#install.packages("ISLR")
library(ISLR)
help("Carseats")
head(Carseats)
## Sales CompPrice Income Advertising Population Price ShelveLoc Age Education
## 1 9.50 138 73 11 276 120 Bad 42 17
## 2 11.22 111 48 16 260 83 Good 65 10
## 3 10.06 113 35 10 269 80 Medium 59 12
## 4 7.40 117 100 4 466 97 Medium 55 14
## 5 4.15 141 64 3 340 128 Bad 38 13
## 6 10.81 124 113 13 501 72 Bad 78 16
## Urban US
## 1 Yes Yes
## 2 Yes Yes
## 3 Yes Yes
## 4 Yes Yes
## 5 Yes No
## 6 No Yes
summary(Carseats)
## Sales CompPrice Income Advertising
## Min. : 0.000 Min. : 77 Min. : 21.00 Min. : 0.000
## 1st Qu.: 5.390 1st Qu.:115 1st Qu.: 42.75 1st Qu.: 0.000
## Median : 7.490 Median :125 Median : 69.00 Median : 5.000
## Mean : 7.496 Mean :125 Mean : 68.66 Mean : 6.635
## 3rd Qu.: 9.320 3rd Qu.:135 3rd Qu.: 91.00 3rd Qu.:12.000
## Max. :16.270 Max. :175 Max. :120.00 Max. :29.000
## Population Price ShelveLoc Age Education
## Min. : 10.0 Min. : 24.0 Bad : 96 Min. :25.00 Min. :10.0
## 1st Qu.:139.0 1st Qu.:100.0 Good : 85 1st Qu.:39.75 1st Qu.:12.0
## Median :272.0 Median :117.0 Medium:219 Median :54.50 Median :14.0
## Mean :264.8 Mean :115.8 Mean :53.32 Mean :13.9
## 3rd Qu.:398.5 3rd Qu.:131.0 3rd Qu.:66.00 3rd Qu.:16.0
## Max. :509.0 Max. :191.0 Max. :80.00 Max. :18.0
## Urban US
## No :118 No :142
## Yes:282 Yes:258
##
##
##
##
#library(ggplot2)
library(alr4)
## Loading required package: car
## Loading required package: carData
## Loading required package: effects
## lattice theme set by effectsTheme()
## See ?effectsTheme for details.
#p<-ggplot(Carseats,aes(x=Price, y=Sales)) + geom_point()
plot(Carseats$Sales~Carseats$Price)
m1<-lm(Sales~Price,data=Carseats)
summary(m1)
##
## Call:
## lm(formula = Sales ~ Price, data = Carseats)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.5224 -1.8442 -0.1459 1.6503 7.5108
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.641915 0.632812 21.558 <2e-16 ***
## Price -0.053073 0.005354 -9.912 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.532 on 398 degrees of freedom
## Multiple R-squared: 0.198, Adjusted R-squared: 0.196
## F-statistic: 98.25 on 1 and 398 DF, p-value: < 2.2e-16
#The linear regression model shows me that as the sales increase on average, the price will very slightly decrease. I see this in the slope of price as it is negative. As sales increase, the price will decrease by $0.053.
#Problem 2
library(alr4)
head(oldfaith)
## Duration Interval
## 1 216 79
## 2 108 54
## 3 200 74
## 4 137 62
## 5 272 85
## 6 173 55
dim(oldfaith)
## [1] 270 2
summary(oldfaith)
## Duration Interval
## Min. : 96.0 Min. :43.00
## 1st Qu.:130.0 1st Qu.:58.00
## Median :240.0 Median :76.00
## Mean :209.9 Mean :71.11
## 3rd Qu.:267.8 3rd Qu.:82.00
## Max. :306.0 Max. :96.00
plot(Interval~Duration,data=oldfaith)
o1<-lm(Interval~Duration,data=oldfaith)
summary(o1)
##
## Call:
## lm(formula = Interval ~ Duration, data = oldfaith)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.3337 -4.5250 0.0612 3.7683 16.9722
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.987808 1.181217 28.77 <2e-16 ***
## Duration 0.176863 0.005352 33.05 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.004 on 268 degrees of freedom
## Multiple R-squared: 0.8029, Adjusted R-squared: 0.8022
## F-statistic: 1092 on 1 and 268 DF, p-value: < 2.2e-16
#The linear regression model shows me that as the intervals increase, the duration of eruptions also increases. The slope of the duration being positive shows me this. The slope for duration is statistically significant at 0.01 significance level (2x10^-6<0.01), so there is some relationship between duration and interval. The multiple R-squared shows how much variance the dependent variable can have, which in this model is 0.8029. This tells me that there can be some significant variance in the dependent variable. The adjusted R-squared checks for bias in the independent variable and corrects it. The adjusted R-squared is 0.8022, which tells me there can be some significant bias in the independent variable.