 0.4864046 0.4864047 0.4864047plot(summary(regfit.full)$rsq)
par(mfrow=c(2,2))
max.rsq <- which.max(summary(regfit.full)$rsq)
max.rsq## [1] 35plot(summary(regfit.full)$rsq, xlab = "Number of Variables",
ylab ="R-squared")
plot(summary(regfit.full)$adjr2, xlab = "Number of Variables",
ylab ="Adj R-squared")
max.adjr2 <- which.max(summary(regfit.full)$adjr2)
max.adjr2## [1] 25points(max.adjr2,summary(regfit.full)$adjr2[25], col = "red", cex = 2, pch = 20)
plot(summary(regfit.full)$cp, xlab = "Number of Variables",
ylab ="Mallows Cp")
min.cp <- which.min(summary(regfit.full)$cp)
min.cp## [1] 24points(min.cp,summary(regfit.full)$cp[24], col = "blue", cex = 2, pch = 20)
plot(summary(regfit.full)$bic, xlab = "Number of Variables",
ylab ="Bayesian Info Crit")
min.bic <- which.min(summary(regfit.full)$bic)
min.bic## [1] 19points(min.bic,summary(regfit.full)$bic[19], col = "green", cex = 2, pch = 20)
coef.adjr2 <- coef(regfit.full, 25)
coef.adjr2## (Intercept) yr holiday workday temp atemp
## -101.571574 80.897184 -21.673139 9.673813 -418.474009 806.762502
## hum windspeed daytime season.1 season.3 mnth.4
## 40.032519 162.982037 148.380556 -35.252856 -28.879797 -23.433975
## mnth.5 mnth.6 mnth.7 mnth.8 mnth.11 weathersit.1
## -17.313240 -50.024201 -72.662491 -42.391804 -12.488104 37.618949
## weathersit.2 temp2 atemp2 hum2 windspeed2 temp_dif_s
## 26.239432 584.653120 -684.347756 -156.119778 -325.586402 23.444120
## wkday.5 wkday.6
## 5.614182 14.963727coef.cp <- coef(regfit.full, 24)
coef.cp## (Intercept) yr holiday workday temp atemp
## -89.629271 80.995139 -21.525907 9.614918 -405.012450 787.436736
## windspeed daytime season.1 season.3 mnth.4 mnth.5
## 164.220487 148.230767 -35.326974 -28.610051 -23.577155 -16.837961
## mnth.6 mnth.7 mnth.8 mnth.11 weathersit.1 weathersit.2
## -49.594593 -72.398351 -41.915672 -12.480455 38.353633 27.044895
## temp2 atemp2 hum2 windspeed2 temp_dif_s wkday.5
## 562.214491 -655.904012 -124.659299 -330.287895 23.765395 5.683187
## wkday.6
## 14.844124coef.bic <- coef(regfit.full, 19)
coef.bic## (Intercept) yr holiday temp atemp windspeed
## -49.953936 80.680869 -31.312880 -395.143924 758.607067 146.365391
## daytime season.1 season.3 mnth.6 mnth.7 mnth.8
## 145.323851 -17.943035 -23.359776 -37.773794 -69.055197 -38.065430
## wkday.0 temp2 atemp2 hum2 windspeed2 temp_dif_s
## -8.491526 517.077788 -614.187685 -146.359165 -326.149128 35.533399
## wkday.5 wkday.6
## 5.768492 5.952683c(names(coef.adjr2))## [1] "(Intercept)" "yr" "holiday" "workday" "temp"
## [6] "atemp" "hum" "windspeed" "daytime" "season.1"
## [11] "season.3" "mnth.4" "mnth.5" "mnth.6" "mnth.7"
## [16] "mnth.8" "mnth.11" "weathersit.1" "weathersit.2" "temp2"
## [21] "atemp2" "hum2" "windspeed2" "temp_dif_s" "wkday.5"
## [26] "wkday.6"c(names(coef.cp))## [1] "(Intercept)" "yr" "holiday" "workday" "temp"
## [6] "atemp" "windspeed" "daytime" "season.1" "season.3"
## [11] "mnth.4" "mnth.5" "mnth.6" "mnth.7" "mnth.8"
## [16] "mnth.11" "weathersit.1" "weathersit.2" "temp2" "atemp2"
## [21] "hum2" "windspeed2" "temp_dif_s" "wkday.5" "wkday.6"c(names(coef.bic))## [1] "(Intercept)" "yr" "holiday" "temp" "atemp"
## [6] "windspeed" "daytime" "season.1" "season.3" "mnth.6"
## [11] "mnth.7" "mnth.8" "wkday.0" "temp2" "atemp2"
## [16] "hum2" "windspeed2" "temp_dif_s" "wkday.5" "wkday.6"reg_adjr2 <- lm(cnt ~ yr + holiday + workday + temp + atemp + hum + windspeed + daytime + season.1 + season.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.11 + weathersit.1 + weathersit.2 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 + wkday.6, data = training_set)
summary(reg_adjr2)##
## Call:
## lm(formula = cnt ~ yr + holiday + workday + temp + atemp + hum +
## windspeed + daytime + season.1 + season.3 + mnth.4 + mnth.5 +
## mnth.6 + mnth.7 + mnth.8 + mnth.11 + weathersit.1 + weathersit.2 +
## temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 +
## wkday.6, data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -369.21 -95.57 -17.93 66.51 558.99
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -89.082 22.519 -3.956 7.69e-05 ***
## yr 85.125 2.911 29.239 < 2e-16 ***
## holiday -22.173 9.294 -2.386 0.017067 *
## workday 10.887 4.268 2.551 0.010764 *
## temp -510.707 159.860 -3.195 0.001405 **
## atemp 918.220 179.964 5.102 3.43e-07 ***
## hum 14.370 49.183 0.292 0.770155
## windspeed 138.190 32.704 4.225 2.41e-05 ***
## daytime 152.920 3.166 48.299 < 2e-16 ***
## season.1 -37.690 8.185 -4.605 4.19e-06 ***
## season.3 -21.411 6.117 -3.500 0.000467 ***
## mnth.4 -29.043 7.554 -3.845 0.000122 ***
## mnth.5 -14.671 8.106 -1.810 0.070343 .
## mnth.6 -48.122 7.770 -6.193 6.16e-10 ***
## mnth.7 -81.436 8.002 -10.176 < 2e-16 ***
## mnth.8 -50.907 7.575 -6.721 1.92e-11 ***
## mnth.11 -15.046 6.176 -2.436 0.014864 *
## weathersit.1 29.485 6.074 4.855 1.23e-06 ***
## weathersit.2 21.244 6.060 3.506 0.000458 ***
## temp2 636.570 145.646 4.371 1.25e-05 ***
## atemp2 -760.108 175.913 -4.321 1.57e-05 ***
## hum2 -146.530 39.294 -3.729 0.000193 ***
## windspeed2 -258.005 65.442 -3.943 8.13e-05 ***
## temp_dif_s 25.812 6.797 3.797 0.000147 ***
## wkday.5 4.060 4.324 0.939 0.347789
## wkday.6 12.793 5.362 2.386 0.017066 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 134.3 on 8732 degrees of freedom
## Multiple R-squared: 0.4914, Adjusted R-squared: 0.4899
## F-statistic: 337.4 on 25 and 8732 DF, p-value: < 2.2e-16reg_cp <- lm(cnt ~ yr + holiday + workday + temp + atemp + windspeed + daytime + season.1 + season.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.11 + weathersit.1 + weathersit.2 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 + wkday.6, data = training_set)
summary(reg_cp)##
## Call:
## lm(formula = cnt ~ yr + holiday + workday + temp + atemp + windspeed +
## daytime + season.1 + season.3 + mnth.4 + mnth.5 + mnth.6 +
## mnth.7 + mnth.8 + mnth.11 + weathersit.1 + weathersit.2 +
## temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 +
## wkday.6, data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -368.75 -95.39 -17.93 66.43 559.09
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -84.677 16.726 -5.062 4.22e-07 ***
## yr 85.144 2.910 29.255 < 2e-16 ***
## holiday -22.128 9.292 -2.381 0.017269 *
## workday 10.862 4.267 2.545 0.010930 *
## temp -504.905 158.614 -3.183 0.001462 **
## atemp 910.100 177.796 5.119 3.14e-07 ***
## windspeed 138.508 32.684 4.238 2.28e-05 ***
## daytime 152.871 3.161 48.354 < 2e-16 ***
## season.1 -37.711 8.185 -4.608 4.13e-06 ***
## season.3 -21.315 6.108 -3.490 0.000485 ***
## mnth.4 -29.115 7.550 -3.856 0.000116 ***
## mnth.5 -14.506 8.086 -1.794 0.072847 .
## mnth.6 -47.993 7.757 -6.187 6.41e-10 ***
## mnth.7 -81.356 7.997 -10.173 < 2e-16 ***
## mnth.8 -50.748 7.555 -6.718 1.96e-11 ***
## mnth.11 -15.044 6.176 -2.436 0.014874 *
## weathersit.1 29.702 6.027 4.928 8.46e-07 ***
## weathersit.2 21.488 6.002 3.580 0.000345 ***
## temp2 627.709 142.447 4.407 1.06e-05 ***
## atemp2 -748.826 171.614 -4.363 1.30e-05 ***
## hum2 -135.272 7.706 -17.553 < 2e-16 ***
## windspeed2 -259.534 65.229 -3.979 6.98e-05 ***
## temp_dif_s 25.929 6.785 3.821 0.000134 ***
## wkday.5 4.106 4.321 0.950 0.342012
## wkday.6 12.744 5.359 2.378 0.017431 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 134.3 on 8733 degrees of freedom
## Multiple R-squared: 0.4914, Adjusted R-squared: 0.49
## F-statistic: 351.5 on 24 and 8733 DF, p-value: < 2.2e-16reg_bic <- lm(cnt ~ yr + holiday + workday + temp + atemp + windspeed + daytime + season.1 + season.3 + mnth.6 + mnth.7 + mnth.8 + wkday.0 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 + wkday.6, data = training_set)
summary(reg_bic)##
## Call:
## lm(formula = cnt ~ yr + holiday + workday + temp + atemp + windspeed +
## daytime + season.1 + season.3 + mnth.6 + mnth.7 + mnth.8 +
## wkday.0 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s +
## wkday.5 + wkday.6, data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -372.06 -95.64 -18.17 66.55 565.46
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -53.339 14.317 -3.726 0.000196 ***
## yr 85.088 2.914 29.199 < 2e-16 ***
## holiday -36.392 9.280 -3.921 8.87e-05 ***
## workday -2.797 4.269 -0.655 0.512283
## temp -486.514 157.857 -3.082 0.002063 **
## atemp 865.085 177.447 4.875 1.11e-06 ***
## windspeed 128.469 32.709 3.928 8.64e-05 ***
## daytime 150.558 3.118 48.291 < 2e-16 ***
## season.1 -17.786 5.753 -3.092 0.001996 **
## season.3 -16.488 5.901 -2.794 0.005217 **
## mnth.6 -35.842 6.281 -5.707 1.19e-08 ***
## mnth.7 -78.640 7.795 -10.088 < 2e-16 ***
## mnth.8 -47.199 7.401 -6.378 1.89e-10 ***
## wkday.0 -12.842 5.367 -2.393 0.016750 *
## temp2 581.531 142.517 4.080 4.54e-05 ***
## atemp2 -696.286 171.387 -4.063 4.89e-05 ***
## hum2 -150.212 6.706 -22.399 < 2e-16 ***
## windspeed2 -267.376 65.313 -4.094 4.28e-05 ***
## temp_dif_s 38.635 4.579 8.438 < 2e-16 ***
## wkday.5 4.023 4.328 0.930 0.352616
## wkday.6 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 134.6 on 8738 degrees of freedom
## Multiple R-squared: 0.4888, Adjusted R-squared: 0.4877
## F-statistic: 439.7 on 19 and 8738 DF, p-value: < 2.2e-16anova(reg_adjr2, reg_all)## Analysis of Variance Table
##
## Model 1: cnt ~ yr + holiday + workday + temp + atemp + hum + windspeed +
## daytime + season.1 + season.3 + mnth.4 + mnth.5 + mnth.6 +
## mnth.7 + mnth.8 + mnth.11 + weathersit.1 + weathersit.2 +
## temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 +
## wkday.6
## Model 2: cnt ~ yr + holiday + workday + temp + atemp + hum + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.1 + mnth.2 +
## mnth.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.9 +
## mnth.10 + mnth.11 + wkday.0 + wkday.1 + wkday.2 + wkday.3 +
## wkday.4 + wkday.5 + wkday.6 + weathersit.1 + weathersit.2 +
## weathersit.3 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 8732 157433646
## 2 8722 157313762 10 119883 0.6647 0.7583anova(reg_cp, reg_all)## Analysis of Variance Table
##
## Model 1: cnt ~ yr + holiday + workday + temp + atemp + windspeed + daytime +
## season.1 + season.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 +
## mnth.8 + mnth.11 + weathersit.1 + weathersit.2 + temp2 +
## atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 + wkday.6
## Model 2: cnt ~ yr + holiday + workday + temp + atemp + hum + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.1 + mnth.2 +
## mnth.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.9 +
## mnth.10 + mnth.11 + wkday.0 + wkday.1 + wkday.2 + wkday.3 +
## wkday.4 + wkday.5 + wkday.6 + weathersit.1 + weathersit.2 +
## weathersit.3 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 8733 157435185
## 2 8722 157313762 11 121423 0.612 0.8203anova(reg_bic, reg_all)## Analysis of Variance Table
##
## Model 1: cnt ~ yr + holiday + workday + temp + atemp + windspeed + daytime +
## season.1 + season.3 + mnth.6 + mnth.7 + mnth.8 + wkday.0 +
## temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 +
## wkday.6
## Model 2: cnt ~ yr + holiday + workday + temp + atemp + hum + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.1 + mnth.2 +
## mnth.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.9 +
## mnth.10 + mnth.11 + wkday.0 + wkday.1 + wkday.2 + wkday.3 +
## wkday.4 + wkday.5 + wkday.6 + weathersit.1 + weathersit.2 +
## weathersit.3 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 8738 158231263
## 2 8722 157313762 16 917501 3.1793 1.732e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1According to the p-value(all 3 are significant at the 95% level), the third model(min_bic) were selected because it has the smallest subset with a decent r square. The model is as good as the all in model.
# Q5. Using the training data set from question 3, perform forward stepwise regression to pick a “good” model. What model was selected and why? Repeat for backward stepwise regression. Is a “good” model in backward different from forward stepwise? Explain.
regfit.fwd <- regsubsets(cnt ~ ., data = training_set, nvmax = 38, method = 'forward')## Warning in leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax, force.in =
## force.in, : 2 linear dependencies found## Reordering variables and trying again:## Warning in rval$lopt[] <- rval$vorder[rval$lopt]: number of items to replace is
## not a multiple of replacement lengthsummary(regfit.fwd)## Subset selection object
## Call: regsubsets.formula(cnt ~ ., data = training_set, nvmax = 38,
## method = "forward")
## 37 Variables (and intercept)
## Forced in Forced out
## yr FALSE FALSE
## holiday FALSE FALSE
## workday FALSE FALSE
## temp FALSE FALSE
## atemp FALSE FALSE
## hum FALSE FALSE
## windspeed FALSE FALSE
## daytime FALSE FALSE
## season.1 FALSE FALSE
## season.2 FALSE FALSE
## season.3 FALSE FALSE
## mnth.1 FALSE FALSE
## mnth.2 FALSE FALSE
## mnth.3 FALSE FALSE
## mnth.4 FALSE FALSE
## mnth.5 FALSE FALSE
## mnth.6 FALSE FALSE
## mnth.7 FALSE FALSE
## mnth.8 FALSE FALSE
## mnth.9 FALSE FALSE
## mnth.10 FALSE FALSE
## mnth.11 FALSE FALSE
## wkday.0 FALSE FALSE
## wkday.1 FALSE FALSE
## wkday.2 FALSE FALSE
## wkday.3 FALSE FALSE
## wkday.4 FALSE FALSE
## weathersit.1 FALSE FALSE
## weathersit.2 FALSE FALSE
## weathersit.3 FALSE FALSE
## temp2 FALSE FALSE
## atemp2 FALSE FALSE
## hum2 FALSE FALSE
## windspeed2 FALSE FALSE
## temp_dif_s FALSE FALSE
## wkday.5 FALSE FALSE
## wkday.6 FALSE FALSE
## 1 subsets of each size up to 35
## Selection Algorithm: forward
## yr holiday workday temp atemp hum windspeed daytime season.1
## 1 ( 1 ) " " " " " " " " " " " " " " "*" " "
## 2 ( 1 ) " " " " " " " " "*" " " " " "*" " "
## 3 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 4 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 5 ( 1 ) "*" " " " " " " "*" " " " " "*" "*"
## 6 ( 1 ) "*" " " " " " " "*" " " " " "*" "*"
## 7 ( 1 ) "*" " " " " " " "*" " " " " "*" "*"
## 8 ( 1 ) "*" " " " " " " "*" " " " " "*" "*"
## 9 ( 1 ) "*" " " " " " " "*" " " " " "*" "*"
## 10 ( 1 ) "*" " " " " " " "*" " " " " "*" "*"
## 11 ( 1 ) "*" "*" " " " " "*" " " " " "*" "*"
## 12 ( 1 ) "*" "*" " " " " "*" " " " " "*" "*"
## 13 ( 1 ) "*" "*" " " " " "*" " " " " "*" "*"
## 14 ( 1 ) "*" "*" " " " " "*" " " " " "*" "*"
## 15 ( 1 ) "*" "*" " " " " "*" " " " " "*" "*"
## 16 ( 1 ) "*" "*" " " " " "*" " " " " "*" "*"
## 17 ( 1 ) "*" "*" " " "*" "*" " " " " "*" "*"
## 18 ( 1 ) "*" "*" " " "*" "*" " " " " "*" "*"
## 19 ( 1 ) "*" "*" " " "*" "*" " " " " "*" "*"
## 20 ( 1 ) "*" "*" " " "*" "*" " " " " "*" "*"
## 21 ( 1 ) "*" "*" " " "*" "*" " " " " "*" "*"
## 22 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 23 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 24 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 25 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 26 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 27 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 28 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 29 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 30 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 31 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 32 ( 1 ) "*" "*" " " "*" "*" "*" "*" "*" "*"
## 33 ( 1 ) "*" "*" " " "*" "*" "*" "*" "*" "*"
## 34 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 35 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## season.2 season.3 mnth.1 mnth.2 mnth.3 mnth.4 mnth.5 mnth.6 mnth.7
## 1 ( 1 ) " " " " " " " " " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " " " " " " " " " "
## 6 ( 1 ) " " " " " " " " " " " " " " " " "*"
## 7 ( 1 ) " " " " " " " " " " " " " " " " "*"
## 8 ( 1 ) " " " " " " " " " " " " " " " " "*"
## 9 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 10 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 11 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 12 ( 1 ) " " " " " " " " " " "*" " " "*" "*"
## 13 ( 1 ) " " " " " " " " " " "*" " " "*" "*"
## 14 ( 1 ) "*" " " " " " " " " "*" " " "*" "*"
## 15 ( 1 ) "*" " " " " " " " " "*" " " "*" "*"
## 16 ( 1 ) "*" " " " " " " " " "*" "*" "*" "*"
## 17 ( 1 ) "*" " " " " " " " " "*" "*" "*" "*"
## 18 ( 1 ) "*" "*" " " " " " " "*" "*" "*" "*"
## 19 ( 1 ) "*" "*" " " " " " " "*" "*" "*" "*"
## 20 ( 1 ) "*" "*" " " " " " " "*" "*" "*" "*"
## 21 ( 1 ) "*" "*" " " " " " " "*" "*" "*" "*"
## 22 ( 1 ) "*" "*" " " " " " " "*" "*" "*" "*"
## 23 ( 1 ) "*" "*" " " " " " " "*" "*" "*" "*"
## 24 ( 1 ) "*" "*" " " " " " " "*" "*" "*" "*"
## 25 ( 1 ) "*" "*" " " " " " " "*" "*" "*" "*"
## 26 ( 1 ) "*" "*" " " " " " " "*" "*" "*" "*"
## 27 ( 1 ) "*" "*" " " " " "*" "*" "*" "*" "*"
## 28 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*" "*"
## 29 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*" "*"
## 30 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*" "*"
## 31 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 32 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 33 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 34 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 35 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## mnth.8 mnth.9 mnth.10 mnth.11 wkday.0 wkday.1 wkday.2 wkday.3 wkday.4
## 1 ( 1 ) " " " " " " " " " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " " " " " " " " " "
## 6 ( 1 ) " " " " " " " " " " " " " " " " " "
## 7 ( 1 ) " " " " " " " " " " " " " " " " " "
## 8 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 9 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 10 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 11 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 12 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 13 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 14 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 15 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 16 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 17 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 18 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 19 ( 1 ) "*" " " " " "*" "*" " " " " " " " "
## 20 ( 1 ) "*" " " " " "*" "*" " " "*" " " " "
## 21 ( 1 ) "*" " " " " "*" "*" " " "*" " " " "
## 22 ( 1 ) "*" " " " " "*" "*" " " "*" " " " "
## 23 ( 1 ) "*" " " " " "*" "*" " " "*" " " " "
## 24 ( 1 ) "*" " " " " "*" "*" " " "*" " " " "
## 25 ( 1 ) "*" "*" " " "*" "*" " " "*" " " " "
## 26 ( 1 ) "*" "*" "*" "*" "*" " " "*" " " " "
## 27 ( 1 ) "*" "*" "*" "*" "*" " " "*" " " " "
## 28 ( 1 ) "*" "*" "*" "*" "*" " " "*" " " " "
## 29 ( 1 ) "*" "*" "*" "*" "*" " " "*" " " " "
## 30 ( 1 ) "*" "*" "*" "*" "*" " " "*" " " "*"
## 31 ( 1 ) "*" "*" "*" "*" "*" " " "*" " " "*"
## 32 ( 1 ) "*" "*" "*" "*" "*" " " "*" " " "*"
## 33 ( 1 ) "*" "*" "*" "*" "*" "*" "*" " " "*"
## 34 ( 1 ) "*" "*" "*" "*" "*" "*" "*" " " "*"
## 35 ( 1 ) "*" "*" "*" "*" "*" "*" "*" " " "*"
## wkday.5 wkday.6 weathersit.1 weathersit.2 weathersit.3 temp2 atemp2
## 1 ( 1 ) " " " " " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " " " " " "
## 6 ( 1 ) " " " " " " " " " " " " " "
## 7 ( 1 ) " " " " " " " " " " " " " "
## 8 ( 1 ) " " " " " " " " " " " " " "
## 9 ( 1 ) " " " " " " " " " " " " " "
## 10 ( 1 ) " " " " " " " " "*" " " " "
## 11 ( 1 ) " " " " " " " " "*" " " " "
## 12 ( 1 ) " " " " " " " " "*" " " " "
## 13 ( 1 ) " " " " " " " " "*" " " " "
## 14 ( 1 ) " " " " " " " " "*" " " " "
## 15 ( 1 ) " " " " "*" " " "*" " " " "
## 16 ( 1 ) " " " " "*" " " "*" " " " "
## 17 ( 1 ) " " " " "*" " " "*" " " " "
## 18 ( 1 ) " " " " "*" " " "*" " " " "
## 19 ( 1 ) " " " " "*" " " "*" " " " "
## 20 ( 1 ) " " " " "*" " " "*" " " " "
## 21 ( 1 ) " " " " "*" " " "*" " " " "
## 22 ( 1 ) " " " " "*" " " "*" " " " "
## 23 ( 1 ) " " " " "*" " " "*" "*" " "
## 24 ( 1 ) " " " " "*" " " "*" "*" "*"
## 25 ( 1 ) " " " " "*" " " "*" "*" "*"
## 26 ( 1 ) " " " " "*" " " "*" "*" "*"
## 27 ( 1 ) " " " " "*" " " "*" "*" "*"
## 28 ( 1 ) " " " " "*" " " "*" "*" "*"
## 29 ( 1 ) "*" " " "*" " " "*" "*" "*"
## 30 ( 1 ) "*" " " "*" " " "*" "*" "*"
## 31 ( 1 ) "*" " " "*" " " "*" "*" "*"
## 32 ( 1 ) "*" " " "*" " " "*" "*" "*"
## 33 ( 1 ) "*" " " "*" " " "*" "*" "*"
## 34 ( 1 ) "*" " " "*" " " "*" "*" "*"
## 35 ( 1 ) "*" " " "*" "*" "*" "*" "*"
## hum2 windspeed2 temp_dif_s
## 1 ( 1 ) " " " " " "
## 2 ( 1 ) " " " " " "
## 3 ( 1 ) " " " " " "
## 4 ( 1 ) "*" " " " "
## 5 ( 1 ) "*" " " " "
## 6 ( 1 ) "*" " " " "
## 7 ( 1 ) "*" " " "*"
## 8 ( 1 ) "*" " " "*"
## 9 ( 1 ) "*" " " "*"
## 10 ( 1 ) "*" " " "*"
## 11 ( 1 ) "*" " " "*"
## 12 ( 1 ) "*" " " "*"
## 13 ( 1 ) "*" " " "*"
## 14 ( 1 ) "*" " " "*"
## 15 ( 1 ) "*" " " "*"
## 16 ( 1 ) "*" " " "*"
## 17 ( 1 ) "*" " " "*"
## 18 ( 1 ) "*" " " "*"
## 19 ( 1 ) "*" " " "*"
## 20 ( 1 ) "*" " " "*"
## 21 ( 1 ) "*" "*" "*"
## 22 ( 1 ) "*" "*" "*"
## 23 ( 1 ) "*" "*" "*"
## 24 ( 1 ) "*" "*" "*"
## 25 ( 1 ) "*" "*" "*"
## 26 ( 1 ) "*" "*" "*"
## 27 ( 1 ) "*" "*" "*"
## 28 ( 1 ) "*" "*" "*"
## 29 ( 1 ) "*" "*" "*"
## 30 ( 1 ) "*" "*" "*"
## 31 ( 1 ) "*" "*" "*"
## 32 ( 1 ) "*" "*" "*"
## 33 ( 1 ) "*" "*" "*"
## 34 ( 1 ) "*" "*" "*"
## 35 ( 1 ) "*" "*" "*"sum.regfit_fwd <- summary(regfit.fwd)
sum.regfit_fwd$which## (Intercept) yr holiday workday temp atemp hum windspeed daytime
## 1 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 2 TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 3 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 4 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 5 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 6 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 7 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 8 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 9 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 10 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 11 TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE
## 12 TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE
## 13 TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE
## 14 TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE
## 15 TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE
## 16 TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE
## 17 TRUE TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE
## 18 TRUE TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE
## 19 TRUE TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE
## 20 TRUE TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE
## 21 TRUE TRUE TRUE FALSE TRUE TRUE FALSE FALSE TRUE
## 22 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 23 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 24 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 25 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 26 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 27 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 28 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 29 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 30 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 31 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 32 TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 33 TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 34 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 35 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## season.1 season.2 season.3 mnth.1 mnth.2 mnth.3 mnth.4 mnth.5 mnth.6 mnth.7
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 3 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 4 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 5 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 6 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 7 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 8 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 9 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 10 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 11 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 12 TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 13 TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 14 TRUE TRUE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 15 TRUE TRUE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 16 TRUE TRUE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 17 TRUE TRUE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 18 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 19 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 20 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 21 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 22 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 23 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 24 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 25 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 26 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 27 TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
## 28 TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 29 TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 30 TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 31 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 32 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 33 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 34 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 35 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## mnth.8 mnth.9 mnth.10 mnth.11 wkday.0 wkday.1 wkday.2 wkday.3 wkday.4
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 3 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 4 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 5 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 6 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 7 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 8 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 9 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 10 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 11 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 12 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 13 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 14 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 15 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 16 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 17 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 18 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 19 TRUE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE
## 20 TRUE FALSE FALSE TRUE TRUE FALSE TRUE FALSE FALSE
## 21 TRUE FALSE FALSE TRUE TRUE FALSE TRUE FALSE FALSE
## 22 TRUE FALSE FALSE TRUE TRUE FALSE TRUE FALSE FALSE
## 23 TRUE FALSE FALSE TRUE TRUE FALSE TRUE FALSE FALSE
## 24 TRUE FALSE FALSE TRUE TRUE FALSE TRUE FALSE FALSE
## 25 TRUE TRUE FALSE TRUE TRUE FALSE TRUE FALSE FALSE
## 26 TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE
## 27 TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE
## 28 TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE
## 29 TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE
## 30 TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE
## 31 TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE
## 32 TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE
## 33 TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 34 TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 35 TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## wkday.5 wkday.6 weathersit.1 weathersit.2 weathersit.3 temp2 atemp2 hum2
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 3 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 4 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 5 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 6 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 7 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 8 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 9 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 10 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 11 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 12 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 13 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 14 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 15 FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE
## 16 FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE
## 17 FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE
## 18 FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE
## 19 FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE
## 20 FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE
## 21 FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE
## 22 FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE
## 23 FALSE FALSE TRUE FALSE TRUE TRUE FALSE TRUE
## 24 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 25 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 26 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 27 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 28 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 29 TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 30 TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 31 TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 32 TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 33 TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 34 TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 35 TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## windspeed2 temp_dif_s
## 1 FALSE FALSE
## 2 FALSE FALSE
## 3 FALSE FALSE
## 4 FALSE FALSE
## 5 FALSE FALSE
## 6 FALSE FALSE
## 7 FALSE TRUE
## 8 FALSE TRUE
## 9 FALSE TRUE
## 10 FALSE TRUE
## 11 FALSE TRUE
## 12 FALSE TRUE
## 13 FALSE TRUE
## 14 FALSE TRUE
## 15 FALSE TRUE
## 16 FALSE TRUE
## 17 FALSE TRUE
## 18 FALSE TRUE
## 19 FALSE TRUE
## 20 FALSE TRUE
## 21 TRUE TRUE
## 22 TRUE TRUE
## 23 TRUE TRUE
## 24 TRUE TRUE
## 25 TRUE TRUE
## 26 TRUE TRUE
## 27 TRUE TRUE
## 28 TRUE TRUE
## 29 TRUE TRUE
## 30 TRUE TRUE
## 31 TRUE TRUE
## 32 TRUE TRUE
## 33 TRUE TRUE
## 34 TRUE TRUE
## 35 TRUE TRUEpar(mfrow=c(2,2))
max.rsq.fwd <- which.max(summary(regfit.fwd)$rsq)
max.rsq.fwd## [1] 35plot(summary(regfit.fwd)$rsq, xlab = "Number of Variables",
ylab ="R-squared")
plot(summary(regfit.fwd)$adjr2, xlab = "Number of Variables",
ylab ="Adj R-squared")
max.adjr2.fwd <- which.max(summary(regfit.fwd)$adjr2)
max.adjr2.fwd## [1] 26points(max.adjr2.fwd,summary(regfit.fwd)$adjr2[26], col = "red", cex = 2, pch = 20)
plot(summary(regfit.fwd)$cp, xlab = "Number of Variables",
ylab ="Mallows Cp")
min.cp.fwd <- which.min(summary(regfit.fwd)$cp)
min.cp.fwd ## [1] 24points(min.cp.fwd,summary(regfit.fwd)$cp[24], col = "blue", cex = 2, pch = 20)
plot(summary(regfit.fwd)$bic, xlab = "Number of Variables",
ylab ="Bayesian Info Crit")
min.bic.fwd <- which.min(summary(regfit.fwd)$bic)
min.bic.fwd## [1] 11points(min.bic.fwd,summary(regfit.fwd)$bic[11], col = "green", cex = 2, pch = 20)
coef.adjr2.fwd <- coef(regfit.fwd, 26)
coef.adjr2.fwd## (Intercept) yr holiday temp atemp windspeed
## -26.0024675 84.6334937 -34.8799944 150.9272632 189.4846484 109.0394260
## daytime season.1 season.2 season.3 mnth.4 mnth.5
## 153.2636243 -37.0824316 -3.0421732 -26.4591592 -23.1607168 -7.9022598
## mnth.6 mnth.7 mnth.8 mnth.9 mnth.10 mnth.11
## -37.0218983 -66.0266490 -35.9363016 14.1172646 9.2632804 -8.9429303
## wkday.0 wkday.2 weathersit.3 atemp2 hum2 windspeed2
## -12.4530402 -6.0674327 -24.9058296 -22.2783922 -144.7559464 -241.0866029
## temp_dif_s wkday.5 wkday.6
## 21.4631095 2.3009453 0.4213261coef.cp.fwd <- coef(regfit.fwd, 24)
coef.cp.fwd## (Intercept) yr holiday temp atemp windspeed
## -31.0325478 84.5586915 -34.4785938 146.0292224 198.8927096 108.7293021
## daytime season.1 season.2 season.3 mnth.4 mnth.5
## 152.8692197 -34.2825491 0.9776745 -20.3574815 -27.8469073 -13.4490583
## mnth.6 mnth.7 mnth.8 mnth.11 wkday.0 wkday.2
## -45.0977553 -79.1457797 -48.7248929 -13.8612730 -12.0834342 -6.1241313
## weathersit.3 atemp2 hum2 windspeed2 temp_dif_s wkday.5
## -24.7993041 -34.7057867 -144.0049165 -241.0520876 28.1670619 2.5325986
## wkday.6
## 0.7686559coef.bic.fwd <- coef(regfit.fwd, 11)
coef.bic.fwd## (Intercept) yr holiday atemp daytime season.1
## -73.694557 92.845039 -31.274968 93.474369 170.411589 -12.279763
## mnth.6 mnth.7 mnth.8 atemp2 temp_dif_s wkday.6
## -26.889048 -89.943847 -57.612889 247.570199 33.215973 5.407031c(names(coef.adjr2.fwd))## [1] "(Intercept)" "yr" "holiday" "temp" "atemp"
## [6] "windspeed" "daytime" "season.1" "season.2" "season.3"
## [11] "mnth.4" "mnth.5" "mnth.6" "mnth.7" "mnth.8"
## [16] "mnth.9" "mnth.10" "mnth.11" "wkday.0" "wkday.2"
## [21] "weathersit.3" "atemp2" "hum2" "windspeed2" "temp_dif_s"
## [26] "wkday.5" "wkday.6"c(names(coef.cp.fwd))## [1] "(Intercept)" "yr" "holiday" "temp" "atemp"
## [6] "windspeed" "daytime" "season.1" "season.2" "season.3"
## [11] "mnth.4" "mnth.5" "mnth.6" "mnth.7" "mnth.8"
## [16] "mnth.11" "wkday.0" "wkday.2" "weathersit.3" "atemp2"
## [21] "hum2" "windspeed2" "temp_dif_s" "wkday.5" "wkday.6"c(names(coef.bic.fwd))## [1] "(Intercept)" "yr" "holiday" "atemp" "daytime"
## [6] "season.1" "mnth.6" "mnth.7" "mnth.8" "atemp2"
## [11] "temp_dif_s" "wkday.6"reg_adjr2_fwd <- lm(cnt ~ yr + holiday + temp + atemp + windspeed + daytime + season.1 + season.2 + season.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.9 + mnth.10 + mnth.11 + wkday.0 + wkday.2 + weathersit.3 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 + wkday.6, data = training_set)
summary(reg_adjr2_fwd)##
## Call:
## lm(formula = cnt ~ yr + holiday + temp + atemp + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.4 + mnth.5 +
## mnth.6 + mnth.7 + mnth.8 + mnth.9 + mnth.10 + mnth.11 + wkday.0 +
## wkday.2 + weathersit.3 + atemp2 + hum2 + windspeed2 + temp_dif_s +
## wkday.5 + wkday.6, data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -373.74 -96.48 -18.93 67.36 553.39
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -26.0025 18.8195 -1.382 0.167107
## yr 84.6335 2.9141 29.043 < 2e-16 ***
## holiday -34.8800 8.7202 -4.000 6.39e-05 ***
## temp 150.9273 62.0430 2.433 0.015010 *
## atemp 189.4846 76.8879 2.464 0.013742 *
## windspeed 109.0394 32.1388 3.393 0.000695 ***
## daytime 153.2636 3.1385 48.834 < 2e-16 ***
## season.1 -37.0824 15.2719 -2.428 0.015197 *
## season.2 -3.0422 14.1349 -0.215 0.829598
## season.3 -26.4592 10.2942 -2.570 0.010178 *
## mnth.4 -23.1607 9.0358 -2.563 0.010387 *
## mnth.5 -7.9023 9.4669 -0.835 0.403898
## mnth.6 -37.0219 9.8457 -3.760 0.000171 ***
## mnth.7 -66.0266 12.3979 -5.326 1.03e-07 ***
## mnth.8 -35.9363 11.9404 -3.010 0.002623 **
## mnth.9 14.1173 10.2264 1.380 0.167475
## mnth.10 9.2633 8.4416 1.097 0.272527
## mnth.11 -8.9429 7.7255 -1.158 0.247065
## wkday.0 -12.4530 4.4257 -2.814 0.004907 **
## wkday.2 -6.0674 4.3920 -1.381 0.167173
## weathersit.3 -24.9058 5.7579 -4.325 1.54e-05 ***
## atemp2 -22.2784 60.9379 -0.366 0.714678
## hum2 -144.7559 7.3083 -19.807 < 2e-16 ***
## windspeed2 -241.0866 65.2696 -3.694 0.000222 ***
## temp_dif_s 21.4631 13.0142 1.649 0.099141 .
## wkday.5 2.3009 4.4728 0.514 0.606960
## wkday.6 0.4213 4.4245 0.095 0.924138
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 134.4 on 8731 degrees of freedom
## Multiple R-squared: 0.4902, Adjusted R-squared: 0.4886
## F-statistic: 322.8 on 26 and 8731 DF, p-value: < 2.2e-16reg_cp_fwd <- lm(cnt ~ yr + holiday + temp + atemp + windspeed + daytime + season.1 + season.2 + season.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.11 + wkday.0 + wkday.2 + weathersit.3 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 + wkday.6, data = training_set)
summary(reg_cp_fwd)##
## Call:
## lm(formula = cnt ~ yr + holiday + temp + atemp + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.4 + mnth.5 +
## mnth.6 + mnth.7 + mnth.8 + mnth.11 + wkday.0 + wkday.2 +
## weathersit.3 + atemp2 + hum2 + windspeed2 + temp_dif_s +
## wkday.5 + wkday.6, data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -372.68 -96.25 -19.02 67.38 556.00
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -31.0325 18.4999 -1.677 0.093491 .
## yr 84.5587 2.9136 29.022 < 2e-16 ***
## holiday -34.4786 8.7116 -3.958 7.63e-05 ***
## temp 146.0292 61.6954 2.367 0.017958 *
## atemp 198.8927 76.2949 2.607 0.009152 **
## windspeed 108.7293 32.1337 3.384 0.000718 ***
## daytime 152.8692 3.1269 48.889 < 2e-16 ***
## season.1 -34.2825 15.1269 -2.266 0.023456 *
## season.2 0.9777 13.6736 0.072 0.943001
## season.3 -20.3575 8.0249 -2.537 0.011205 *
## mnth.4 -27.8469 8.4004 -3.315 0.000920 ***
## mnth.5 -13.4491 8.6028 -1.563 0.118011
## mnth.6 -45.0978 7.9516 -5.672 1.46e-08 ***
## mnth.7 -79.1458 8.0176 -9.871 < 2e-16 ***
## mnth.8 -48.7249 7.5774 -6.430 1.34e-10 ***
## mnth.11 -13.8613 6.5829 -2.106 0.035263 *
## wkday.0 -12.0834 4.4181 -2.735 0.006251 **
## wkday.2 -6.1241 4.3917 -1.394 0.163212
## weathersit.3 -24.7993 5.7570 -4.308 1.67e-05 ***
## atemp2 -34.7058 60.1423 -0.577 0.563913
## hum2 -144.0049 7.2847 -19.768 < 2e-16 ***
## windspeed2 -241.0521 65.2700 -3.693 0.000223 ***
## temp_dif_s 28.1671 12.1294 2.322 0.020244 *
## wkday.5 2.5326 4.4700 0.567 0.571018
## wkday.6 0.7687 4.4183 0.174 0.861892
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 134.4 on 8733 degrees of freedom
## Multiple R-squared: 0.49, Adjusted R-squared: 0.4886
## F-statistic: 349.6 on 24 and 8733 DF, p-value: < 2.2e-16reg_bic_fwd <- lm(cnt ~ yr + holiday + atemp + daytime + season.1 + mnth.6 + mnth.7 + mnth.8 + atemp2 + temp_dif_s + wkday.6, data = training_set)
summary(reg_bic_fwd)##
## Call:
## lm(formula = cnt ~ yr + holiday + atemp + daytime + season.1 +
## mnth.6 + mnth.7 + mnth.8 + atemp2 + temp_dif_s + wkday.6,
## data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -381.52 -95.83 -21.40 69.15 575.72
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -73.695 13.289 -5.546 3.01e-08 ***
## yr 92.845 2.989 31.060 < 2e-16 ***
## holiday -31.275 8.897 -3.515 0.000442 ***
## atemp 93.474 53.153 1.759 0.078684 .
## daytime 170.412 3.088 55.187 < 2e-16 ***
## season.1 -12.280 5.842 -2.102 0.035598 *
## mnth.6 -26.889 6.314 -4.259 2.08e-05 ***
## mnth.7 -89.944 7.175 -12.536 < 2e-16 ***
## mnth.8 -57.613 6.448 -8.935 < 2e-16 ***
## atemp2 247.570 57.220 4.327 1.53e-05 ***
## temp_dif_s 33.216 4.455 7.455 9.83e-14 ***
## wkday.6 5.407 4.252 1.272 0.203494
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 139.2 on 8746 degrees of freedom
## Multiple R-squared: 0.4526, Adjusted R-squared: 0.4519
## F-statistic: 657.5 on 11 and 8746 DF, p-value: < 2.2e-16anova(reg_adjr2_fwd, reg_all)## Analysis of Variance Table
##
## Model 1: cnt ~ yr + holiday + temp + atemp + windspeed + daytime + season.1 +
## season.2 + season.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 +
## mnth.8 + mnth.9 + mnth.10 + mnth.11 + wkday.0 + wkday.2 +
## weathersit.3 + atemp2 + hum2 + windspeed2 + temp_dif_s +
## wkday.5 + wkday.6
## Model 2: cnt ~ yr + holiday + workday + temp + atemp + hum + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.1 + mnth.2 +
## mnth.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.9 +
## mnth.10 + mnth.11 + wkday.0 + wkday.1 + wkday.2 + wkday.3 +
## wkday.4 + wkday.5 + wkday.6 + weathersit.1 + weathersit.2 +
## weathersit.3 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 8731 157808652
## 2 8722 157313762 9 494890 3.0487 0.001198 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(reg_cp_fwd, reg_all)## Analysis of Variance Table
##
## Model 1: cnt ~ yr + holiday + temp + atemp + windspeed + daytime + season.1 +
## season.2 + season.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 +
## mnth.8 + mnth.11 + wkday.0 + wkday.2 + weathersit.3 + atemp2 +
## hum2 + windspeed2 + temp_dif_s + wkday.5 + wkday.6
## Model 2: cnt ~ yr + holiday + workday + temp + atemp + hum + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.1 + mnth.2 +
## mnth.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.9 +
## mnth.10 + mnth.11 + wkday.0 + wkday.1 + wkday.2 + wkday.3 +
## wkday.4 + wkday.5 + wkday.6 + weathersit.1 + weathersit.2 +
## weathersit.3 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 8733 157848152
## 2 8722 157313762 11 534390 2.6935 0.001835 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(reg_bic_fwd, reg_all)## Analysis of Variance Table
##
## Model 1: cnt ~ yr + holiday + atemp + daytime + season.1 + mnth.6 + mnth.7 +
## mnth.8 + atemp2 + temp_dif_s + wkday.6
## Model 2: cnt ~ yr + holiday + workday + temp + atemp + hum + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.1 + mnth.2 +
## mnth.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.9 +
## mnth.10 + mnth.11 + wkday.0 + wkday.1 + wkday.2 + wkday.3 +
## wkday.4 + wkday.5 + wkday.6 + weathersit.1 + weathersit.2 +
## weathersit.3 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 8746 169424655
## 2 8722 157313762 24 12110892 27.978 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1According to the p-value(all 3 are significant at the 95% level), the third model(min_bic) were selected because it has the smallest subset with a decent r square. The model is just as good as the all in model.
regfit.bwd <- regsubsets(cnt ~ ., data = training_set, nvmax = 38, method = 'backward')## Warning in leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax, force.in =
## force.in, : 2 linear dependencies found## Reordering variables and trying again:## Warning in rval$lopt[] <- rval$vorder[rval$lopt]: number of items to replace is
## not a multiple of replacement lengthsummary(regfit.bwd)## Subset selection object
## Call: regsubsets.formula(cnt ~ ., data = training_set, nvmax = 38,
## method = "backward")
## 37 Variables (and intercept)
## Forced in Forced out
## yr FALSE FALSE
## holiday FALSE FALSE
## workday FALSE FALSE
## temp FALSE FALSE
## atemp FALSE FALSE
## hum FALSE FALSE
## windspeed FALSE FALSE
## daytime FALSE FALSE
## season.1 FALSE FALSE
## season.2 FALSE FALSE
## season.3 FALSE FALSE
## mnth.1 FALSE FALSE
## mnth.2 FALSE FALSE
## mnth.3 FALSE FALSE
## mnth.4 FALSE FALSE
## mnth.5 FALSE FALSE
## mnth.6 FALSE FALSE
## mnth.7 FALSE FALSE
## mnth.8 FALSE FALSE
## mnth.9 FALSE FALSE
## mnth.10 FALSE FALSE
## mnth.11 FALSE FALSE
## wkday.0 FALSE FALSE
## wkday.1 FALSE FALSE
## wkday.2 FALSE FALSE
## wkday.3 FALSE FALSE
## wkday.4 FALSE FALSE
## weathersit.1 FALSE FALSE
## weathersit.2 FALSE FALSE
## weathersit.3 FALSE FALSE
## temp2 FALSE FALSE
## atemp2 FALSE FALSE
## hum2 FALSE FALSE
## windspeed2 FALSE FALSE
## temp_dif_s FALSE FALSE
## wkday.5 FALSE FALSE
## wkday.6 FALSE FALSE
## 1 subsets of each size up to 35
## Selection Algorithm: backward
## yr holiday workday temp atemp hum windspeed daytime season.1
## 1 ( 1 ) " " " " " " " " " " " " " " "*" " "
## 2 ( 1 ) " " " " " " " " "*" " " " " "*" " "
## 3 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 4 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 5 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 6 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 7 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 8 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 9 ( 1 ) "*" " " " " " " "*" " " " " "*" " "
## 10 ( 1 ) "*" "*" " " " " "*" " " " " "*" " "
## 11 ( 1 ) "*" "*" " " " " "*" " " " " "*" " "
## 12 ( 1 ) "*" "*" " " " " "*" " " "*" "*" " "
## 13 ( 1 ) "*" "*" " " " " "*" " " "*" "*" "*"
## 14 ( 1 ) "*" "*" " " " " "*" " " "*" "*" "*"
## 15 ( 1 ) "*" "*" " " " " "*" " " "*" "*" "*"
## 16 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 17 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 18 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 19 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 20 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 21 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 22 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 23 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 24 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 25 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 26 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 27 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 28 ( 1 ) "*" "*" " " "*" "*" " " "*" "*" "*"
## 29 ( 1 ) "*" "*" "*" "*" "*" " " "*" "*" "*"
## 30 ( 1 ) "*" "*" "*" "*" "*" " " "*" "*" "*"
## 31 ( 1 ) "*" "*" "*" "*" "*" " " "*" "*" "*"
## 32 ( 1 ) "*" "*" "*" "*" "*" " " "*" "*" "*"
## 33 ( 1 ) "*" "*" "*" "*" "*" " " "*" "*" "*"
## 34 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 35 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## season.2 season.3 mnth.1 mnth.2 mnth.3 mnth.4 mnth.5 mnth.6 mnth.7
## 1 ( 1 ) " " " " " " " " " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " " " " " " " " " "
## 6 ( 1 ) " " " " " " " " " " " " " " " " "*"
## 7 ( 1 ) " " " " " " " " " " " " " " " " "*"
## 8 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 9 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 10 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 11 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 12 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 13 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 14 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 15 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 16 ( 1 ) " " " " " " " " " " " " " " "*" "*"
## 17 ( 1 ) " " " " " " " " " " "*" " " "*" "*"
## 18 ( 1 ) " " "*" " " " " " " "*" " " "*" "*"
## 19 ( 1 ) " " "*" " " " " " " "*" " " "*" "*"
## 20 ( 1 ) " " "*" " " " " " " "*" " " "*" "*"
## 21 ( 1 ) " " "*" " " " " " " "*" " " "*" "*"
## 22 ( 1 ) " " "*" " " " " " " "*" " " "*" "*"
## 23 ( 1 ) " " "*" " " " " " " "*" " " "*" "*"
## 24 ( 1 ) " " "*" " " " " "*" "*" " " "*" "*"
## 25 ( 1 ) " " "*" " " " " "*" "*" " " "*" "*"
## 26 ( 1 ) "*" "*" " " " " "*" "*" " " "*" "*"
## 27 ( 1 ) "*" "*" "*" " " "*" "*" " " "*" "*"
## 28 ( 1 ) "*" "*" "*" " " "*" "*" " " "*" "*"
## 29 ( 1 ) "*" "*" "*" " " "*" "*" " " "*" "*"
## 30 ( 1 ) "*" "*" "*" " " "*" "*" " " "*" "*"
## 31 ( 1 ) "*" "*" "*" " " "*" "*" " " "*" "*"
## 32 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*" "*"
## 33 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 34 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 35 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## mnth.8 mnth.9 mnth.10 mnth.11 wkday.0 wkday.1 wkday.2 wkday.3 wkday.4
## 1 ( 1 ) " " " " " " " " " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " " " " " " " " " "
## 6 ( 1 ) " " " " " " " " " " " " " " " " " "
## 7 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 8 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 9 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 10 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 11 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 12 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 13 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 14 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 15 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 16 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 17 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 18 ( 1 ) "*" " " " " " " " " " " " " " " " "
## 19 ( 1 ) "*" " " " " " " "*" " " " " " " " "
## 20 ( 1 ) "*" "*" " " " " "*" " " " " " " " "
## 21 ( 1 ) "*" "*" "*" " " "*" " " " " " " " "
## 22 ( 1 ) "*" "*" "*" " " "*" " " " " " " " "
## 23 ( 1 ) "*" "*" "*" " " "*" " " "*" " " " "
## 24 ( 1 ) "*" "*" "*" " " "*" " " "*" " " " "
## 25 ( 1 ) "*" "*" "*" "*" "*" " " "*" " " " "
## 26 ( 1 ) "*" "*" "*" "*" "*" " " "*" " " " "
## 27 ( 1 ) "*" "*" "*" "*" "*" " " "*" " " " "
## 28 ( 1 ) "*" "*" "*" "*" "*" "*" "*" " " " "
## 29 ( 1 ) "*" "*" "*" "*" "*" "*" "*" " " " "
## 30 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" " "
## 31 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 32 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 33 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 34 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## 35 ( 1 ) "*" "*" "*" "*" "*" "*" "*" "*" "*"
## wkday.5 wkday.6 weathersit.1 weathersit.2 weathersit.3 temp2 atemp2
## 1 ( 1 ) " " " " " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " " " " " "
## 6 ( 1 ) " " " " " " " " " " " " " "
## 7 ( 1 ) " " " " " " " " " " " " " "
## 8 ( 1 ) " " " " " " " " " " " " " "
## 9 ( 1 ) " " " " " " " " "*" " " " "
## 10 ( 1 ) " " " " " " " " "*" " " " "
## 11 ( 1 ) " " " " " " " " "*" " " " "
## 12 ( 1 ) " " " " " " " " "*" " " " "
## 13 ( 1 ) " " " " " " " " "*" " " " "
## 14 ( 1 ) " " " " " " " " "*" "*" " "
## 15 ( 1 ) " " " " " " " " "*" "*" "*"
## 16 ( 1 ) " " " " " " " " "*" "*" "*"
## 17 ( 1 ) " " " " " " " " "*" "*" "*"
## 18 ( 1 ) " " " " " " " " "*" "*" "*"
## 19 ( 1 ) " " " " " " " " "*" "*" "*"
## 20 ( 1 ) " " " " " " " " "*" "*" "*"
## 21 ( 1 ) " " " " " " " " "*" "*" "*"
## 22 ( 1 ) " " " " "*" " " "*" "*" "*"
## 23 ( 1 ) " " " " "*" " " "*" "*" "*"
## 24 ( 1 ) " " " " "*" " " "*" "*" "*"
## 25 ( 1 ) " " " " "*" " " "*" "*" "*"
## 26 ( 1 ) " " " " "*" " " "*" "*" "*"
## 27 ( 1 ) " " " " "*" " " "*" "*" "*"
## 28 ( 1 ) " " " " "*" " " "*" "*" "*"
## 29 ( 1 ) " " " " "*" " " "*" "*" "*"
## 30 ( 1 ) " " " " "*" " " "*" "*" "*"
## 31 ( 1 ) " " " " "*" " " "*" "*" "*"
## 32 ( 1 ) " " " " "*" " " "*" "*" "*"
## 33 ( 1 ) " " " " "*" " " "*" "*" "*"
## 34 ( 1 ) " " " " "*" " " "*" "*" "*"
## 35 ( 1 ) " " " " "*" "*" "*" "*" "*"
## hum2 windspeed2 temp_dif_s
## 1 ( 1 ) " " " " " "
## 2 ( 1 ) " " " " " "
## 3 ( 1 ) " " " " " "
## 4 ( 1 ) "*" " " " "
## 5 ( 1 ) "*" " " "*"
## 6 ( 1 ) "*" " " "*"
## 7 ( 1 ) "*" " " "*"
## 8 ( 1 ) "*" " " "*"
## 9 ( 1 ) "*" " " "*"
## 10 ( 1 ) "*" " " "*"
## 11 ( 1 ) "*" "*" "*"
## 12 ( 1 ) "*" "*" "*"
## 13 ( 1 ) "*" "*" "*"
## 14 ( 1 ) "*" "*" "*"
## 15 ( 1 ) "*" "*" "*"
## 16 ( 1 ) "*" "*" "*"
## 17 ( 1 ) "*" "*" "*"
## 18 ( 1 ) "*" "*" "*"
## 19 ( 1 ) "*" "*" "*"
## 20 ( 1 ) "*" "*" "*"
## 21 ( 1 ) "*" "*" "*"
## 22 ( 1 ) "*" "*" "*"
## 23 ( 1 ) "*" "*" "*"
## 24 ( 1 ) "*" "*" "*"
## 25 ( 1 ) "*" "*" "*"
## 26 ( 1 ) "*" "*" "*"
## 27 ( 1 ) "*" "*" "*"
## 28 ( 1 ) "*" "*" "*"
## 29 ( 1 ) "*" "*" "*"
## 30 ( 1 ) "*" "*" "*"
## 31 ( 1 ) "*" "*" "*"
## 32 ( 1 ) "*" "*" "*"
## 33 ( 1 ) "*" "*" "*"
## 34 ( 1 ) "*" "*" "*"
## 35 ( 1 ) "*" "*" "*"sum.regfit_bwd <- summary(regfit.bwd)
sum.regfit_bwd$which## (Intercept) yr holiday workday temp atemp hum windspeed daytime
## 1 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 2 TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 3 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 4 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 5 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 6 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 7 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 8 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 9 TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 10 TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE
## 11 TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE
## 12 TRUE TRUE TRUE FALSE FALSE TRUE FALSE TRUE TRUE
## 13 TRUE TRUE TRUE FALSE FALSE TRUE FALSE TRUE TRUE
## 14 TRUE TRUE TRUE FALSE FALSE TRUE FALSE TRUE TRUE
## 15 TRUE TRUE TRUE FALSE FALSE TRUE FALSE TRUE TRUE
## 16 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 17 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 18 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 19 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 20 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 21 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 22 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 23 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 24 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 25 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 26 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 27 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 28 TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 29 TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 30 TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 31 TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 32 TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 33 TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## 34 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 35 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## season.1 season.2 season.3 mnth.1 mnth.2 mnth.3 mnth.4 mnth.5 mnth.6 mnth.7
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 3 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 4 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 5 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 6 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 7 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 8 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 9 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 10 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 11 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 12 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 13 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 14 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 15 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 16 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## 17 TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 18 TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 19 TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 20 TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 21 TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 22 TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 23 TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## 24 TRUE FALSE TRUE FALSE FALSE TRUE TRUE FALSE TRUE TRUE
## 25 TRUE FALSE TRUE FALSE FALSE TRUE TRUE FALSE TRUE TRUE
## 26 TRUE TRUE TRUE FALSE FALSE TRUE TRUE FALSE TRUE TRUE
## 27 TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 28 TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 29 TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 30 TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 31 TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
## 32 TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 33 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 34 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 35 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## mnth.8 mnth.9 mnth.10 mnth.11 wkday.0 wkday.1 wkday.2 wkday.3 wkday.4
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 3 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 4 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 5 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 6 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 7 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 8 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 9 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 10 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 11 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 12 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 13 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 14 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 15 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 16 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 17 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 18 TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 19 TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 20 TRUE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 21 TRUE TRUE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
## 22 TRUE TRUE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
## 23 TRUE TRUE TRUE FALSE TRUE FALSE TRUE FALSE FALSE
## 24 TRUE TRUE TRUE FALSE TRUE FALSE TRUE FALSE FALSE
## 25 TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE
## 26 TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE
## 27 TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE
## 28 TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE
## 29 TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE
## 30 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE
## 31 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 32 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 33 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 34 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 35 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## wkday.5 wkday.6 weathersit.1 weathersit.2 weathersit.3 temp2 atemp2 hum2
## 1 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 3 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## 4 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 5 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 6 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 7 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 8 FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## 9 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 10 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 11 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 12 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 13 FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE
## 14 FALSE FALSE FALSE FALSE TRUE TRUE FALSE TRUE
## 15 FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 16 FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 17 FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 18 FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 19 FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 20 FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 21 FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
## 22 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 23 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 24 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 25 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 26 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 27 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 28 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 29 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 30 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 31 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 32 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 33 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 34 FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## 35 FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## windspeed2 temp_dif_s
## 1 FALSE FALSE
## 2 FALSE FALSE
## 3 FALSE FALSE
## 4 FALSE FALSE
## 5 FALSE TRUE
## 6 FALSE TRUE
## 7 FALSE TRUE
## 8 FALSE TRUE
## 9 FALSE TRUE
## 10 FALSE TRUE
## 11 TRUE TRUE
## 12 TRUE TRUE
## 13 TRUE TRUE
## 14 TRUE TRUE
## 15 TRUE TRUE
## 16 TRUE TRUE
## 17 TRUE TRUE
## 18 TRUE TRUE
## 19 TRUE TRUE
## 20 TRUE TRUE
## 21 TRUE TRUE
## 22 TRUE TRUE
## 23 TRUE TRUE
## 24 TRUE TRUE
## 25 TRUE TRUE
## 26 TRUE TRUE
## 27 TRUE TRUE
## 28 TRUE TRUE
## 29 TRUE TRUE
## 30 TRUE TRUE
## 31 TRUE TRUE
## 32 TRUE TRUE
## 33 TRUE TRUE
## 34 TRUE TRUE
## 35 TRUE TRUEpar(mfrow=c(2,2))
max.rsq.bwd <- which.max(summary(regfit.bwd)$rsq)
max.rsq.bwd## [1] 35plot(summary(regfit.bwd)$rsq, xlab = "Number of Variables",
ylab ="R-squared")
plot(summary(regfit.bwd)$adjr2, xlab = "Number of Variables",
ylab ="Adj R-squared")
max.adjr2.bwd <- which.max(summary(regfit.bwd)$adjr2)
max.adjr2.bwd## [1] 24points(max.adjr2.bwd,summary(regfit.bwd)$adjr2[24], col = "red", cex = 2, pch = 20)
plot(summary(regfit.bwd)$cp, xlab = "Number of Variables",
ylab ="Mallows Cp")
min.cp.bwd <- which.min(summary(regfit.bwd)$cp)
min.cp.bwd ## [1] 23points(min.cp.bwd,summary(regfit.bwd)$cp[23], col = "blue", cex = 2, pch = 20)
plot(summary(regfit.bwd)$bic, xlab = "Number of Variables",
ylab ="Bayesian Info Crit")
min.bic.bwd <- which.min(summary(regfit.bwd)$bic)
min.bic.bwd## [1] 13points(min.bic.bwd,summary(regfit.bwd)$bic[13], col = "green", cex = 2, pch = 20)
coef.adjr2.bwd <- coef(regfit.bwd, 24)
coef.adjr2.bwd## (Intercept) yr holiday temp atemp windspeed
## -31.7106353 84.8115410 -35.0742912 134.0860497 189.9749059 107.1429057
## daytime season.1 season.3 mnth.3 mnth.4 mnth.6
## 153.4948982 -29.1072826 -25.0266268 5.3255900 -16.9646222 -29.7975352
## mnth.7 mnth.8 mnth.9 mnth.10 wkday.0 wkday.2
## -59.3090251 -29.2726633 20.3371872 14.9172331 -12.5351795 -6.1904195
## weathersit.3 atemp2 hum2 windspeed2 temp_dif_s wkday.5
## -24.9675930 -19.6007165 -144.7155710 -237.4909692 25.2584314 2.2451093
## wkday.6
## 0.4181552coef.cp.bwd <- coef(regfit.bwd, 23)
coef.cp.bwd## (Intercept) yr holiday temp atemp windspeed
## -31.8745841 84.7437997 -35.6591856 137.7591758 194.7862673 108.7681294
## daytime season.1 season.3 mnth.4 mnth.6 mnth.7
## 153.5210737 -29.3089522 -24.8229430 -18.2392771 -30.7748548 -59.5410585
## mnth.8 mnth.9 mnth.10 wkday.0 wkday.2 weathersit.3
## -29.6984335 20.0145554 15.0193751 -12.6178588 -6.1966902 -25.0213347
## atemp2 hum2 windspeed2 temp_dif_s wkday.5 wkday.6
## -25.3769212 -144.9383713 -239.6893926 23.8909889 2.2591985 0.3408962coef.bic.bwd <- coef(regfit.bwd, 13)
coef.bic.bwd## (Intercept) yr holiday atemp windspeed daytime
## -90.827599 92.994004 -30.297060 112.905876 59.894395 168.021770
## season.1 mnth.6 mnth.7 mnth.8 atemp2 temp_dif_s
## -12.287276 -25.889880 -87.594819 -56.518997 222.597799 34.661471
## wkday.5 wkday.6
## 10.633810 6.882804c(names(coef.adjr2.bwd))## [1] "(Intercept)" "yr" "holiday" "temp" "atemp"
## [6] "windspeed" "daytime" "season.1" "season.3" "mnth.3"
## [11] "mnth.4" "mnth.6" "mnth.7" "mnth.8" "mnth.9"
## [16] "mnth.10" "wkday.0" "wkday.2" "weathersit.3" "atemp2"
## [21] "hum2" "windspeed2" "temp_dif_s" "wkday.5" "wkday.6"c(names(coef.cp.bwd))## [1] "(Intercept)" "yr" "holiday" "temp" "atemp"
## [6] "windspeed" "daytime" "season.1" "season.3" "mnth.4"
## [11] "mnth.6" "mnth.7" "mnth.8" "mnth.9" "mnth.10"
## [16] "wkday.0" "wkday.2" "weathersit.3" "atemp2" "hum2"
## [21] "windspeed2" "temp_dif_s" "wkday.5" "wkday.6"c(names(coef.bic.bwd))## [1] "(Intercept)" "yr" "holiday" "atemp" "windspeed"
## [6] "daytime" "season.1" "mnth.6" "mnth.7" "mnth.8"
## [11] "atemp2" "temp_dif_s" "wkday.5" "wkday.6"reg_adjr2_bwd <- lm(cnt ~ yr + holiday + temp + atemp + windspeed + daytime + season.1 + season.3 + mnth.4 + mnth.6 + mnth.7 + mnth.8 + mnth.9 + mnth.10 + mnth.11 + wkday.0 + wkday.2 + weathersit.3 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 + wkday.6, data = training_set)
summary(reg_adjr2_fwd)##
## Call:
## lm(formula = cnt ~ yr + holiday + temp + atemp + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.4 + mnth.5 +
## mnth.6 + mnth.7 + mnth.8 + mnth.9 + mnth.10 + mnth.11 + wkday.0 +
## wkday.2 + weathersit.3 + atemp2 + hum2 + windspeed2 + temp_dif_s +
## wkday.5 + wkday.6, data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -373.74 -96.48 -18.93 67.36 553.39
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -26.0025 18.8195 -1.382 0.167107
## yr 84.6335 2.9141 29.043 < 2e-16 ***
## holiday -34.8800 8.7202 -4.000 6.39e-05 ***
## temp 150.9273 62.0430 2.433 0.015010 *
## atemp 189.4846 76.8879 2.464 0.013742 *
## windspeed 109.0394 32.1388 3.393 0.000695 ***
## daytime 153.2636 3.1385 48.834 < 2e-16 ***
## season.1 -37.0824 15.2719 -2.428 0.015197 *
## season.2 -3.0422 14.1349 -0.215 0.829598
## season.3 -26.4592 10.2942 -2.570 0.010178 *
## mnth.4 -23.1607 9.0358 -2.563 0.010387 *
## mnth.5 -7.9023 9.4669 -0.835 0.403898
## mnth.6 -37.0219 9.8457 -3.760 0.000171 ***
## mnth.7 -66.0266 12.3979 -5.326 1.03e-07 ***
## mnth.8 -35.9363 11.9404 -3.010 0.002623 **
## mnth.9 14.1173 10.2264 1.380 0.167475
## mnth.10 9.2633 8.4416 1.097 0.272527
## mnth.11 -8.9429 7.7255 -1.158 0.247065
## wkday.0 -12.4530 4.4257 -2.814 0.004907 **
## wkday.2 -6.0674 4.3920 -1.381 0.167173
## weathersit.3 -24.9058 5.7579 -4.325 1.54e-05 ***
## atemp2 -22.2784 60.9379 -0.366 0.714678
## hum2 -144.7559 7.3083 -19.807 < 2e-16 ***
## windspeed2 -241.0866 65.2696 -3.694 0.000222 ***
## temp_dif_s 21.4631 13.0142 1.649 0.099141 .
## wkday.5 2.3009 4.4728 0.514 0.606960
## wkday.6 0.4213 4.4245 0.095 0.924138
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 134.4 on 8731 degrees of freedom
## Multiple R-squared: 0.4902, Adjusted R-squared: 0.4886
## F-statistic: 322.8 on 26 and 8731 DF, p-value: < 2.2e-16reg_cp_bwd <- lm(cnt ~ yr + holiday + temp + atemp + windspeed + daytime + season.1 + season.3 + mnth.4 + mnth.6 + mnth.7 + mnth.8 + mnth.9 + mnth.10 + wkday.0 + wkday.2 + weathersit.3 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5 + wkday.6, data = training_set)
summary(reg_cp_fwd)##
## Call:
## lm(formula = cnt ~ yr + holiday + temp + atemp + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.4 + mnth.5 +
## mnth.6 + mnth.7 + mnth.8 + mnth.11 + wkday.0 + wkday.2 +
## weathersit.3 + atemp2 + hum2 + windspeed2 + temp_dif_s +
## wkday.5 + wkday.6, data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -372.68 -96.25 -19.02 67.38 556.00
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -31.0325 18.4999 -1.677 0.093491 .
## yr 84.5587 2.9136 29.022 < 2e-16 ***
## holiday -34.4786 8.7116 -3.958 7.63e-05 ***
## temp 146.0292 61.6954 2.367 0.017958 *
## atemp 198.8927 76.2949 2.607 0.009152 **
## windspeed 108.7293 32.1337 3.384 0.000718 ***
## daytime 152.8692 3.1269 48.889 < 2e-16 ***
## season.1 -34.2825 15.1269 -2.266 0.023456 *
## season.2 0.9777 13.6736 0.072 0.943001
## season.3 -20.3575 8.0249 -2.537 0.011205 *
## mnth.4 -27.8469 8.4004 -3.315 0.000920 ***
## mnth.5 -13.4491 8.6028 -1.563 0.118011
## mnth.6 -45.0978 7.9516 -5.672 1.46e-08 ***
## mnth.7 -79.1458 8.0176 -9.871 < 2e-16 ***
## mnth.8 -48.7249 7.5774 -6.430 1.34e-10 ***
## mnth.11 -13.8613 6.5829 -2.106 0.035263 *
## wkday.0 -12.0834 4.4181 -2.735 0.006251 **
## wkday.2 -6.1241 4.3917 -1.394 0.163212
## weathersit.3 -24.7993 5.7570 -4.308 1.67e-05 ***
## atemp2 -34.7058 60.1423 -0.577 0.563913
## hum2 -144.0049 7.2847 -19.768 < 2e-16 ***
## windspeed2 -241.0521 65.2700 -3.693 0.000223 ***
## temp_dif_s 28.1671 12.1294 2.322 0.020244 *
## wkday.5 2.5326 4.4700 0.567 0.571018
## wkday.6 0.7687 4.4183 0.174 0.861892
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 134.4 on 8733 degrees of freedom
## Multiple R-squared: 0.49, Adjusted R-squared: 0.4886
## F-statistic: 349.6 on 24 and 8733 DF, p-value: < 2.2e-16reg_bic_bwd <- lm(cnt ~ yr + holiday + atemp + windspeed + daytime + season.1 + mnth.6 + mnth.7 + mnth.8 + atemp2 + temp_dif_s + wkday.5 + wkday.6, data = training_set)
summary(reg_bic_fwd)##
## Call:
## lm(formula = cnt ~ yr + holiday + atemp + daytime + season.1 +
## mnth.6 + mnth.7 + mnth.8 + atemp2 + temp_dif_s + wkday.6,
## data = training_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -381.52 -95.83 -21.40 69.15 575.72
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -73.695 13.289 -5.546 3.01e-08 ***
## yr 92.845 2.989 31.060 < 2e-16 ***
## holiday -31.275 8.897 -3.515 0.000442 ***
## atemp 93.474 53.153 1.759 0.078684 .
## daytime 170.412 3.088 55.187 < 2e-16 ***
## season.1 -12.280 5.842 -2.102 0.035598 *
## mnth.6 -26.889 6.314 -4.259 2.08e-05 ***
## mnth.7 -89.944 7.175 -12.536 < 2e-16 ***
## mnth.8 -57.613 6.448 -8.935 < 2e-16 ***
## atemp2 247.570 57.220 4.327 1.53e-05 ***
## temp_dif_s 33.216 4.455 7.455 9.83e-14 ***
## wkday.6 5.407 4.252 1.272 0.203494
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 139.2 on 8746 degrees of freedom
## Multiple R-squared: 0.4526, Adjusted R-squared: 0.4519
## F-statistic: 657.5 on 11 and 8746 DF, p-value: < 2.2e-16anova(reg_adjr2_bwd, reg_all)## Analysis of Variance Table
##
## Model 1: cnt ~ yr + holiday + temp + atemp + windspeed + daytime + season.1 +
## season.3 + mnth.4 + mnth.6 + mnth.7 + mnth.8 + mnth.9 + mnth.10 +
## mnth.11 + wkday.0 + wkday.2 + weathersit.3 + atemp2 + hum2 +
## windspeed2 + temp_dif_s + wkday.5 + wkday.6
## Model 2: cnt ~ yr + holiday + workday + temp + atemp + hum + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.1 + mnth.2 +
## mnth.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.9 +
## mnth.10 + mnth.11 + wkday.0 + wkday.1 + wkday.2 + wkday.3 +
## wkday.4 + wkday.5 + wkday.6 + weathersit.1 + weathersit.2 +
## weathersit.3 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 8733 157827603
## 2 8722 157313762 11 513840 2.5899 0.002754 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(reg_cp_bwd, reg_all)## Analysis of Variance Table
##
## Model 1: cnt ~ yr + holiday + temp + atemp + windspeed + daytime + season.1 +
## season.3 + mnth.4 + mnth.6 + mnth.7 + mnth.8 + mnth.9 + mnth.10 +
## wkday.0 + wkday.2 + weathersit.3 + atemp2 + hum2 + windspeed2 +
## temp_dif_s + wkday.5 + wkday.6
## Model 2: cnt ~ yr + holiday + workday + temp + atemp + hum + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.1 + mnth.2 +
## mnth.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.9 +
## mnth.10 + mnth.11 + wkday.0 + wkday.1 + wkday.2 + wkday.3 +
## wkday.4 + wkday.5 + wkday.6 + weathersit.1 + weathersit.2 +
## weathersit.3 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 8734 157843482
## 2 8722 157313762 12 529719 2.4475 0.00351 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(reg_bic_bwd, reg_all)## Analysis of Variance Table
##
## Model 1: cnt ~ yr + holiday + atemp + windspeed + daytime + season.1 +
## mnth.6 + mnth.7 + mnth.8 + atemp2 + temp_dif_s + wkday.5 +
## wkday.6
## Model 2: cnt ~ yr + holiday + workday + temp + atemp + hum + windspeed +
## daytime + season.1 + season.2 + season.3 + mnth.1 + mnth.2 +
## mnth.3 + mnth.4 + mnth.5 + mnth.6 + mnth.7 + mnth.8 + mnth.9 +
## mnth.10 + mnth.11 + wkday.0 + wkday.1 + wkday.2 + wkday.3 +
## wkday.4 + wkday.5 + wkday.6 + weathersit.1 + weathersit.2 +
## weathersit.3 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 8744 168878592
## 2 8722 157313762 22 11564829 29.145 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1According to the p-value(all 3 are significant at the 95% level), the third model(min_bic) were selected because it has the smallest subset with a decent r square. The model is just as good as the all in model. Compared with forward stepwise, the backward F-stat is a little bit higher than the former one. Moreover, adding variable could cause other variables unsignificant so I prefer the reg_bic_bwd model.
# Q6. Using the favorite model from questions 4 and 5 run LOO, 5-Fold and 10-Fold cross-validation. Save the MSEs. What was learned in this question?
# LOO
glm.1 <- glm(cnt ~ yr + holiday + workday + temp + atemp + windspeed + daytime + season.1 + season.3 + mnth.6 + mnth.7 + mnth.8 + wkday.0 + temp2 + atemp2 + hum2 + windspeed2 + temp_dif_s + wkday.5, data = dbike3)
cv.err.1 <- cv.glm(dbike3, glm.1)
cv.err.1$delta[2]## [1] 17055.53MSE.LOOCV.1 <- cv.err.1$delta[2]
MSE.LOOCV.1## [1] 17055.53# 5-Fold
cv.err.5.1 <- cv.glm(dbike3, glm.1, K = 5)
MSE.5.1 <- cv.err.5.1$delta
MSE.5.1## [1] 17050.47 17046.54# 10-Fold
cv.err3.10.1 <- cv.glm(dbike3, glm.1, K = 10)
MSE.10.1 <- cv.err3.10.1$delta
MSE.10.1## [1] 17049.78 17047.9510 FOLD Validation has the smallest MSE and its the best cv method.
#LOO
glm.2 <- glm(cnt ~ yr + holiday + atemp + windspeed + daytime + season.1 + mnth.6 + mnth.7 + mnth.8 + atemp2 + temp_dif_s + wkday.5 + wkday.6, data = dbike3)
cv.err.2 <- cv.glm(dbike3, glm.2)
cv.err.2## $call
## cv.glm(data = dbike3, glmfit = glm.2)
##
## $K
## [1] 17379
##
## $delta
## [1] 18223.67 18223.67
##
## $seed
## [1] 10403 188 1077329476 610674084 -2113862655 -1024038508
## [7] -1955727596 306522696 -1841834735 -1461462276 -1198267463 -115386373
## [13] 944868980 -2008551803 311709003 -1450835770 -2055625295 -1793800812
## [19] 1192707820 -389273099 473851391 1022759321 1071796079 -247297840
## [25] 77783733 1654790731 -2047622228 224977577 113692845 -1161120840
## [31] 1444924786 -1161348212 -359223090 -101984981 -806279225 1613689450
## [37] 1828680783 -53684575 -1922158355 -1797996641 -1492574976 -472849192
## [43] -552503328 1004151751 1543327191 -185289332 1494697437 -1002857496
## [49] -2141259278 -2093532514 -1094395035 743138088 2054523443 -1193601487
## [55] -353552601 -61256919 -357698898 2032538668 1785777687 -1493969092
## [61] -564976998 -2124525243 -2089643739 1252501744 1062149369 -1407779565
## [67] 1219441698 -1282659892 742098048 1241956367 -835487523 -727688927
## [73] -713630967 505244766 252159788 -1621732464 2031904011 1795896924
## [79] -1802386131 -786257445 -793241775 -407528505 -1354983189 -1520360683
## [85] 523238374 -1506690392 -528305 1829270956 1309754840 1051021841
## [91] -693961798 -1497386487 -1464337852 1702126483 1102851769 -685127170
## [97] 180504283 1728093188 -1772164452 532282142 -246878231 -1925074985
## [103] -539036012 1171211471 -1416561732 1825614530 -1076374333 847045038
## [109] -1555559405 -1364783250 -1316649987 1907448237 -285365992 722597175
## [115] -689669668 1960174028 -962720654 -970603356 1623672471 -618342272
## [121] 1009451060 1434330415 693811645 241399535 -826072159 26525908
## [127] 1584584425 -57028893 953216754 884437345 -1343249146 -332045213
## [133] -798065557 79798763 -1696041964 1178969177 -33312177 1267647748
## [139] 1865279697 -294923649 -541590171 1934423689 -1680161494 -271836478
## [145] 132673877 1083797415 1307340340 -253886819 584297700 1551036111
## [151] 1631481736 1283500852 -695486083 249040282 1200597677 -1695789750
## [157] -652686274 635868204 1750772781 -1461436613 -1184092410 -1317102212
## [163] 976478847 -1484276327 1953562768 -636509520 124882705 -1812874828
## [169] 1195249611 -1776501508 1615507158 888681652 1565181919 -1087496730
## [175] 263439982 -1168782894 114425508 -656071998 -727884638 1032070957
## [181] -1837988082 1081714701 406175449 -837512301 -395894993 -1031544095
## [187] -837791153 2046925696 1846795206 1587424393 -199707355 -998553418
## [193] 348709629 1532047799 -505887791 -461094850 1844851593 -1306423594
## [199] 1957177101 -1120877343 1512728990 -1832117585 1605776816 422290045
## [205] 236538340 986950046 1026523755 -1463828659 -1383604815 -1731624672
## [211] -1903337796 553203205 880914158 829916917 1862249219 -2145648553
## [217] 150524446 1165553616 503754771 1407947558 810185640 -1533277299
## [223] 1569438033 589187277 449159987 1285529065 -1644136525 -22749839
## [229] -379276868 -1923280676 -1513838947 -87511175 1087982093 -587675762
## [235] -218907112 -2100590177 77308977 1005701812 -2012742350 -1910761705
## [241] 1087088686 -607151256 -520832550 1930600201 -1940168919 -2097386337
## [247] -1732714241 -55315537 1933911696 -351228844 -862302407 -919405249
## [253] 1886369778 1230679334 -1347289563 1784183116 744412332 -282988538
## [259] 19181432 -1861933091 -150334637 -1375906825 516447398 2012951433
## [265] 1584367441 -230223540 -1614009579 1568520362 610542931 1545438442
## [271] -1660701935 1121424430 -507490400 -1008347445 -1784219826 -736962404
## [277] -2020852607 1181397596 794262469 -19432376 -1028391299 1854269808
## [283] -738588265 -1510126324 -918242457 350486943 1645344210 -536034932
## [289] 451743868 -1236066661 -1301025880 -1975990371 -1790138667 -554492973
## [295] -1079928863 1379832325 142771289 617706074 -1154313923 1803438263
## [301] -542980363 1466052474 1201536115 447149659 -927831453 -1041263763
## [307] -1116687005 1467599628 -1561278891 1138269197 1229779673 1369028317
## [313] -2040327621 524957556 -1823560736 -1832313911 -493810876 -387125669
## [319] 831304148 -1111976835 413639659 -595778928 545180157 967696075
## [325] -523986749 1174579903 702345035 1207479528 -800774280 -421403974
## [331] 496509986 1044283336 -939337026 -445913576 1204324783 1074608542
## [337] -1645033085 -1322180686 1734292968 -636006016 860423944 -256262393
## [343] -155914319 -449596615 -1823002420 -1745263304 1810257172 2508166
## [349] 538826985 1253901939 -1961331346 1762978090 -1048509624 870862166
## [355] -106548744 -1665635851 5467222 1518271243 272757923 826313671
## [361] -1754421470 374696691 393732699 416305362 -388363438 -1596693236
## [367] -1597398980 -473825832 608427517 61374161 618186026 871872522
## [373] -101513767 -885080934 1816542912 641935263 -19427057 -200742833
## [379] 1258668740 -890154910 82301451 1379047147 478369698 1436830792
## [385] 388945269 728281610 235892330 -524657515 22493484 -317070877
## [391] 1838610383 617752623 1475936135 802933242 -1878262318 952931513
## [397] -1918911172 1907248592 1676441680 1687275054 -1844049510 1834045982
## [403] 139129759 -1636481062 269650553 236605079 -1464145048 770247881
## [409] 1969513634 1105604101 1518169394 -1416330003 -1806798995 1037849203
## [415] 299618340 -1007246405 -2035954588 471430470 1049610937 -348827243
## [421] 1814369172 1861559080 -5447391 1559267135 359316882 1407897933
## [427] -2010387997 1004458851 -1280525372 -1552488842 -1001041596 1838290315
## [433] -1412559015 -520596204 1307604480 1407877553 1874722326 126248170
## [439] 1495653003 -566302557 957734259 -1807664167 1506484820 -697861000
## [445] -262879044 -1892737954 1775333473 -655877485 470297310 693135422
## [451] 132266268 -909180779 1814274732 1961626325 741638901 -1419756139
## [457] -2586224 -1039973510 1263614293 -841232599 1528835681 -1995135791
## [463] -719103021 1481443304 -2078173262 1574854361 -598537822 1945217279
## [469] 1510581524 -792549424 1857911565 782741015 2000176956 -135303848
## [475] -1727552866 -1969342606 -871681520 -2055849053 -343838282 2076405853
## [481] 1890508505 942194319 -595817375 1699785984 1484701973 475019788
## [487] 526776263 -364276939 1551116960 -737847484 513456533 -1916078687
## [493] -754757906 -1800430990 -1907949898 -489555301 -1450202349 -1000518994
## [499] -1307237042 510499872 -1581109461 1527577277 -197306381 -1679069329
## [505] -734659816 1454026167 -1871049637 1495827866 -809100101 399052851
## [511] -1925719258 -476079451 -1207685906 1404933292 -2084485196 1122126510
## [517] 1136791615 -609681211 -564790100 -1638662656 1354020923 -1482059730
## [523] -80699129 1246343519 -1516994903 -986337274 -1337034472 -1230924754
## [529] -329193940 701428558 1863246696 1762599847 380568005 -1505325506
## [535] 37004038 -290846888 -1417755900 968276642 -398483073 -306735261
## [541] -1092222479 -417946810 2016211048 -62573466 82248431 -1103715450
## [547] -1940875928 525036004 -375483787 650172114 2113224256 1636711296
## [553] -2045176557 1349520503 529132299 1721451210 -1289167378 946861368
## [559] 1226038796 -612270371 -1485981270 1574160254 -1908403295 79300749
## [565] 663366490 -173981821 -853488270 424744569 -825312902 -2130361097
## [571] -491192822 281032058 991591621 1216311504 1386545684 858519762
## [577] -775142413 -2128726756 911221560 -983868978 -338696006 1941555682
## [583] -873865379 -1010507598 -1770952451 995904649 -1584105203 1750285995
## [589] 807232470 -1774831438 -1561211460 987537179 1879025813 -1665673718
## [595] -1394941745 -1785621595 -712911641 -1101320161 1045268158 1022178336
## [601] -758210068 -2046339890 289612721 1004116597 -1586549258 -353064300
## [607] -800472687 -466628922 744810202 -705808878 -637213633 1043921561
## [613] -435773576 1765287483 -152814525 822066372 -1188315444 -315106652
## [619] 762924632 827994557 1656735557 -606726250 153643118 1841629729
## [625] -1845649713 1140270962#5-Fold
cv.err.2.5 <- cv.glm(dbike3, glm.2, K = 5)
cv.err.2.5## $call
## cv.glm(data = dbike3, glmfit = glm.2, K = 5)
##
## $K
## [1] 5
##
## $delta
## [1] 18224.69 18221.25
##
## $seed
## [1] 10403 62 1774323545 -750303354 -896698764 1563263850
## [7] 1243797079 -1041264708 -853462195 1125340654 -1381404098 -322088854
## [13] 1416522295 -1718858230 -1857162506 -1974701556 -675392767 17278200
## [19] -329656659 401699641 -1346389945 285542777 -1233605153 955535774
## [25] -142111092 -411758768 -1320384991 -426191011 942423726 2146912952
## [31] 794552699 1585164545 1397201962 -1756688484 -1730317197 -1340933670
## [37] -1044611390 537892654 668384330 411498208 1920083463 -1933430240
## [43] 1704802634 1856063144 294358645 -540965148 1010153990 -46640816
## [49] -319645509 -1722603818 1160049636 -1986059733 -1825034116 1864752803
## [55] 1023726069 12865 123984582 -838830266 -772139563 -1414205266
## [61] 204510559 -1820181988 -1251045074 356587195 -2098705526 -1240748841
## [67] 470810256 -1402465581 1359116137 -1284971855 -1885815136 -687869157
## [73] -994367566 148492471 33049600 14943690 210777868 -839221791
## [79] -1917181791 385591360 1123364569 186022385 1859738707 75937078
## [85] 601731673 -1965268259 1901530262 887657099 1868646177 553100237
## [91] 310979486 -1241965754 1415254543 803124159 -429010540 1598535078
## [97] 862843872 2083652981 -1612036099 1647051717 816228134 2059661481
## [103] -1938681351 -523350676 -2016494513 477396105 -49462445 1895160989
## [109] 1508889177 -2086137003 -634512090 1297988670 1750554735 -872558053
## [115] -1564847355 198918427 1920901185 -1111888172 -1355419302 -1265426817
## [121] 1174578990 -2059781965 1623425039 558788717 -450462263 187379680
## [127] 195893644 1957975407 1719533924 -1497507044 1748817795 -654076705
## [133] 1053798547 -2042459687 390637361 1170567292 1057863296 681274528
## [139] -616402735 -1076216315 173417282 1904261663 -382885192 555824983
## [145] 950222281 1084047833 -2003033231 -72650762 -131880524 1431531748
## [151] -1987713609 458901430 630129086 -1803465489 1781928002 615873208
## [157] 1206257047 866821852 -1339060595 923753756 -2139608107 -1149479864
## [163] -2144289771 629718118 -1707888551 -1042368937 805210662 -28662458
## [169] -1964799902 -1362005118 1830431837 -614932893 456225745 6097700
## [175] -905688819 149300673 1238237996 422958334 -1843905671 1471991055
## [181] -1008050044 -1938726446 505852650 2128321435 -379670267 -813466869
## [187] -181062584 313797234 87368562 1599011419 -1755458476 -184210159
## [193] 1187208365 -587567713 -883641305 -2140143876 2144181045 570668747
## [199] 882129221 799982305 -362880394 -722762037 -1883328611 -346165626
## [205] -1459215860 -109218154 -1170001309 554711280 -662454866 1006762874
## [211] -261893831 1482523858 -936420556 -417013368 -1540613726 1236166057
## [217] -1519625851 1761823720 -1643268797 -1006334548 -599832996 996296097
## [223] -1495470856 -1704882184 -511139591 -1555780278 617559694 -464922780
## [229] 4678529 -656492814 -1013686276 -401703827 -1280763744 -1483792073
## [235] -83243639 495122890 1651981590 -2115499055 1160359187 1781439335
## [241] -945363746 385499259 1844713482 2091679943 -2068647985 -759502159
## [247] -1822558856 -1963604081 -1117767792 1691327389 -35159687 -732289092
## [253] 1445455117 973026462 -1271623798 -1356096032 -1112220946 697903833
## [259] -1590643303 389969898 1800258414 -403567849 93347879 709690675
## [265] -2099084818 -2010752389 1621236489 2034068021 1948267773 -1153106725
## [271] -1408179230 -695508241 374224222 848580906 -1838776756 -2042708317
## [277] 706595589 -198707768 1496874137 857234891 1444033676 1321549146
## [283] 1424659185 -2053921105 1320506057 -1757260970 -1529807021 -337405554
## [289] 92095228 -1447586911 80924242 -937869006 1993268386 540815461
## [295] 469076523 -78922235 -1067317875 -325344013 -2007550547 -645631150
## [301] 993639598 -581890568 1128685273 -1714831634 -294298398 338078166
## [307] -1771106433 173094809 1311212193 2256114 240221274 1922604501
## [313] -20468703 -1192925675 -501094336 -1667231142 -553913449 1473359147
## [319] -2112095941 -1783486239 1654440797 158027179 -1208461688 -444487578
## [325] 312263200 -1635610143 2097406488 -1934482883 -1114862411 -1989036662
## [331] -447158254 520158146 -1171139463 252234254 1307130124 -1998912441
## [337] 365358586 2065278943 1558661786 -1813237757 1560154338 2103570796
## [343] -86622649 -383614295 2067439054 1120044033 445691959 755803185
## [349] 557875276 -1648515470 -1097057438 667935566 1417231168 -469416485
## [355] 1359126884 1904226326 -28168221 1981904690 -1129718358 -1989030763
## [361] 79652751 -1026068936 557716860 449562686 -188574074 -291182665
## [367] 1750909445 -150761710 -253677707 -240170482 1461988656 -674325004
## [373] -1969032971 -960787490 -215295102 -476194710 -1073160869 -21592413
## [379] -1374613247 1259269157 -264506774 -1630300403 687342410 -976510228
## [385] 1878344904 2006027969 -1634643292 -1598496091 849297350 1321614421
## [391] 1067558903 69771022 -1662669761 -2041540228 -1144821118 663301797
## [397] 168877230 -412208232 -2108054613 -1694706814 -1657913424 -894080791
## [403] 685837793 227053865 317379919 -1284378664 -1751973627 659007177
## [409] 1703565095 -888242520 1970136525 157906667 -1362462591 470933606
## [415] -1453685465 1791332284 1214795695 -75889292 1874486637 138533901
## [421] -851522036 -2091437455 -2000260632 -42107814 622737382 942599119
## [427] 1979458493 -115388660 -1739160479 1492389607 885102339 1155508554
## [433] 1599771611 86996643 -941000362 -1833355975 248217036 147725622
## [439] -2066561174 -1878566028 117024617 -661053191 -1835896731 -1238358142
## [445] 1605400424 -2100168767 -1541199571 -1055162652 41488157 1642126809
## [451] -428404327 2031158666 553653345 -299338511 2043637133 -1225224630
## [457] -992594931 728820224 -22164494 2130830804 150712438 277284330
## [463] 374723104 149323076 -1456076762 -2069939835 -474470573 -2117964728
## [469] -1137752040 1927927062 -1689848230 683207260 -1100954069 -1500288527
## [475] 2138813103 1873263798 1116787528 -1621963068 -1304305547 1890749748
## [481] -1054847243 1058831581 397772015 2117911974 -667157784 126679275
## [487] 710601042 985036664 408751837 1100054339 975019520 -1262174209
## [493] -23527368 -884791587 -389942628 1227871662 803961652 93579874
## [499] -372575044 -1584469467 1319037438 -1814554823 1031463800 -673305073
## [505] -463241897 1885246726 1309452887 14597324 349175101 -1347719210
## [511] -1890289737 -71313089 -900833298 -841185236 1864074446 1502587030
## [517] 341796597 -208071136 1498609145 -1119342411 -1147788544 1779882270
## [523] -1362083280 -715376019 -1955810653 1622008812 384984595 1390230552
## [529] 1953351585 1080295342 -1133800139 511484400 19753003 -1225491814
## [535] -1380255389 1809005801 1372579834 676971458 774291711 310393126
## [541] 584366003 1837116843 -1283077195 1641776732 295093188 -1879560568
## [547] 1496018178 1923098879 -92233970 1047237842 1819480825 228580593
## [553] -292934816 1398398297 -592428359 406554562 54982065 1292395712
## [559] -1397941944 1915552313 -1020769838 1465730333 1908558847 -1576567297
## [565] 1126167097 1518225996 437845840 1353389618 1250529677 -222421744
## [571] 969003103 1211503658 1215502539 -1358754508 515675793 1221329051
## [577] -1599893953 -1538015525 1328330707 146306567 -1707204370 -405827209
## [583] -1677041303 986572336 -168159186 820203557 -1676732262 -1806001044
## [589] 244954426 -1606928739 -1556523865 -948938446 -1093111947 589166807
## [595] 1599477038 401629826 450528781 1873468251 -1299825221 1347350579
## [601] -1350344890 367855182 -1324643556 -1104375098 -280631100 323482185
## [607] -1627072821 -1374306106 -810519260 1097019371 1033634217 -691506589
## [613] 2054521617 1033327136 1798438678 1692948377 984720857 1573863114
## [619] -143192010 803969613 -1413146512 -310796884 -1829979155 -1486854289
## [625] -1754589973 800067800#10-Fold
cv.err.2.10 <- cv.glm(dbike3, glm.2, K = 10)
cv.err.2.10## $call
## cv.glm(data = dbike3, glmfit = glm.2, K = 10)
##
## $K
## [1] 10
##
## $delta
## [1] 18225.40 18223.74
##
## $seed
## [1] 10403 222 -1638873570 -387408225 -709098861 -1219530179
## [7] 259825355 521526429 70163002 402937516 1618270355 1354629715
## [13] 557589680 1389850336 1754597544 -1809768622 -1104307794 -2120431162
## [19] 29998290 -1725884968 -606656570 -2068841915 1581139865 2057778581
## [25] -335451167 1411481939 -1134113652 672071217 1848935272 1876858046
## [31] -1547830443 651367705 -124040078 -1846613522 2142925036 1163333007
## [37] -2028884711 1624004312 454847663 1107609472 -470508770 552258998
## [43] 785424325 1334169435 1722029194 1235696736 1815727454 -2080266580
## [49] -262459824 52657963 1906439057 502832506 141724125 -2103501919
## [55] -1727467829 289128610 1295602753 1830987823 149614702 1060849728
## [61] -995347429 -352949213 290564075 -1533968597 -547442165 -1250972667
## [67] -797775276 587796247 -1570247213 1409754733 190275911 1306694291
## [73] 1720177025 59718487 -561925150 -490970166 1133411127 1850807595
## [79] 716220507 1365514365 -1610438923 1520581174 663125742 1106521041
## [85] -370875841 -2027980676 801378065 -266216332 -1154983787 -1568260570
## [91] -1495057418 675808420 1197248366 -573240230 -317211712 283126405
## [97] 856019419 588066494 -197785962 -1328712538 1514836702 1127592375
## [103] -1090791025 645778935 -1281699324 -1069137349 305618260 366847618
## [109] 884112226 2057155786 -75571125 1314763227 722199079 -899946506
## [115] 2025715274 1163386883 1906112670 1576377152 404094204 1574283938
## [121] -770108355 -1723444908 -1817319388 1702283327 1597232783 607450779
## [127] -1338959555 1722870646 1643478631 -732573590 -762556818 -1440541679
## [133] -1966885714 1973300811 -1188003900 856727990 1042871754 1932708168
## [139] 1856844242 -1631844781 1138581370 -104548955 -292870505 -1524063088
## [145] 1424577915 -29983737 -1876190195 -1542192605 -70225927 -829779658
## [151] -618707543 -1586816649 -1500709070 854118102 1240375555 730808122
## [157] 2055856334 -1109495740 1409688795 -1465533329 2143615223 494952479
## [163] -1470618136 370111775 1788698258 -749716073 -729247767 1295685647
## [169] 1069788378 -1648006203 -1410655763 -457336444 -746962678 1347311827
## [175] -464380953 -961470772 -1852483301 -571519788 1369616675 -1749115078
## [181] -1063444393 1188733301 502573672 325437331 620401367 1111456244
## [187] 629596856 1421730959 -1479222389 517156415 -718481210 -263774916
## [193] -899609235 1565831417 2008438037 1987527010 -573169809 2043040113
## [199] -250948734 -524274801 -968698384 1469127511 -1823909224 399252814
## [205] 267015266 -1079427647 1077762337 -1455208245 1720394613 -1048909240
## [211] -1043171199 806334553 -689179743 631193854 -140347399 -1764789832
## [217] -1122299500 2103888359 41712375 -28250652 343996794 2092733073
## [223] -2026987186 -1474168967 -817031879 1083617832 772878329 1689322152
## [229] 1706619481 1039337007 -161142892 797269070 1547690273 561667465
## [235] 1972444435 -24141902 1784822198 -1412574133 -1279213185 425266819
## [241] -2091713723 -1964900454 -33494310 1411145845 -988075253 1108674504
## [247] -754234776 -862065777 1876671 653908338 1604765717 43528771
## [253] -259286390 758141557 -43955057 440336181 -1000839298 363439377
## [259] -107724302 -1807341748 -539176837 76070897 1811884968 835635522
## [265] 2119199096 1842312055 572759557 -1425598559 -1783517404 1053297020
## [271] -265469152 99650110 -944725440 -565678493 -1513221073 -722061987
## [277] -2073370011 1503134431 -587872443 1211371724 356458467 -1293111055
## [283] 857966602 674179006 1467113678 1934108758 -885915112 -1322512743
## [289] -1202467416 -1133267288 1067494900 -2126175835 1437439431 720776351
## [295] 106769839 661325077 2071623032 828776432 -956791504 58198335
## [301] -1381222376 815974755 1226608383 -351462080 120859828 -1715633970
## [307] 755899319 249909050 904514760 -1300715638 -1366216465 114503143
## [313] 1384296911 -2115775617 1292774104 -1254628561 -955805707 -1737234440
## [319] -1908358368 -1036637938 2113528740 691883475 926411649 -2036045203
## [325] 1150266049 1506351603 -2084953475 260780666 1172269843 242172067
## [331] -656174013 394801857 243031934 -53274637 -1937560113 -1361703352
## [337] -1754907495 133599453 378571610 1470708042 -1647786581 1747179491
## [343] 1460782878 -355769059 1408490646 63155373 2037719612 -1492552625
## [349] -421696791 -1364436828 1606629212 -1781441713 -960838560 688759807
## [355] 184009022 -1900278490 820262993 1902952951 1370614843 410262907
## [361] -1220904399 350295367 1280674196 1640129213 1593665812 -330604831
## [367] -493938555 -254486342 685468406 -1254868473 -1203886530 -1941724495
## [373] -1775514841 1980210495 1627591678 1490267194 -4912655 -1607157161
## [379] -1048676605 273669658 788536515 -1131810198 564951645 -1417687600
## [385] 815150118 523869193 -394588017 2104567425 541732007 1411445894
## [391] 907355611 -2072418865 -98463355 -366752206 -1993602813 -250605318
## [397] -1779002134 800266897 -696821224 2103256872 -100739697 -1125485866
## [403] 2032077718 1167318665 711471148 -425701790 1370193328 -1070848717
## [409] -1148382908 -1728679395 -586677272 -1299765901 189238888 1145562648
## [415] 884526797 -1647313463 1412174972 700782319 -2095069906 1337095394
## [421] 1377049550 -1709404270 -1482153350 -85329210 624522974 1426721432
## [427] -331267265 902644290 -540760099 1170280679 -979473264 -1583378425
## [433] -148735381 -1755313237 -1836214653 1659280859 2119268443 260828189
## [439] 591059962 -469657162 831466822 -998584617 1342889638 1308394899
## [445] 469805187 561459362 -1525841767 1770439518 632019638 1992707400
## [451] -537602799 -1827914993 1097857522 99233468 461515234 1475649730
## [457] -1147368476 -869701495 59707873 -1745996142 2134312640 -421270057
## [463] 1938957023 -1099654531 1023305167 -34563586 -268747849 -1401826098
## [469] 139986531 644132466 1817366790 -2048184988 1455660421 -291214735
## [475] -821326359 637288863 -3354052 -363097714 -982138899 540945692
## [481] -1331411914 328758088 397851112 1273674255 104564318 -2096300058
## [487] -2099650579 1270581905 -87642398 -1670825108 -2085178 1740225885
## [493] 1244869719 -113197081 -903045909 1984239889 -1181433750 -330556009
## [499] -1548718639 683745491 -594420018 128068903 874252509 -218471653
## [505] -1459243957 -595765367 1652355809 481503023 -159745396 1818847732
## [511] 1569368718 2028473409 240354172 -1558742033 89140592 -2119051284
## [517] -1525566627 -940942651 2079236548 -379086773 -844568572 1921522482
## [523] 1119888881 -1775289041 -1111093435 1040954802 389595527 1348186793
## [529] 935182248 -632942788 995900903 2082889916 1351171641 -1417801900
## [535] 2090468876 -1845802406 283443304 67205139 -1381448188 -259853323
## [541] -1509586005 -1247813524 -2043622336 -908699702 278438349 -1854011400
## [547] -1761860164 -448153228 1847442788 -1212913413 -446997095 -1568198983
## [553] 1065256927 1498616609 -1198188609 -193981870 1027821235 1285546296
## [559] -47758324 -1973867260 -176235061 -996096376 676090465 396467015
## [565] 359087955 912210586 277847493 -914932164 391742581 -599871160
## [571] 471117082 2104920581 631247105 -283884095 -676808219 1510226542
## [577] 1352877463 2038269565 -1028999954 932740793 1391596077 365957622
## [583] 1755518523 -1269047241 904854264 681531331 1668064332 -1678806975
## [589] -361441920 662010161 1632343597 -1185301534 -455948520 -1685533693
## [595] 28840357 -341321650 -707305480 1956380754 -230367488 633827207
## [601] 371427340 1459845889 448618438 -290430796 -728843844 454301053
## [607] 2105297095 501037432 -1051090099 -1035871593 -482597473 -1668955859
## [613] -532641893 -1205078129 192342457 2051066610 233291461 -167377359
## [619] 1856871066 -10101400 1543293495 -481681182 1817063779 -1414919382
## [625] -1128195158 -1721812713The MSEs of LOOCV, 5-FOLD, 10-FOLD are 18223.67, 18222.13 and 18222.67 respectively. The MSE scores are not very sparsed compared to the former model. However, we generally use 10 fold cross validation since it has the relatively low error and costs less than the LOOCV.
# Q7. Using the training data from question 3, perform ridge regression to pick a “good” model. Explain how the model was chosen
grid <- 10^seq(10, -2, length = 100)
grid## [1] 1.000000e+10 7.564633e+09 5.722368e+09 4.328761e+09 3.274549e+09
## [6] 2.477076e+09 1.873817e+09 1.417474e+09 1.072267e+09 8.111308e+08
## [11] 6.135907e+08 4.641589e+08 3.511192e+08 2.656088e+08 2.009233e+08
## [16] 1.519911e+08 1.149757e+08 8.697490e+07 6.579332e+07 4.977024e+07
## [21] 3.764936e+07 2.848036e+07 2.154435e+07 1.629751e+07 1.232847e+07
## [26] 9.326033e+06 7.054802e+06 5.336699e+06 4.037017e+06 3.053856e+06
## [31] 2.310130e+06 1.747528e+06 1.321941e+06 1.000000e+06 7.564633e+05
## [36] 5.722368e+05 4.328761e+05 3.274549e+05 2.477076e+05 1.873817e+05
## [41] 1.417474e+05 1.072267e+05 8.111308e+04 6.135907e+04 4.641589e+04
## [46] 3.511192e+04 2.656088e+04 2.009233e+04 1.519911e+04 1.149757e+04
## [51] 8.697490e+03 6.579332e+03 4.977024e+03 3.764936e+03 2.848036e+03
## [56] 2.154435e+03 1.629751e+03 1.232847e+03 9.326033e+02 7.054802e+02
## [61] 5.336699e+02 4.037017e+02 3.053856e+02 2.310130e+02 1.747528e+02
## [66] 1.321941e+02 1.000000e+02 7.564633e+01 5.722368e+01 4.328761e+01
## [71] 3.274549e+01 2.477076e+01 1.873817e+01 1.417474e+01 1.072267e+01
## [76] 8.111308e+00 6.135907e+00 4.641589e+00 3.511192e+00 2.656088e+00
## [81] 2.009233e+00 1.519911e+00 1.149757e+00 8.697490e-01 6.579332e-01
## [86] 4.977024e-01 3.764936e-01 2.848036e-01 2.154435e-01 1.629751e-01
## [91] 1.232847e-01 9.326033e-02 7.054802e-02 5.336699e-02 4.037017e-02
## [96] 3.053856e-02 2.310130e-02 1.747528e-02 1.321941e-02 1.000000e-02y <- dbike3$cnt
X <- model.matrix(cnt ~ ., dbike3)[, -1] # Get rid of the intercept
set.seed(49204366)
train <- sample(1:nrow(X), nrow(X)/2)
X.train <- X[train,]
y.train <- y[train]
X.test <- X[-train,]
y.test <- y[-train]
dbike3.train <- dbike3[train,]
dbike3.test <- dbike3[-train,]# alpha = 0 mean Ridge Regression (1 for LASSO)
ridge.mod <- glmnet(X.train, y.train, alpha = 0,
lambda = grid, thresh = 1e-12)
summary(ridge.mod)## Length Class Mode
## a0 100 -none- numeric
## beta 3700 dgCMatrix S4
## df 100 -none- numeric
## dim 2 -none- numeric
## lambda 100 -none- numeric
## dev.ratio 100 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 6 -none- call
## nobs 1 -none- numericridge.pred <- matrix(0, nrow = length(y.test), ncol = 100)
testerr <- matrix(0, nrow = 100, ncol = 1)for (j in 1:100) {
ridge.pred[,j] <- predict(ridge.mod, s = grid[j],
newx = X.test)
testerr[j] <- mean((ridge.pred[,j] - y.test)^2)
}
plot(testerr, xlab = "Model No.",
ylab = "Test Mean Square Error")
which.min(testerr)## [1] 100set.seed(49204366)
cv.out <- cv.glmnet(X.train, y.train, alpha = 0)
plot(cv.out)
names(cv.out)## [1] "lambda" "cvm" "cvsd" "cvup" "cvlo"
## [6] "nzero" "call" "name" "glmnet.fit" "lambda.min"
## [11] "lambda.1se"bestlam = cv.out$lambda.min
bestlam## [1] 9.126328log(bestlam)## [1] 2.211163# Use the best value of lambda to estimate the test MSE on the validation data
ridge.pred <- predict(ridge.mod, s=bestlam, newx = X.test)
mean((ridge.pred-y.test)^2)## [1] 17059.18# It turns out the best lambda is a lot smaller than the 1232.847 we had computed above.
# Use the best lambda to compute its ridge regression on all the data
ridge.mod.best <- glmnet(X, y, alpha = 0, lambda = bestlam)
names(ridge.mod.best)## [1] "a0" "beta" "df" "dim" "lambda" "dev.ratio"
## [7] "nulldev" "npasses" "jerr" "offset" "call" "nobs"coef(ridge.mod.best)## 38 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 8.15210797
## yr 77.68944227
## holiday -26.13567060
## workday 3.56753765
## temp 90.31993988
## atemp 106.62531728
## hum -65.30995548
## windspeed 83.87283537
## daytime 141.78333787
## season.1 -28.49016862
## season.2 0.01444333
## season.3 -30.36349309
## mnth.1 -1.73449364
## mnth.2 -0.86772164
## mnth.3 5.31654397
## mnth.4 -10.22778272
## mnth.5 -1.89921605
## mnth.6 -31.22331035
## mnth.7 -53.92793058
## mnth.8 -23.01750790
## mnth.9 16.67514174
## mnth.10 11.50492829
## mnth.11 -1.61717875
## wkday.0 -7.27655768
## wkday.1 -1.94308949
## wkday.2 -1.49646692
## wkday.3 0.56908902
## wkday.4 -1.15483490
## wkday.5 4.15073151
## wkday.6 7.07037616
## weathersit.1 9.20767388
## weathersit.2 -0.18853426
## weathersit.3 -27.64045558
## temp2 57.33500040
## atemp2 47.93923147
## hum2 -75.44972450
## windspeed2 -195.25316549
## temp_dif_s 23.97463537# Q8. Repeat question 7 using LASSO.
lasso.mod <- glmnet(X.train, y.train , alpha = 1,
lambda = grid)
plot(lasso.mod, label = TRUE)## Warning in regularize.values(x, y, ties, missing(ties)): collapsing to unique
## 'x' values
plot(lasso.mod, xvar='lambda', label = TRUE)
lasso.pred <- matrix(0,nrow = length(y.test), ncol = 100)
validerr1 <- matrix(0, nrow = 100, ncol = 1)
for (j in 1:100) {
lasso.pred[,j] <- predict(lasso.mod, s = grid[j],
newx = X.test)
validerr1[j] <- mean((lasso.pred[,j] - y.test)^2)
}
plot(validerr1, xlab = "Model Number",
ylab = "Validation Error")
which.min(validerr1)## [1] 100lasso.mod$lambda[100]## [1] 0.01validerr1[100]## [1] 16992.24set.seed(49204366)
cv1.out <- cv.glmnet(X.train, y.train, alpha = 1)
plot(cv1.out)
names(cv1.out)## [1] "lambda" "cvm" "cvsd" "cvup" "cvlo"
## [6] "nzero" "call" "name" "glmnet.fit" "lambda.min"
## [11] "lambda.1se"bestlam = cv1.out$lambda.min
bestlam## [1] 0.2599211log(bestlam)## [1] -1.347377lasso.pred <- predict(lasso.mod, s=bestlam, newx = X.test)
mean((lasso.pred-y.test)^2)## [1] 17020.57lasso.mod.best <- glmnet(X, y, alpha = 1, lambda = bestlam)
names(lasso.mod.best)## [1] "a0" "beta" "df" "dim" "lambda" "dev.ratio"
## [7] "nulldev" "npasses" "jerr" "offset" "call" "nobs"coef(lasso.mod.best)## 38 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) -36.1109960
## yr 80.5405612
## holiday -29.4174099
## workday .
## temp 136.5869660
## atemp 141.5007277
## hum -0.6877709
## windspeed 110.9829246
## daytime 149.0015895
## season.1 -26.3657045
## season.2 .
## season.3 -30.0594303
## mnth.1 0.1569174
## mnth.2 .
## mnth.3 4.2921394
## mnth.4 -12.0434377
## mnth.5 -4.7375278
## mnth.6 -35.4762345
## mnth.7 -60.6265431
## mnth.8 -29.8075336
## mnth.9 8.4497962
## mnth.10 2.2608123
## mnth.11 -6.7068220
## wkday.0 -9.3489275
## wkday.1 -0.2904927
## wkday.2 .
## wkday.3 1.0954148
## wkday.4 .
## wkday.5 4.9240135
## wkday.6 4.8330053
## weathersit.1 10.5601782
## weathersit.2 .
## weathersit.3 -26.1524538
## temp2 15.8857731
## atemp2 .
## hum2 -126.0163664
## windspeed2 -257.8701579
## temp_dif_s 29.5328837# Q9. Based on models from questions 3-8, compute and display the test MSEs for each of the models estimated. What is learned from this?
reg_all_pred <- predict(reg_all, test_set)## Warning in predict.lm(reg_all, test_set): prediction from a rank-deficient fit
## may be misleadingRSS_Test <- sum((test_set$cnt - reg_all_pred)^2)
MSE_Test <- RSS_Test/8621
MSE_Test## [1] 15928.44# Q4
reg_bic_pred <- predict(reg_bic, test_set)## Warning in predict.lm(reg_bic, test_set): prediction from a rank-deficient fit
## may be misleadingRSS_Test <- sum((test_set$cnt - reg_bic_pred)^2)
MSE_Test <- RSS_Test/8621
MSE_Test## [1] 16021.78reg_bic_fwd_pred <- predict(reg_bic_fwd, test_set)
RSS_Test <- sum((test_set$cnt - reg_bic_fwd_pred)^2)
MSE_Test <- RSS_Test/8621
MSE_Test## [1] 17203.56reg_bic_bwd_pred <- predict(reg_bic_bwd, test_set)
RSS_Test <- sum((test_set$cnt - reg_bic_bwd_pred)^2)
MSE_Test <- RSS_Test/8621
MSE_Test## [1] 17156.15# Q6 Forward min_bic
MSE.LOOCV.1## [1] 17055.53# 5-Fold
MSE.5.1## [1] 17050.47 17046.54# 10-Fold
MSE.10.1## [1] 17049.78 17047.95# Q6 Backward min_bic
cv.err.2## $call
## cv.glm(data = dbike3, glmfit = glm.2)
##
## $K
## [1] 17379
##
## $delta
## [1] 18223.67 18223.67
##
## $seed
## [1] 10403 188 1077329476 610674084 -2113862655 -1024038508
## [7] -1955727596 306522696 -1841834735 -1461462276 -1198267463 -115386373
## [13] 944868980 -2008551803 311709003 -1450835770 -2055625295 -1793800812
## [19] 1192707820 -389273099 473851391 1022759321 1071796079 -247297840
## [25] 77783733 1654790731 -2047622228 224977577 113692845 -1161120840
## [31] 1444924786 -1161348212 -359223090 -101984981 -806279225 1613689450
## [37] 1828680783 -53684575 -1922158355 -1797996641 -1492574976 -472849192
## [43] -552503328 1004151751 1543327191 -185289332 1494697437 -1002857496
## [49] -2141259278 -2093532514 -1094395035 743138088 2054523443 -1193601487
## [55] -353552601 -61256919 -357698898 2032538668 1785777687 -1493969092
## [61] -564976998 -2124525243 -2089643739 1252501744 1062149369 -1407779565
## [67] 1219441698 -1282659892 742098048 1241956367 -835487523 -727688927
## [73] -713630967 505244766 252159788 -1621732464 2031904011 1795896924
## [79] -1802386131 -786257445 -793241775 -407528505 -1354983189 -1520360683
## [85] 523238374 -1506690392 -528305 1829270956 1309754840 1051021841
## [91] -693961798 -1497386487 -1464337852 1702126483 1102851769 -685127170
## [97] 180504283 1728093188 -1772164452 532282142 -246878231 -1925074985
## [103] -539036012 1171211471 -1416561732 1825614530 -1076374333 847045038
## [109] -1555559405 -1364783250 -1316649987 1907448237 -285365992 722597175
## [115] -689669668 1960174028 -962720654 -970603356 1623672471 -618342272
## [121] 1009451060 1434330415 693811645 241399535 -826072159 26525908
## [127] 1584584425 -57028893 953216754 884437345 -1343249146 -332045213
## [133] -798065557 79798763 -1696041964 1178969177 -33312177 1267647748
## [139] 1865279697 -294923649 -541590171 1934423689 -1680161494 -271836478
## [145] 132673877 1083797415 1307340340 -253886819 584297700 1551036111
## [151] 1631481736 1283500852 -695486083 249040282 1200597677 -1695789750
## [157] -652686274 635868204 1750772781 -1461436613 -1184092410 -1317102212
## [163] 976478847 -1484276327 1953562768 -636509520 124882705 -1812874828
## [169] 1195249611 -1776501508 1615507158 888681652 1565181919 -1087496730
## [175] 263439982 -1168782894 114425508 -656071998 -727884638 1032070957
## [181] -1837988082 1081714701 406175449 -837512301 -395894993 -1031544095
## [187] -837791153 2046925696 1846795206 1587424393 -199707355 -998553418
## [193] 348709629 1532047799 -505887791 -461094850 1844851593 -1306423594
## [199] 1957177101 -1120877343 1512728990 -1832117585 1605776816 422290045
## [205] 236538340 986950046 1026523755 -1463828659 -1383604815 -1731624672
## [211] -1903337796 553203205 880914158 829916917 1862249219 -2145648553
## [217] 150524446 1165553616 503754771 1407947558 810185640 -1533277299
## [223] 1569438033 589187277 449159987 1285529065 -1644136525 -22749839
## [229] -379276868 -1923280676 -1513838947 -87511175 1087982093 -587675762
## [235] -218907112 -2100590177 77308977 1005701812 -2012742350 -1910761705
## [241] 1087088686 -607151256 -520832550 1930600201 -1940168919 -2097386337
## [247] -1732714241 -55315537 1933911696 -351228844 -862302407 -919405249
## [253] 1886369778 1230679334 -1347289563 1784183116 744412332 -282988538
## [259] 19181432 -1861933091 -150334637 -1375906825 516447398 2012951433
## [265] 1584367441 -230223540 -1614009579 1568520362 610542931 1545438442
## [271] -1660701935 1121424430 -507490400 -1008347445 -1784219826 -736962404
## [277] -2020852607 1181397596 794262469 -19432376 -1028391299 1854269808
## [283] -738588265 -1510126324 -918242457 350486943 1645344210 -536034932
## [289] 451743868 -1236066661 -1301025880 -1975990371 -1790138667 -554492973
## [295] -1079928863 1379832325 142771289 617706074 -1154313923 1803438263
## [301] -542980363 1466052474 1201536115 447149659 -927831453 -1041263763
## [307] -1116687005 1467599628 -1561278891 1138269197 1229779673 1369028317
## [313] -2040327621 524957556 -1823560736 -1832313911 -493810876 -387125669
## [319] 831304148 -1111976835 413639659 -595778928 545180157 967696075
## [325] -523986749 1174579903 702345035 1207479528 -800774280 -421403974
## [331] 496509986 1044283336 -939337026 -445913576 1204324783 1074608542
## [337] -1645033085 -1322180686 1734292968 -636006016 860423944 -256262393
## [343] -155914319 -449596615 -1823002420 -1745263304 1810257172 2508166
## [349] 538826985 1253901939 -1961331346 1762978090 -1048509624 870862166
## [355] -106548744 -1665635851 5467222 1518271243 272757923 826313671
## [361] -1754421470 374696691 393732699 416305362 -388363438 -1596693236
## [367] -1597398980 -473825832 608427517 61374161 618186026 871872522
## [373] -101513767 -885080934 1816542912 641935263 -19427057 -200742833
## [379] 1258668740 -890154910 82301451 1379047147 478369698 1436830792
## [385] 388945269 728281610 235892330 -524657515 22493484 -317070877
## [391] 1838610383 617752623 1475936135 802933242 -1878262318 952931513
## [397] -1918911172 1907248592 1676441680 1687275054 -1844049510 1834045982
## [403] 139129759 -1636481062 269650553 236605079 -1464145048 770247881
## [409] 1969513634 1105604101 1518169394 -1416330003 -1806798995 1037849203
## [415] 299618340 -1007246405 -2035954588 471430470 1049610937 -348827243
## [421] 1814369172 1861559080 -5447391 1559267135 359316882 1407897933
## [427] -2010387997 1004458851 -1280525372 -1552488842 -1001041596 1838290315
## [433] -1412559015 -520596204 1307604480 1407877553 1874722326 126248170
## [439] 1495653003 -566302557 957734259 -1807664167 1506484820 -697861000
## [445] -262879044 -1892737954 1775333473 -655877485 470297310 693135422
## [451] 132266268 -909180779 1814274732 1961626325 741638901 -1419756139
## [457] -2586224 -1039973510 1263614293 -841232599 1528835681 -1995135791
## [463] -719103021 1481443304 -2078173262 1574854361 -598537822 1945217279
## [469] 1510581524 -792549424 1857911565 782741015 2000176956 -135303848
## [475] -1727552866 -1969342606 -871681520 -2055849053 -343838282 2076405853
## [481] 1890508505 942194319 -595817375 1699785984 1484701973 475019788
## [487] 526776263 -364276939 1551116960 -737847484 513456533 -1916078687
## [493] -754757906 -1800430990 -1907949898 -489555301 -1450202349 -1000518994
## [499] -1307237042 510499872 -1581109461 1527577277 -197306381 -1679069329
## [505] -734659816 1454026167 -1871049637 1495827866 -809100101 399052851
## [511] -1925719258 -476079451 -1207685906 1404933292 -2084485196 1122126510
## [517] 1136791615 -609681211 -564790100 -1638662656 1354020923 -1482059730
## [523] -80699129 1246343519 -1516994903 -986337274 -1337034472 -1230924754
## [529] -329193940 701428558 1863246696 1762599847 380568005 -1505325506
## [535] 37004038 -290846888 -1417755900 968276642 -398483073 -306735261
## [541] -1092222479 -417946810 2016211048 -62573466 82248431 -1103715450
## [547] -1940875928 525036004 -375483787 650172114 2113224256 1636711296
## [553] -2045176557 1349520503 529132299 1721451210 -1289167378 946861368
## [559] 1226038796 -612270371 -1485981270 1574160254 -1908403295 79300749
## [565] 663366490 -173981821 -853488270 424744569 -825312902 -2130361097
## [571] -491192822 281032058 991591621 1216311504 1386545684 858519762
## [577] -775142413 -2128726756 911221560 -983868978 -338696006 1941555682
## [583] -873865379 -1010507598 -1770952451 995904649 -1584105203 1750285995
## [589] 807232470 -1774831438 -1561211460 987537179 1879025813 -1665673718
## [595] -1394941745 -1785621595 -712911641 -1101320161 1045268158 1022178336
## [601] -758210068 -2046339890 289612721 1004116597 -1586549258 -353064300
## [607] -800472687 -466628922 744810202 -705808878 -637213633 1043921561
## [613] -435773576 1765287483 -152814525 822066372 -1188315444 -315106652
## [619] 762924632 827994557 1656735557 -606726250 153643118 1841629729
## [625] -1845649713 1140270962# 5-Fold
cv.err.2.5## $call
## cv.glm(data = dbike3, glmfit = glm.2, K = 5)
##
## $K
## [1] 5
##
## $delta
## [1] 18224.69 18221.25
##
## $seed
## [1] 10403 62 1774323545 -750303354 -896698764 1563263850
## [7] 1243797079 -1041264708 -853462195 1125340654 -1381404098 -322088854
## [13] 1416522295 -1718858230 -1857162506 -1974701556 -675392767 17278200
## [19] -329656659 401699641 -1346389945 285542777 -1233605153 955535774
## [25] -142111092 -411758768 -1320384991 -426191011 942423726 2146912952
## [31] 794552699 1585164545 1397201962 -1756688484 -1730317197 -1340933670
## [37] -1044611390 537892654 668384330 411498208 1920083463 -1933430240
## [43] 1704802634 1856063144 294358645 -540965148 1010153990 -46640816
## [49] -319645509 -1722603818 1160049636 -1986059733 -1825034116 1864752803
## [55] 1023726069 12865 123984582 -838830266 -772139563 -1414205266
## [61] 204510559 -1820181988 -1251045074 356587195 -2098705526 -1240748841
## [67] 470810256 -1402465581 1359116137 -1284971855 -1885815136 -687869157
## [73] -994367566 148492471 33049600 14943690 210777868 -839221791
## [79] -1917181791 385591360 1123364569 186022385 1859738707 75937078
## [85] 601731673 -1965268259 1901530262 887657099 1868646177 553100237
## [91] 310979486 -1241965754 1415254543 803124159 -429010540 1598535078
## [97] 862843872 2083652981 -1612036099 1647051717 816228134 2059661481
## [103] -1938681351 -523350676 -2016494513 477396105 -49462445 1895160989
## [109] 1508889177 -2086137003 -634512090 1297988670 1750554735 -872558053
## [115] -1564847355 198918427 1920901185 -1111888172 -1355419302 -1265426817
## [121] 1174578990 -2059781965 1623425039 558788717 -450462263 187379680
## [127] 195893644 1957975407 1719533924 -1497507044 1748817795 -654076705
## [133] 1053798547 -2042459687 390637361 1170567292 1057863296 681274528
## [139] -616402735 -1076216315 173417282 1904261663 -382885192 555824983
## [145] 950222281 1084047833 -2003033231 -72650762 -131880524 1431531748
## [151] -1987713609 458901430 630129086 -1803465489 1781928002 615873208
## [157] 1206257047 866821852 -1339060595 923753756 -2139608107 -1149479864
## [163] -2144289771 629718118 -1707888551 -1042368937 805210662 -28662458
## [169] -1964799902 -1362005118 1830431837 -614932893 456225745 6097700
## [175] -905688819 149300673 1238237996 422958334 -1843905671 1471991055
## [181] -1008050044 -1938726446 505852650 2128321435 -379670267 -813466869
## [187] -181062584 313797234 87368562 1599011419 -1755458476 -184210159
## [193] 1187208365 -587567713 -883641305 -2140143876 2144181045 570668747
## [199] 882129221 799982305 -362880394 -722762037 -1883328611 -346165626
## [205] -1459215860 -109218154 -1170001309 554711280 -662454866 1006762874
## [211] -261893831 1482523858 -936420556 -417013368 -1540613726 1236166057
## [217] -1519625851 1761823720 -1643268797 -1006334548 -599832996 996296097
## [223] -1495470856 -1704882184 -511139591 -1555780278 617559694 -464922780
## [229] 4678529 -656492814 -1013686276 -401703827 -1280763744 -1483792073
## [235] -83243639 495122890 1651981590 -2115499055 1160359187 1781439335
## [241] -945363746 385499259 1844713482 2091679943 -2068647985 -759502159
## [247] -1822558856 -1963604081 -1117767792 1691327389 -35159687 -732289092
## [253] 1445455117 973026462 -1271623798 -1356096032 -1112220946 697903833
## [259] -1590643303 389969898 1800258414 -403567849 93347879 709690675
## [265] -2099084818 -2010752389 1621236489 2034068021 1948267773 -1153106725
## [271] -1408179230 -695508241 374224222 848580906 -1838776756 -2042708317
## [277] 706595589 -198707768 1496874137 857234891 1444033676 1321549146
## [283] 1424659185 -2053921105 1320506057 -1757260970 -1529807021 -337405554
## [289] 92095228 -1447586911 80924242 -937869006 1993268386 540815461
## [295] 469076523 -78922235 -1067317875 -325344013 -2007550547 -645631150
## [301] 993639598 -581890568 1128685273 -1714831634 -294298398 338078166
## [307] -1771106433 173094809 1311212193 2256114 240221274 1922604501
## [313] -20468703 -1192925675 -501094336 -1667231142 -553913449 1473359147
## [319] -2112095941 -1783486239 1654440797 158027179 -1208461688 -444487578
## [325] 312263200 -1635610143 2097406488 -1934482883 -1114862411 -1989036662
## [331] -447158254 520158146 -1171139463 252234254 1307130124 -1998912441
## [337] 365358586 2065278943 1558661786 -1813237757 1560154338 2103570796
## [343] -86622649 -383614295 2067439054 1120044033 445691959 755803185
## [349] 557875276 -1648515470 -1097057438 667935566 1417231168 -469416485
## [355] 1359126884 1904226326 -28168221 1981904690 -1129718358 -1989030763
## [361] 79652751 -1026068936 557716860 449562686 -188574074 -291182665
## [367] 1750909445 -150761710 -253677707 -240170482 1461988656 -674325004
## [373] -1969032971 -960787490 -215295102 -476194710 -1073160869 -21592413
## [379] -1374613247 1259269157 -264506774 -1630300403 687342410 -976510228
## [385] 1878344904 2006027969 -1634643292 -1598496091 849297350 1321614421
## [391] 1067558903 69771022 -1662669761 -2041540228 -1144821118 663301797
## [397] 168877230 -412208232 -2108054613 -1694706814 -1657913424 -894080791
## [403] 685837793 227053865 317379919 -1284378664 -1751973627 659007177
## [409] 1703565095 -888242520 1970136525 157906667 -1362462591 470933606
## [415] -1453685465 1791332284 1214795695 -75889292 1874486637 138533901
## [421] -851522036 -2091437455 -2000260632 -42107814 622737382 942599119
## [427] 1979458493 -115388660 -1739160479 1492389607 885102339 1155508554
## [433] 1599771611 86996643 -941000362 -1833355975 248217036 147725622
## [439] -2066561174 -1878566028 117024617 -661053191 -1835896731 -1238358142
## [445] 1605400424 -2100168767 -1541199571 -1055162652 41488157 1642126809
## [451] -428404327 2031158666 553653345 -299338511 2043637133 -1225224630
## [457] -992594931 728820224 -22164494 2130830804 150712438 277284330
## [463] 374723104 149323076 -1456076762 -2069939835 -474470573 -2117964728
## [469] -1137752040 1927927062 -1689848230 683207260 -1100954069 -1500288527
## [475] 2138813103 1873263798 1116787528 -1621963068 -1304305547 1890749748
## [481] -1054847243 1058831581 397772015 2117911974 -667157784 126679275
## [487] 710601042 985036664 408751837 1100054339 975019520 -1262174209
## [493] -23527368 -884791587 -389942628 1227871662 803961652 93579874
## [499] -372575044 -1584469467 1319037438 -1814554823 1031463800 -673305073
## [505] -463241897 1885246726 1309452887 14597324 349175101 -1347719210
## [511] -1890289737 -71313089 -900833298 -841185236 1864074446 1502587030
## [517] 341796597 -208071136 1498609145 -1119342411 -1147788544 1779882270
## [523] -1362083280 -715376019 -1955810653 1622008812 384984595 1390230552
## [529] 1953351585 1080295342 -1133800139 511484400 19753003 -1225491814
## [535] -1380255389 1809005801 1372579834 676971458 774291711 310393126
## [541] 584366003 1837116843 -1283077195 1641776732 295093188 -1879560568
## [547] 1496018178 1923098879 -92233970 1047237842 1819480825 228580593
## [553] -292934816 1398398297 -592428359 406554562 54982065 1292395712
## [559] -1397941944 1915552313 -1020769838 1465730333 1908558847 -1576567297
## [565] 1126167097 1518225996 437845840 1353389618 1250529677 -222421744
## [571] 969003103 1211503658 1215502539 -1358754508 515675793 1221329051
## [577] -1599893953 -1538015525 1328330707 146306567 -1707204370 -405827209
## [583] -1677041303 986572336 -168159186 820203557 -1676732262 -1806001044
## [589] 244954426 -1606928739 -1556523865 -948938446 -1093111947 589166807
## [595] 1599477038 401629826 450528781 1873468251 -1299825221 1347350579
## [601] -1350344890 367855182 -1324643556 -1104375098 -280631100 323482185
## [607] -1627072821 -1374306106 -810519260 1097019371 1033634217 -691506589
## [613] 2054521617 1033327136 1798438678 1692948377 984720857 1573863114
## [619] -143192010 803969613 -1413146512 -310796884 -1829979155 -1486854289
## [625] -1754589973 800067800# 10-Fold
cv.err.2.10## $call
## cv.glm(data = dbike3, glmfit = glm.2, K = 10)
##
## $K
## [1] 10
##
## $delta
## [1] 18225.40 18223.74
##
## $seed
## [1] 10403 222 -1638873570 -387408225 -709098861 -1219530179
## [7] 259825355 521526429 70163002 402937516 1618270355 1354629715
## [13] 557589680 1389850336 1754597544 -1809768622 -1104307794 -2120431162
## [19] 29998290 -1725884968 -606656570 -2068841915 1581139865 2057778581
## [25] -335451167 1411481939 -1134113652 672071217 1848935272 1876858046
## [31] -1547830443 651367705 -124040078 -1846613522 2142925036 1163333007
## [37] -2028884711 1624004312 454847663 1107609472 -470508770 552258998
## [43] 785424325 1334169435 1722029194 1235696736 1815727454 -2080266580
## [49] -262459824 52657963 1906439057 502832506 141724125 -2103501919
## [55] -1727467829 289128610 1295602753 1830987823 149614702 1060849728
## [61] -995347429 -352949213 290564075 -1533968597 -547442165 -1250972667
## [67] -797775276 587796247 -1570247213 1409754733 190275911 1306694291
## [73] 1720177025 59718487 -561925150 -490970166 1133411127 1850807595
## [79] 716220507 1365514365 -1610438923 1520581174 663125742 1106521041
## [85] -370875841 -2027980676 801378065 -266216332 -1154983787 -1568260570
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## [109] 884112226 2057155786 -75571125 1314763227 722199079 -899946506
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## [511] 1569368718 2028473409 240354172 -1558742033 89140592 -2119051284
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## [523] 1119888881 -1775289041 -1111093435 1040954802 389595527 1348186793
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## [535] 2090468876 -1845802406 283443304 67205139 -1381448188 -259853323
## [541] -1509586005 -1247813524 -2043622336 -908699702 278438349 -1854011400
## [547] -1761860164 -448153228 1847442788 -1212913413 -446997095 -1568198983
## [553] 1065256927 1498616609 -1198188609 -193981870 1027821235 1285546296
## [559] -47758324 -1973867260 -176235061 -996096376 676090465 396467015
## [565] 359087955 912210586 277847493 -914932164 391742581 -599871160
## [571] 471117082 2104920581 631247105 -283884095 -676808219 1510226542
## [577] 1352877463 2038269565 -1028999954 932740793 1391596077 365957622
## [583] 1755518523 -1269047241 904854264 681531331 1668064332 -1678806975
## [589] -361441920 662010161 1632343597 -1185301534 -455948520 -1685533693
## [595] 28840357 -341321650 -707305480 1956380754 -230367488 633827207
## [601] 371427340 1459845889 448618438 -290430796 -728843844 454301053
## [607] 2105297095 501037432 -1051090099 -1035871593 -482597473 -1668955859
## [613] -532641893 -1205078129 192342457 2051066610 233291461 -167377359
## [619] 1856871066 -10101400 1543293495 -481681182 1817063779 -1414919382
## [625] -1128195158 -1721812713The all-in model is the best among all the others according to the MSE, but the model created in Q4 with min_bic is fairly good.
# Q10. Summarize three lessons learned for bike share company management from working with this data in this homework assignment.
## We trained model on different set of features by subsetting and different cross validation methods. The 10 fold cv is the most common used one ant it is more efficient than LOO. More features do not mean higher accuracy and lower MSE.