Section 1: Dataset Description
The “Bike-sharing” dataset was found in the UCI Machine Learning Repository : http://archive.ics.uci.edu/ml/datasets.html. It is a collection of databases, domain theories and data generators which are used by the machine learning community for empirical analysis. Bike sharing systems are a new way of traditional bike rentals. The following link : https://archive.ics.uci.edu/ml/datasets/Bike+Sharing+Dataset was used to obtain the dataset. We can find two different datasets here, one containing the daily count of rental bikes between years 2011 and 2012 and one with addition of hourly count for the same years, in Capital bikeshare system.
For this project, I am only taking into account, the daily count and NOT the hourly count of bike rentals.
bike.sharing <- read.delim("C:/Users/Rushil/Desktop/bike.sharing.txt") ### Importing the data set
nrow(bike.sharing) ### number of rows in the dataset
## [1] 731
ncol(bike.sharing) ### number of columns in the dataset
## [1] 16
names(bike.sharing) ### names of the columns in the dataset
## [1] "instant" "dteday" "season" "yr" "mnth"
## [6] "holiday" "weekday" "workingday" "weathersit" "temp"
## [11] "atemp" "hum" "windspeed" "casual" "registered"
## [16] "cnt"
dim(bike.sharing) ### dimensions of the dataset.
## [1] 731 16
There were 731 rows and 16 columns originally in the dataset. A number of new columns were created for this project which will be described shortly.
The names of the original columns and their descriptions are as follows:
1) instant: refers to the record index.
2) dteday: refers to the date.
3) season: season wherein (1:winter,2:spring, 3:summer, 4:fall)
4) yr: year(0:2011, 1:2012).
5) mnth: months, 1 to 12.
6) holiday: whether the day is a holiday (0) or not (1).
7) weekday: refers to the day of the week (0 to 6).
8) workingday: if the day is neither weekend nor a holiday then it is represented as 1, otherwise 0.
9) weathersit: refers to the weather situation, wherein 1: Clear, Few clouds, Partly cloudy. 2: Mist + Cloudy, Mist + Broken clouds, Mist + Few clouds, Mist. 3: Light Snow, Light Rain + Thunderstorm + Scattered clouds, Light Rain + Scattered clouds. 4: Heavy Rain + Ice Pallets + Thunderstorm + Mist, Snow + Fog
10) temp: refers to normalized temperature in Celsius. The values are derived via (t-t_min)/(t_max-t_min), t_min=-8, t_max=+39 (only in hourly scale).
11) atemp: refers to normalized feeling temperature in Celsius. The values are derived via (t-t_min)/(t_max-t_min), t_min=-16, t_max=+50 (only in hourly scale).
12) hum: refers to normalized humidity. The values are divided to 100 (max).
13) windspeed: refers to normalized wind speed. The values are divided to 67 (max).
14) casual: refers to number of casual users.
15) registered: refers to number of registered users.
16) cnt: refers to total count of rental bikes including both casual and registered users.
Newly added columns:
1) converted.temp: refers to the converted temperatures from normalised to raw temperatures using the given formula (t-t_min)/(t_max-t_min), t_min=-8, t_max=+39.
2) converted.atemp: refers to the converted temperatures from normalised feeling temperatures to raw feeling temperatures using the given formula (t-t_min)/(t_max-t_min), t_min=-16, t_max=+50.
3) mean.converted.temp.atemp: refers to the total temperature, calculated by determining the means of converted.temp(converted real temperature) and converted.atemp(converted feeling of the temperature).
Note:
The new columns were added in the copy (bike.sharingcopy) of the dataset which was created for the project.
Additionally, the season column was recoded from numbers to characters in the bike.sharingcopy dataset.
For the analysis of temperature, feeling of temperature, and season, the newly added or recoded columns were considered.
Section 3: Data Analysis
### Loading required package for analysis
library(yarrr)
### Before starting to answer the questions I am going to check for the nature of the values in the dataset.
### Checking for null values in the dataset
is.null(bike.sharing)
## [1] FALSE
### Checking to see if all the values in the vectors are integers
is.integer(bike.sharing)
## [1] FALSE
### Checking for a general summary and NA values
summary(is.na(bike.sharing))
## instant dteday season yr
## Mode :logical Mode :logical Mode :logical Mode :logical
## FALSE:731 FALSE:731 FALSE:731 FALSE:731
## NA's :0 NA's :0 NA's :0 NA's :0
## mnth holiday weekday workingday
## Mode :logical Mode :logical Mode :logical Mode :logical
## FALSE:731 FALSE:731 FALSE:731 FALSE:731
## NA's :0 NA's :0 NA's :0 NA's :0
## weathersit temp atemp hum
## Mode :logical Mode :logical Mode :logical Mode :logical
## FALSE:731 FALSE:731 FALSE:731 FALSE:731
## NA's :0 NA's :0 NA's :0 NA's :0
## windspeed casual registered cnt
## Mode :logical Mode :logical Mode :logical Mode :logical
## FALSE:731 FALSE:731 FALSE:731 FALSE:731
## NA's :0 NA's :0 NA's :0 NA's :0
There are no null values in the dataset.
All the values in the vectors are integers.
There are no NA values in the dataset.
Question 1: What is the average number of casual and registered bikes rented on a working day?
### Task 9
### Calculating the average number of casual and registered bikes rented on a working day using dplyr.
require(dplyr) ### Loading dplyr for calculation of mean according to working day.
## Loading required package: dplyr
## Warning: package 'dplyr' was built under R version 3.2.3
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
rentals.workingday <- bike.sharing %>% group_by(workingday)%>% summarise(mean.casual = mean(casual),
mean.registered = mean(registered))
rentals.workingday
## Source: local data frame [2 x 3]
##
## workingday mean.casual mean.registered
## (int) (dbl) (dbl)
## 1 0 1371.134 2959.035
## 2 1 606.570 3978.250
For 1 (Neither a weekend nor a holiday):
1)The mean casual rentals were found to be 606.57.
2)The mean registered rentals were found to be 3978.25.
For 0 (Otherwise):
1)The mean casual rentals were found to be 1371.13.
2)The mean registered rentals were found to be 2959.03.
Question 2: What are the total number of bikes rented per month?
bike.sharingcopy <- bike.sharing ### Making a copy of the dataset.
### Loading beanplot and Rcolorbrewer for making the beanplot
library(RColorBrewer)
## Warning: package 'RColorBrewer' was built under R version 3.2.3
require("beanplot")
## Loading required package: beanplot
## Warning: package 'beanplot' was built under R version 3.2.3
bean.cols <- lapply(brewer.pal(6, "Set3"),
function(x) {return(c(x, "black", "black", "black"))})
### Task 8
### Plotting the dependent variable : total count, for each level of categorical independent variable : months (1:12) using beanplot.
beanplot(cnt ~ mnth,
data = bike.sharingcopy,
main = "Relationship between Months and Total Rentals",
xlab = "Months",
ylab = "Total Rentals",
col = bean.cols ,
lwd = 1,
what = c(1, 1, 1, 1), log = ""
)
Question 3: How did the temperatures change in different seasons? Show histograms of seasons where the highest and the lowest mean and median temperatures were recorded.
### Task 1
### First I will recode the values in the season column from numbers to characters using indexing and reassigning.
### 1 = Winter
### 2 = Spring
### 3 = Summer
### 4 = Fall
as.character(bike.sharingcopy$season,stringsAsFactors=FALSE)
## [1] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
## [18] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
## [35] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
## [52] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
## [69] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "2" "2" "2" "2" "2" "2"
## [86] "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2"
## [103] "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2"
## [120] "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2"
## [137] "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2"
## [154] "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2"
## [171] "2" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3"
## [188] "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3"
## [205] "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3"
## [222] "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3"
## [239] "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3"
## [256] "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "4" "4" "4" "4" "4" "4" "4"
## [273] "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4"
## [290] "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4"
## [307] "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4"
## [324] "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4"
## [341] "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "1" "1" "1"
## [358] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
## [375] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
## [392] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
## [409] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
## [426] "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
## [443] "1" "1" "1" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2"
## [460] "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2"
## [477] "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2"
## [494] "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2"
## [511] "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "2"
## [528] "2" "2" "2" "2" "2" "2" "2" "2" "2" "2" "3" "3" "3" "3" "3" "3" "3"
## [545] "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3"
## [562] "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3"
## [579] "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3"
## [596] "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3"
## [613] "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3" "3"
## [630] "3" "3" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4"
## [647] "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4"
## [664] "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4"
## [681] "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4"
## [698] "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4" "4"
## [715] "4" "4" "4" "4" "4" "4" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1" "1"
winter.vec <- bike.sharingcopy$season =="1"
bike.sharingcopy$season[winter.vec] <- "winter"
spring.vec <- bike.sharingcopy$season =="2"
bike.sharingcopy$season[spring.vec] <- "spring"
summer.vec <- bike.sharingcopy$season =="3"
bike.sharingcopy$season[summer.vec] <- "summer"
fall.vec<- bike.sharingcopy$season =="4"
bike.sharingcopy$season[fall.vec] <- "fall"
table(bike.sharingcopy$season)
##
## fall spring summer winter
## 178 184 188 181
### Task 10
### Next, I am going t create a custom function to convert the normalised temperatures using the formula given in the dataset description, (t-t_min)/(t_max-t_min), t_min=-8, t_max=+39.
### x = (t-t_min)/(t_max-t_min), where x is the the normalised temperature, t is the temperature to be found, t-min is -8 and t-max is 39.
### Custom function for converting normalised (real) temperatures to raw temperatures.
formula.temp <- function(x, max, min){
output <- x * (max - min) + min
return(output)
}
formula.temp(x = bike.sharingcopy$temp, max = 39, min = -8)
## [1] 8.175849 9.083466 1.229108 1.400000 2.666979 1.604356 1.236534
## [8] -0.245000 -1.498349 -0.910849 -0.052723 0.118169 -0.245000 -0.439110
## [15] 2.966651 2.888349 0.264151 2.183349 5.732178 4.298349 0.342500
## [22] -5.220871 -3.463480 -3.422609 2.503466 2.222500 1.165000 1.563466
## [29] 1.236534 2.176534 0.499151 1.032178 4.220000 0.786979 1.931288
## [36] 2.966651 5.434151 4.768349 2.379151 -1.665199 -1.215644 0.887277
## [43] 2.457500 6.876534 11.505000 4.506089 6.958267 12.484151 16.518349
## [50] 10.760849 5.405199 6.256651 0.564434 2.421733 5.895644 9.124356
## [57] 5.277500 8.143466 11.141831 4.533349 7.745000 1.321651 4.298349
## [64] 10.055849 9.696534 4.301733 5.747500 5.904151 10.287277 6.876534
## [71] 7.470849 10.064356 7.285199 6.917377 9.165199 11.505000 17.380000
## [78] 14.207500 7.627500 12.230445 12.758349 8.306979 5.395000 4.415849
## [85] 4.494151 3.893021 4.424356 6.217500 6.100000 4.611651 6.100000
## [92] 6.805000 9.781651 18.946651 11.465849 10.369151 12.562500 7.784151
## [99] 8.097500 12.053349 19.995644 15.617500 11.387500 13.972500 12.993349
## [106] 12.249151 13.463349 16.087500 15.774151 19.965000 13.580849 7.823349
## [113] 13.620000 19.338349 20.513349 21.688349 21.140000 21.022500 15.970000
## [120] 14.207500 13.228349 17.810849 20.983349 11.465849 13.580849 14.520849
## [127] 16.440000 16.831651 17.027500 17.027500 17.497500 17.145000 16.087500
## [134] 16.479151 18.437500 19.142500 18.398349 17.850000 16.949151 17.223349
## [141] 20.317500 20.395849 21.688349 23.020000 23.059151 25.291651 24.038349
## [148] 22.824151 23.372500 26.466651 28.425000 27.915849 25.605000 21.140000
## [155] 21.845000 22.471651 23.881651 25.252500 28.464151 29.991651 27.485000
## [162] 26.075000 24.547500 21.845000 20.395849 21.453349 21.531651 22.510849
## [169] 24.743349 24.860849 21.845000 23.999151 26.466651 26.231651 26.035849
## [176] 24.665000 23.960000 24.077500 26.975849 26.231651 24.743349 25.957500
## [183] 26.701651 25.683349 26.153349 27.093349 25.840000 27.250000 25.330849
## [190] 26.466651 27.132500 27.837500 29.325849 27.093349 23.999151 23.176651
## [197] 24.273349 25.800849 27.093349 28.503349 28.111651 30.305000 31.871651
## [204] 31.910849 31.010000 26.936651 28.268349 28.425000 28.620849 31.401651
## [211] 29.795849 29.874151 28.268349 28.816651 26.388349 25.370000 25.409151
## [218] 25.683349 26.897500 27.955000 28.425000 28.033349 25.722500 25.291651
## [225] 24.234151 23.803349 23.294151 24.939151 25.996651 25.448349 24.195000
## [232] 24.782500 25.409151 24.508349 22.119151 23.646651 24.155849 24.900000
## [239] 23.960000 25.231773 21.923349 22.040849 22.863349 22.785000 22.236651
## [246] 23.450849 25.330849 23.646651 17.380000 20.160849 21.793911 22.550000
## [253] 23.020000 22.706651 22.284356 22.589151 23.646651 19.142500 14.050849
## [260] 15.108349 15.852500 17.810849 18.398349 19.965000 21.531651 20.630849
## [267] 20.513349 21.805849 22.510849 21.923349 21.845000 20.983349 18.515849
## [274] 11.270000 8.763349 10.055849 14.755849 17.301651 15.225849 16.009151
## [281] 16.518349 17.419151 18.829151 18.633349 17.536651 19.690849 17.889151
## [288] 15.813349 16.048349 17.105849 17.027500 17.461733 14.364151 12.092500
## [295] 11.857500 11.818349 13.776651 14.168349 14.755849 14.090000 7.549151
## [302] 3.945849 7.000849 7.980000 10.839151 9.742500 11.191651 10.956651
## [309] 7.353349 8.371651 10.565000 11.191651 10.800000 9.860000 7.235849
## [316] 8.763349 12.719151 16.910000 16.910000 13.463349 8.058349 4.885849
## [323] 7.470849 13.776651 13.032500 11.583349 12.719151 9.546651 9.625000
## [330] 9.664151 13.580849 15.663466 13.541651 7.275000 6.687500 6.765849
## [337] 6.060849 7.549151 10.134151 13.737500 11.270000 4.494151 5.669151
## [344] 4.925000 2.379151 3.201651 5.277500 6.922500 11.857500 9.625000
## [351] 4.141651 3.201651 5.003349 10.134151 12.131651 11.896651 9.546651
## [358] 6.217500 4.914801 7.121733 7.275000 6.059110 3.671651 6.648349
## [365] 11.270000 9.390000 4.833021 -0.950000 -2.947500 4.494151 7.705849
## [372] 10.486651 7.862500 2.535849 6.508712 4.885849 9.977500 4.885849
## [379] 0.460000 -0.166651 0.930000 9.533021 6.256651 0.930000 2.222500
## [386] 0.146651 -0.362500 2.261651 8.097500 5.825849 8.058349 11.975000
## [393] 6.844151 5.277500 4.650849 10.330000 14.050849 10.760849 6.726651
## [400] 4.415849 4.494151 5.282623 8.645849 4.063349 4.455000 5.199151
## [407] 2.535849 -2.007500 2.457500 7.000849 8.371651 6.883349 8.136651
## [414] 8.293349 5.160000 5.160000 5.527822 10.604151 13.345849 11.152500
## [421] 5.669151 5.120849 9.233349 8.880849 8.184356 14.834151 8.606651
## [428] 11.465849 7.314151 3.436651 4.141651 10.995849 16.792500 11.309151
## [435] 5.512500 9.001733 13.933349 18.555000 18.907500 18.202500 12.484151
## [442] 16.165849 14.207500 17.615000 18.359151 16.988349 18.045849 20.278349
## [449] 15.617500 12.562500 12.954151 7.196651 14.755849 15.225849 9.390000
## [456] 11.935849 12.014151 12.393911 13.933349 17.458349 12.445000 10.956651
## [463] 12.562500 15.500000 14.990849 12.993349 8.388712 10.682500 12.797500
## [470] 15.265000 20.513349 23.215849 20.591651 13.776651 15.421651 16.753349
## [477] 18.790000 10.643349 7.118349 11.426651 14.403349 15.421651 13.502500
## [484] 9.703349 13.541651 13.815849 20.826651 18.515849 18.320000 21.492500
## [491] 21.218349 18.437500 17.262500 19.338349 19.025000 15.774151 17.066651
## [498] 18.515849 20.787500 18.946651 20.748349 21.923349 19.886651 18.515849
## [505] 20.200000 21.179151 20.121651 20.905000 21.218349 22.785000 23.960000
## [512] 24.547500 24.430000 25.487500 25.957500 22.863349 23.960000 22.745849
## [519] 19.416651 20.317500 20.082500 17.419151 18.045849 20.317500 22.510849
## [526] 25.409151 26.153349 25.879151 22.706651 22.824151 22.471651 22.040849
## [533] 21.688349 19.847500 18.711651 24.351651 28.777500 29.874151 28.542500
## [540] 26.388349 26.936651 25.644151 21.649151 24.782500 27.210849 31.205849
## [547] 27.955000 30.344151 28.738349 28.699151 29.090849 30.892500 30.931651
## [554] 32.498349 30.657500 25.409151 25.879151 25.683349 25.644151 26.388349
## [561] 25.056651 27.054151 27.876651 30.461651 29.286651 28.190000 23.294151
## [568] 20.004151 23.372500 26.858349 27.289151 26.035849 28.503349 28.738349
## [575] 27.524151 25.918349 26.349151 25.526651 25.722500 27.367500 27.994151
## [582] 29.286651 28.150849 27.367500 26.584151 27.250000 27.524151 25.644151
## [589] 24.547500 24.939151 25.879151 26.153349 25.213349 25.800849 25.996651
## [596] 23.881651 21.884151 21.884151 22.510849 23.372500 24.704151 25.017500
## [603] 23.098349 22.706651 25.056651 26.231651 24.195000 25.213349 27.915849
## [610] 27.406651 24.743349 25.252500 26.114151 26.623349 24.743349 25.056651
## [617] 22.980849 20.670000 19.416651 19.142500 20.160849 20.787500 21.766651
## [624] 20.591651 19.260000 19.299151 21.296651 17.967500 17.693349 20.160849
## [631] 22.550000 16.870849 16.165849 17.850000 21.845000 22.550000 21.100849
## [638] 17.497500 16.753349 16.479151 19.769151 22.902500 22.902500 20.905000
## [645] 18.045849 11.544151 10.016651 12.993349 16.165849 12.445000 12.562500
## [652] 10.486651 16.518349 18.398349 14.011651 13.424151 16.557500 18.476651
## [659] 14.755849 13.815849 14.912500 17.575849 19.612500 17.850000 17.654151
## [666] 16.910000 14.442500 12.680000 6.954554 8.802500 9.194151 8.685000
## [673] 8.136651 7.314151 7.000849 5.199151 5.904151 8.552178 8.998349
## [680] 10.290849 11.779151 14.795000 8.136651 5.590849 7.118349 8.215000
## [687] 7.275000 8.097500 9.899151 9.585849 8.606651 7.980000 9.311651
## [694] 5.081651 3.554151 6.726651 5.708349 5.943349 5.200890 6.021651
## [701] 6.021651 8.332500 13.267500 14.364151 12.601651 4.024151 7.079151
## [708] 9.938349 10.055849 12.484151 8.606651 5.982500 5.904151 5.238349
## [715] 7.235849 9.037500 10.486651 11.309151 7.627500 7.510000 7.353349
## [722] 4.494151 3.554151 2.871288 5.691288 3.436651 3.945849 3.906651
## [729] 3.906651 4.024151 2.144151
### Adding a new column called converted.temp to the bike.sharingcopy dataset.
bike.sharingcopy$converted.temp <- formula.temp(x = bike.sharingcopy$temp, max = 39, min = -8)
### Custom function for converting atemp from normalised atemp to raw atemp.
formula.atemp <- function(x, max, min){
output <- x * (max - min) + min
return(output)
}
formula.atemp(x = bike.sharingcopy$atemp, max = 50, min = -16)
## [1] 7.999250 7.346774 -3.499270 -1.999948 -0.868180 -0.608206
## [7] -2.216626 -5.291236 -8.332450 -6.041392 -3.363376 -5.408782
## [13] -6.041722 -3.564742 0.375392 -0.541678 -4.333114 -0.666022
## [19] 3.695852 0.833300 -5.583022 -10.781406 -9.476619 -8.216620
## [25] -0.521284 -2.562400 -1.499800 -1.261078 -1.999684 0.521252
## [31] -3.707500 -0.521020 0.791522 -4.260052 -0.913258 0.041828
## [37] 3.250286 4.041428 -2.915764 -6.477322 -6.129832 -1.908406
## [43] -0.625036 5.391458 10.291100 0.782084 4.869200 12.291428
## [49] 17.790878 9.832664 2.303780 2.748950 -3.721822 0.217322
## [55] 3.086606 7.130426 2.624672 7.173194 10.407788 1.416014
## [61] 5.124686 -2.791222 0.874814 8.999414 8.172632 -0.261574
## [67] 3.958400 2.916128 9.454088 4.130000 5.499500 9.086006
## [73] 5.912000 4.999748 8.217380 11.081978 18.782594 14.790650
## [79] 5.499500 11.042510 13.082372 6.303974 1.874978 0.916592
## [85] 0.999686 0.522374 0.999884 3.331928 3.625100 0.999950
## [91] 2.707964 4.832042 8.998622 19.833314 10.291100 9.582128
## [97] 12.623936 5.415614 6.540914 12.164642 21.304322 16.541564
## [103] 11.540678 14.540972 13.166258 12.082472 13.415936 17.207636
## [109] 16.291028 21.249872 13.956872 5.248964 13.707986 20.416358
## [115] 21.917000 23.209478 21.959372 22.209314 16.832558 14.625386
## [121] 13.581464 19.166978 22.417214 10.706900 13.166522 15.291722
## [127] 17.832986 18.249578 18.666236 18.499586 18.874400 18.541958
## [133] 16.623800 17.041514 19.376000 20.333792 19.542914 18.792428
## [139] 17.708972 18.916772 21.750350 21.917000 22.959536 23.917658
## [145] 24.625772 27.209408 26.042528 24.417014 24.626300 28.292072
## [151] 31.875278 31.583822 26.500172 22.750778 23.249936 24.709064
## [157] 25.042628 27.292700 32.000414 34.000214 30.417272 28.750508
## [163] 26.459450 23.709164 23.042036 22.791764 23.292836 23.625278
## [169] 26.500964 26.625836 23.292836 26.084636 29.792714 29.792978
## [175] 27.334478 26.458658 26.083514 26.042264 29.708828 27.209408
## [181] 26.042528 27.042692 28.042328 28.125950 27.917522 29.958308
## [187] 29.251778 29.333486 28.251878 27.834428 29.541650 32.167064
## [193] 32.792150 29.500664 25.916864 25.208486 26.125358 28.208978
## [199] 30.459050 33.333614 33.292100 38.540486 39.499136 37.082942
## [205] 36.458714 31.583228 30.000614 29.584022 32.833400 35.873822
## [211] 32.083442 32.166536 30.417272 30.666686 28.875842 27.876008
## [217] 27.333422 28.626164 31.209272 30.416678 31.791986 29.208878
## [223] 27.000386 27.166772 26.626628 25.209608 24.667022 26.625242
## [229] 28.000286 27.709028 25.792586 26.833736 28.584650 26.124764
## [235] 24.000422 25.625672 26.626364 27.542378 25.946696 26.765294
## [241] 24.125228 23.250464 24.333986 24.584786 23.917328 25.792058
## [247] 27.918314 25.292636 18.003200 19.919114 20.653826 22.210436
## [253] 24.125492 24.209114 23.740580 23.834564 25.375400 20.542286
## [259] 14.457350 15.581792 16.375442 18.958550 19.126322 20.335178
## [265] 20.627558 18.460250 21.251192 21.794042 22.876772 21.918650
## [271] 21.960428 21.917792 19.958714 11.248958 6.790922 9.875036
## [277] 15.208628 18.791108 15.708050 17.290664 17.873972 18.582878
## [283] 19.833050 20.042336 18.169322 20.419064 18.958550 16.915850
## [289] 17.208164 17.707850 18.499586 17.913968 14.790650 11.957336
## [295] 12.082472 11.873978 14.166422 14.582750 15.207836 14.165036
## [301] 5.041592 -0.957742 5.207714 7.500158 10.207808 9.748778
## [307] 10.790786 10.623872 5.374364 7.915628 10.457486 11.208236
## [313] 10.999214 8.665586 4.249922 7.624172 12.416300 18.624392
## [319] 17.500214 13.831208 5.332586 1.999586 5.415878 14.165828
## [325] 13.374092 11.831936 12.415442 8.583086 9.124286 9.415742
## [331] 14.082800 16.348052 13.790750 4.540586 4.166564 5.874578
## [337] 4.499864 7.040600 9.999050 14.122400 10.416236 0.957908
## [343] 4.957772 1.583192 0.708164 1.832936 3.875108 6.331892
## [349] 11.207642 7.748450 0.458486 0.208214 2.541578 10.165964
## [355] 12.249122 12.123986 8.915858 3.749972 2.477426 4.825310
## [361] 5.623778 2.478284 1.416872 5.041592 11.331986 8.790986
## [367] 0.652064 -7.665850 -8.123758 2.375192 6.457622 9.791414
## [373] 6.457028 0.333614 5.042516 2.666186 9.207908 0.457892
## [379] -3.916258 -5.332750 -3.416242 8.042348 2.166764 -3.457492
## [385] -1.416772 -4.458250 -5.291500 0.041828 7.041128 3.458186
## [391] 7.499300 11.415278 5.541014 1.999586 1.333250 9.166922
## [397] 14.791508 10.332086 4.416836 1.999850 1.458386 3.564116
## [403] 7.832864 1.583786 1.291208 3.374828 -2.082778 -9.290572
## [409] -0.957742 6.040436 7.207514 5.790692 7.207514 7.458050
## [415] 1.542008 2.043806 3.477458 9.916022 13.333436 11.124086
## [421] 0.874550 1.708328 7.624964 7.332650 6.999020 15.374486
## [427] 7.749572 11.290472 3.999386 -0.082714 0.832772 9.416600
## [433] 18.623864 10.207478 2.332622 7.738220 14.333072 19.833314
## [439] 20.208722 19.166450 12.791114 17.333036 14.624000 19.166186
## [445] 19.543178 17.875028 19.083422 21.624422 16.124378 12.874208
## [451] 12.957500 4.833164 15.082700 15.832064 8.790986 11.832728
## [457] 11.540942 12.215858 14.457878 19.207700 12.456758 9.790622
## [463] 12.124514 16.500050 15.458108 12.791378 6.260084 9.581864
## [469] 12.499328 16.207736 21.875750 24.585050 23.500142 14.164508
## [475] 16.541036 18.041150 19.832786 9.707264 3.874250 10.748678
## [481] 15.040922 15.916478 13.874042 8.915264 13.707986 14.207936
## [487] 22.083386 19.501136 19.457972 23.000522 22.584128 20.084642
## [493] 18.791372 20.793086 20.499650 16.457678 18.374978 19.957922
## [499] 22.625708 20.293400 22.042664 23.334350 21.792458 20.373986
## [505] 21.415928 22.541822 21.334022 22.334450 22.584392 24.042200
## [511] 25.416914 26.417936 26.334050 28.833800 28.417472 24.334514
## [517] 25.667714 24.125492 21.375008 21.958778 22.166678 18.708872
## [523] 19.791272 21.583172 23.458892 26.792222 27.792122 27.541586
## [529] 23.459750 24.333722 25.209278 23.583764 23.250728 21.750350
## [535] 19.959572 27.209672 31.584350 33.667772 31.791986 27.084272
## [541] 28.500764 27.166772 23.250464 26.292272 28.583792 35.916458
## [547] 29.375528 33.541514 30.334508 30.374900 32.334242 34.250222
## [553] 33.667178 37.124258 36.166136 27.167564 27.876536 26.917886
## [559] 27.209078 28.083578 27.958772 30.542936 31.792250 33.875078
## [565] 33.208478 31.166372 24.459650 20.294192 25.126250 29.541122
## [571] 30.625700 27.167564 32.791358 32.458322 30.041864 28.083578
## [577] 29.209142 27.751136 28.042328 30.667808 31.709222 33.583622
## [583] 32.251214 30.876236 30.042986 30.709322 30.167528 28.084172
## [589] 26.125622 26.542214 27.708764 28.667414 27.166442 27.209408
## [595] -0.001600 24.792686 23.834564 23.333822 23.667650 25.042364
## [601] 26.042528 26.708600 24.833936 23.335736 27.209408 27.959300
## [607] 25.958378 27.083414 29.500400 30.375164 26.834000 27.667514
## [613] 29.334608 30.792878 27.251714 27.375464 24.333986 22.209050
## [619] 21.333164 20.583272 21.624950 22.250828 23.209478 22.667222
## [625] 21.166250 20.501300 21.294422 19.666664 19.124672 21.750086
## [631] 24.292208 18.249578 17.165858 19.915814 23.376458 24.126350
## [637] 22.666958 18.999536 18.165758 17.792000 19.793978 23.542778
## [643] 24.126350 22.292342 19.542386 11.707658 9.582128 12.915392
## [649] 17.207372 12.457022 12.582686 9.832136 17.541464 19.583900
## [655] 14.415836 13.707128 17.833250 19.501136 15.207572 14.124314
## [661] 15.874172 19.000064 20.875586 18.959408 18.501500 17.998778
## [667] 14.872886 13.000400 4.453994 7.832600 8.416172 7.498772
## [673] 5.373836 5.749508 4.332950 2.583422 2.124986 6.564806
## [679] 7.457258 9.999842 11.833058 15.375278 5.332850 2.583158
## [685] 5.416472 6.915464 5.541278 6.291236 8.790986 9.124022
## [691] 8.082872 7.124486 8.999414 0.416972 1.000478 6.374264
## [697] 2.582828 3.124292 3.695852 5.375222 4.915664 7.707728
## [703] 14.082536 14.957564 12.248792 1.041464 5.249228 9.707528
## [709] 9.749636 12.747950 6.331958 3.624308 3.416408 3.416672
## [715] 6.333278 8.415908 10.499000 11.040728 6.582692 6.124322
## [721] 3.916622 -0.416542 1.125086 1.087400 3.434690 -1.458022
## [727] -1.041628 0.833036 -0.001600 -0.707800 -1.249858
### Adding a new column called converted.atemp to the bike.sharingcopy dataset.
bike.sharingcopy$converted.atemp <- formula.atemp(x = bike.sharingcopy$atemp, max = 50, min = -16)
### Task 2
### I am going to calculate mean, median and sd of temperature in every season.
### Mean, median and sd of temperature in Spring.
springseason <- subset(bike.sharingcopy, season == "spring")$converted.temp
mean.spring <- mean(springseason)
mean.spring
## [1] 17.58704
median.spring <- median(springseason)
median.spring
## [1] 18.41792
sd.spring <- sd(springseason)
sd.spring
## [1] 5.764548
1)The mean of temperature in spring was found to be 17.59.
2)The median of temperature in spring was found to be 18.42.
3)The standard deviation of temperature in spring was found to be 5.76.
### Mean, median and sd of temperature in summer.
summerseason <- subset(bike.sharingcopy, season == "summer")$converted.temp
mean.summer <- mean(summerseason)
mean.summer
## [1] 25.19654
median.summer <- median(summerseason)
median.summer
## [1] 25.5854
sd.summer <- sd(summerseason)
sd.summer
## [1] 3.329834
1)The mean of temperature in summer was found to be 25.2.
2)The median of temperature in summer was found to be 25.59.
3)The standard deviation of temperature in summer was found to be 3.32.
### Mean, median and sd of temperature in fall.
fallseason <- subset(bike.sharingcopy, season == "fall")$converted.temp
mean.fall <- mean(fallseason)
mean.fall
## [1] 11.87658
median.fall <- median(fallseason)
median.fall
## [1] 11.23083
sd.fall <- sd(fallseason)
sd.fall
## [1] 5.068181
1)The mean of temperature in fall was found to be 11.88.
2)The median of temperature in spring was found to be 11.23.
3)The standard deviation of temperature in spring was found to be 5.06.
### Mean, median and sd of temperature in winter.
winterseason <- subset(bike.sharingcopy, season == "winter")$converted.temp
mean.winter <- mean(winterseason)
mean.winter
## [1] 5.994135
median.winter <- median(winterseason)
median.winter
## [1] 5.434151
sd.winter <- sd(winterseason)
sd.winter
## [1] 4.828546
1)The mean of temperature in winter was found to be 5.99.
2)The median of temperature in winter was found to be 5.43.
3)The standard deviation of temperature in winter was found to be 4.83.
### Task 7
### The highest mean and median temperatures were recorded in the summer season.
### Calculating the limits for the histogram using min and max function and then making the histogram for summer season accordingly.
max(summerseason)
## [1] 32.49835
min(summerseason)
## [1] 14.05085
### The maximum temperature in summer was found to be 32.49.
### The minimum temperature in summer was found to be 14.05.
hist(x = summerseason,
main = "Temperature in Summer",
xlab = "Temperature in Degree Celsius",
ylab = "Days",
xlim = c(12, 35),
ylim = c(0, 45),
breaks = 15,
border = "black",
col = "darkseagreen3")
abline(v = mean.summer, lwd = 2, lty = 1, col = "red")
text(x = 20, y = 25,
labels = paste("Mean = ", round(mean(summerseason),2), sep = ""), col="red" )
abline(v = median.summer, lwd = 2, lty = 3, col = "blue")
text(x = 27, y = 30, labels = paste("Median = ", round(median(summerseason),2), sep = ""), col="blue" )
### The lowest mean and median temperatures were recorded in the winter season.
### calculating the limits for the histogram and then making the histogram for winter season accordingly
max(winterseason)
## [1] 18.9075
min(winterseason)
## [1] -5.220871
### The maximum temperature in winter was found to be 18.90.
### The minimum temperature in winter was found to be -5.22.
hist(x = winterseason,
main = "Temperature in Winter",
xlab = "Temperature in Degree Celsius",
ylab = "Days",
xlim = c(-5, 20),
ylim = c(0, 35),
border = "black",
col = "yellowgreen")
abline(v = mean.winter, lwd = 2, lty = 1, col = "red")
text(x = 10, y = 15,
labels = paste("Mean = ", round(mean(winterseason),2), sep = ""), col="red" )
abline(v = median.winter, lwd = 2, lty = 3, col = "blue")
text(x = 3, y = 5,
labels = paste("Median = ", round(median(winterseason),2), sep = ""), col="blue" )
Question 4: How did the total count of rental bikes change across seasons?
### Task 11
### Calculating the change in total count of bike rentals in different seasons by using a loop code for calculating mean, median and sd of total count of rental bikes for the four seasons.
design.matrix <- expand.grid(
"season" = c("winter", "spring", "summer", "fall"),
"median.cnt" = NA,
"mean.cnt" = NA,
"sd.cnt" = NA,
stringsAsFactors = F
)
design.matrix
## season median.cnt mean.cnt sd.cnt
## 1 winter NA NA NA
## 2 spring NA NA NA
## 3 summer NA NA NA
## 4 fall NA NA NA
for(row.i in 1:nrow(design.matrix)) {
season.i <- design.matrix$season[row.i]
data.temp <- subset(bike.sharingcopy, season == season.i) ### adding the information in a temporary folder.
### Calculating descriptive statistics mean, median and sd.
median.i <- median(data.temp$cnt)
mean.i <- mean(data.temp$cnt)
sd.i <- sd(data.temp$cnt)
### Assigning statistics to row.i of design.matrix
design.matrix$median.cnt[row.i] <- median.i
design.matrix$mean.cnt[row.i] <- mean.i
design.matrix$sd.cnt[row.i] <- sd.i
}
design.matrix
## season median.cnt mean.cnt sd.cnt
## 1 winter 2209.0 2604.133 1399.942
## 2 spring 4941.5 4992.332 1695.977
## 3 summer 5353.5 5644.303 1459.800
## 4 fall 4634.5 4728.163 1699.615
Fall
1)The mean of total rentals in fall was found to be 4728.16.
2)The median of total rentals in fall was found to be 4634.5.
3)The sd of total rentals in fall was found to be 1699.62.
Question 5: What is the difference between temperatures in temp(real temperature)and atemp(feeling of the temperature)?
### First, I will run the apa custom function code for all the analysis requiring apa format results.
apa <- function(test.object, tails = 2, sig.digits = 2, p.lb = .01) {
statistic.id <- substr(names(test.object$statistic), start = 1, stop = 1)
p.value <- test.object$p.value
if(tails == 1) {p.value <- p.value / 2}
if (p.value < p.lb) {p.display <- paste("p < ", p.lb, " (", tails, "-tailed)", sep = "")}
if (p.value > p.lb) {p.display <- paste("p = ", round(p.value, sig.digits), " (", tails, "-tailed)", sep = "")}
add.par <- ""
if(grepl("product-moment", test.object$method)) {
estimate.display <- paste("r = ", round(test.object$estimate, sig.digits), ", ", sep = "")
}
if(grepl("Chi", test.object$method)) {
estimate.display <- ""
add.par <- paste(", N = ", sum(test.object$observed), sep = "")
}
if(grepl("One Sample t-test", test.object$method)) {
estimate.display <- paste("mean = ", round(test.object$estimate, sig.digits), ", ", sep = "")
}
if(grepl("Two Sample t-test", test.object$method)) {
estimate.display <- paste("mean difference = ", round(test.object$estimate[2] - test.object$estimate[1], sig.digits), ", ", sep = "")
}
return(paste(
estimate.display,
statistic.id,
"(",
round(test.object$parameter, sig.digits),
add.par,
") = ",
round(test.object$statistic, sig.digits),
", ",
p.display,
sep = ""
)
)
}
### Task 3
### Calculating t-test for the difference between temp(real temperature) and atemp (feeling of the temperature).
testresult.temp <- t.test(x = bike.sharingcopy$converted.temp, y = bike.sharingcopy$converted.atemp, alternative = "two.sided")
testresult.temp
##
## Welch Two Sample t-test
##
## data: bike.sharingcopy$converted.temp and bike.sharingcopy$converted.atemp
## t = -0.047659, df = 1392.8, p-value = 0.962
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1.0235835 0.9750271
## sample estimates:
## mean of x mean of y
## 15.28309 15.30736
apa(testresult.temp)
## [1] "mean difference = 0.02, t(1392.82) = -0.05, p = 0.96 (2-tailed)"
### There is not a significant difference between real temperature and feeling of the temperature, mean difference = 0.02, t(1392.82) = -0.05, p = 0.96 (2-tailed).
### Alternative Hypothesis confirmed: true difference in means is not equal to 0.
Question 6: Determine the correlation between total temperature (converted.temp + converted.atemp) and total number of rental bikes.
### Task 4
### Determining the correlation between total temperature and total count of bike using cor test.
### For determining the total temperature, first I will find the mean of converted.temp and converted.atemp and add it as a new column in bike.sharingcopy dataset.
bike.sharingcopy$mean.converted.temp.atemp <- (bike.sharingcopy$converted.temp + bike.sharingcopy$converted.atemp)/2
### Correlation between total temperature and total count
cor.mean.converted.temp.atemp <- cor.test(x = bike.sharingcopy$mean.converted.temp.atemp,
y = bike.sharingcopy$cnt)
cor.mean.converted.temp.atemp
##
## Pearson's product-moment correlation
##
## data: bike.sharingcopy$mean.converted.temp.atemp and bike.sharingcopy$cnt
## t = 21.948, df = 729, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.5850170 0.6725248
## sample estimates:
## cor
## 0.6307721
apa(cor.mean.converted.temp.atemp)
## [1] "r = 0.63, t(729) = 21.95, p < 0.01 (2-tailed)"
### There is a significant positive correlation between total temperature and total bike rentals, r = 0.63, t(729) = 21.95, p < 0.01 (2-tailed).
Question 7: Using a scatterplot, show the relationship between temperature(real) and type of bike rentals ; casual and registered.
### Task 6
### creating objects for plotting the relevant data.
Temperature <- bike.sharingcopy$converted.temp
Casual.rentals <- bike.sharingcopy$casual
Registered.rentals <- bike.sharingcopy$registered
### creating a scatterplot for showing correlation between temperature and type of bike rentals; casual and registered with added regression lines.
### For determining the limits of x and y axis I will use min and max function.
min(bike.sharingcopy$casual)
## [1] 2
max(bike.sharingcopy$casual)
## [1] 3410
min(bike.sharingcopy$registered)
## [1] 20
max(bike.sharingcopy$registered)
## [1] 6946
min(bike.sharingcopy$converted.temp)
## [1] -5.220871
max(bike.sharingcopy$converted.temp)
## [1] 32.49835
### The limits of the variables are 40 for temperature and 7000 for bike rentals
### Plotting the correlation using scatterplot
plot(x = 1, y = 1, xlab = "Temperature in degree celsius", ylab = "Bike rentals", type = "n", main = "Correlation between temperature and type of bike rentals",
xlim = c(0, 40), ylim = c(0, 7000))
### Adding points, regression lines and legends in the following code
points(bike.sharingcopy$converted.temp, bike.sharingcopy$casual, pch = 10, col = "purple")
points(bike.sharingcopy$converted.temp, bike.sharingcopy$registered, pch = 10, col = "orange")
legend("topright",legend = c("casual", "registered"), col = c("purple","orange"), pch = c(10, 10), bg = "grey")
abline(lm(bike.sharingcopy$registered ~ bike.sharingcopy$converted.temp), lty = 6, col = "blue")
abline(lm(bike.sharingcopy$casual ~ bike.sharingcopy$converted.temp), lty = 6, col = "red")
abline(lm(bike.sharingcopy$registered ~ bike.sharingcopy$converted.temp), lty = 6, col = "hotpink")
registered <- paste("cor = ", round(cor(bike.sharingcopy$registered, bike.sharingcopy$converted.temp), 2), sep = "")
casual <- paste("cor = ", round(cor(bike.sharingcopy$casual, bike.sharingcopy$converted.temp), 2), sep = "")
legend("left",legend = c(registered, casual) , col = c('red', 'hotpink'),pch = c(10, 10), bg = "grey")
Question 8: Are holidays and weather situation good predictors of total number of bikes rented?
### Task 5
### Regression analysis using lm model.
total.rentals.lm <- lm(cnt ~ weathersit + holiday, data = bike.sharingcopy)
summary(total.rentals.lm)
##
## Call:
## lm(formula = cnt ~ weathersit + holiday, data = bike.sharingcopy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4521.4 -1267.9 -61.4 1494.1 4476.6
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6019.4 188.6 31.910 <2e-16 ***
## weathersit -1067.0 125.5 -8.505 <2e-16 ***
## holiday -912.5 408.9 -2.231 0.026 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1846 on 728 degrees of freedom
## Multiple R-squared: 0.09463, Adjusted R-squared: 0.09215
## F-statistic: 38.05 on 2 and 728 DF, p-value: < 2.2e-16
### The coefficients (Intercept, weathersit and holiday) were found to be 6019.4, -1067.0 and -912.5.
### The df.residuals are 728.
### Use of Anova to test the effect of weather situation and holiday
anova.weathersit <- anova (total.rentals.lm)
anova.weathersit
## Analysis of Variance Table
##
## Response: cnt
## Df Sum Sq Mean Sq F value Pr(>F)
## weathersit 1 242288753 242288753 71.1154 < 2e-16 ***
## holiday 1 16964654 16964654 4.9794 0.02595 *
## Residuals 728 2480281985 3406981
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
### The f-values of weather situation and holiday were found to be :
anova.weathersit$`F value`
## [1] 71.115387 4.979381 NA
#### The p-values of weather situation and holiday were found to be :
anova.weathersit$`Pr(>F)`
## [1] 1.803533e-16 2.595486e-02 NA
### The analysis of variance showed a significant effect for weather situation (F-value = 71.11, Df = 1, p-value < 0.01) but not for holiday (F-value = 4.979, Df = 1, p-value = 0.025).