week4
2023-09-14
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library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(purrr)
library(ggplot2)
bike <- read.csv('D:/FALL 2023/STATISTICS/datasets/bike.csv')## Random sampling of bike dataset
```r
num <-sample(5:10,1)
columns <- c("Seasons", "Holiday", "Rented.Bike.Count", "Visibility", "Humidity", "Snowfall")
subsample_list <- list()
for (i in 1:num) {
# Determine sample size (approximately 50% of the data)
s_size <- round(0.5 * nrow(bike))
# Randomly select rows with replacement
s_index <- sample(1:nrow(bike), size = s_size, replace = TRUE)
# Create the subsample data frame
subsample <- bike[s_index, columns]
# Store the subsample in the list
subsample_list[[i]] <- subsample
}
View(subsample_list)Displaying the dimensions of each subsample
sapply(subsample_list, dim)## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 4380 4380 4380 4380 4380 4380
## [2,] 6 6 6 6 6 6Summaries of the sample data
summary_table <- lapply(subsample_list, function(subsample){
summary_df <-summary(subsample)
knitr::kable(summary_df, caption = "summary statistics")
})
for (i in 1: num){
cat("### Subsample", i, "summary statisics \n")
print(summary_table[[i]])
}## ### Subsample 1 summary statisics
##
##
## Table: summary statistics
##
## | | Seasons | Holiday |Rented.Bike.Count | Visibility | Humidity | Snowfall |
## |:--|:----------------|:----------------|:-----------------|:--------------|:-------------|:---------------|
## | |Length:4380 |Length:4380 |Min. : 0.0 |Min. : 33.0 |Min. : 0.00 |Min. :0.00000 |
## | |Class :character |Class :character |1st Qu.: 192.0 |1st Qu.: 951.5 |1st Qu.:42.00 |1st Qu.:0.00000 |
## | |Mode :character |Mode :character |Median : 490.5 |Median :1681.0 |Median :57.00 |Median :0.00000 |
## | |NA |NA |Mean : 704.9 |Mean :1435.9 |Mean :58.12 |Mean :0.07011 |
## | |NA |NA |3rd Qu.:1062.0 |3rd Qu.:1999.0 |3rd Qu.:74.00 |3rd Qu.:0.00000 |
## | |NA |NA |Max. :3556.0 |Max. :2000.0 |Max. :98.00 |Max. :8.80000 |
## ### Subsample 2 summary statisics
##
##
## Table: summary statistics
##
## | | Seasons | Holiday |Rented.Bike.Count | Visibility | Humidity | Snowfall |
## |:--|:----------------|:----------------|:-----------------|:------------|:-------------|:---------------|
## | |Length:4380 |Length:4380 |Min. : 0.0 |Min. : 27 |Min. : 0.00 |Min. :0.00000 |
## | |Class :character |Class :character |1st Qu.: 193.0 |1st Qu.: 946 |1st Qu.:42.00 |1st Qu.:0.00000 |
## | |Mode :character |Mode :character |Median : 479.5 |Median :1674 |Median :57.00 |Median :0.00000 |
## | |NA |NA |Mean : 704.7 |Mean :1435 |Mean :58.24 |Mean :0.07023 |
## | |NA |NA |3rd Qu.:1071.2 |3rd Qu.:2000 |3rd Qu.:74.00 |3rd Qu.:0.00000 |
## | |NA |NA |Max. :3298.0 |Max. :2000 |Max. :98.00 |Max. :8.80000 |
## ### Subsample 3 summary statisics
##
##
## Table: summary statistics
##
## | | Seasons | Holiday |Rented.Bike.Count | Visibility | Humidity | Snowfall |
## |:--|:----------------|:----------------|:-----------------|:------------|:-------------|:---------------|
## | |Length:4380 |Length:4380 |Min. : 0.0 |Min. : 27 |Min. : 0.00 |Min. :0.00000 |
## | |Class :character |Class :character |1st Qu.: 185.0 |1st Qu.: 895 |1st Qu.:43.00 |1st Qu.:0.00000 |
## | |Mode :character |Mode :character |Median : 479.5 |Median :1662 |Median :57.00 |Median :0.00000 |
## | |NA |NA |Mean : 692.7 |Mean :1420 |Mean :58.52 |Mean :0.07888 |
## | |NA |NA |3rd Qu.:1044.0 |3rd Qu.:2000 |3rd Qu.:75.00 |3rd Qu.:0.00000 |
## | |NA |NA |Max. :3556.0 |Max. :2000 |Max. :98.00 |Max. :8.80000 |
## ### Subsample 4 summary statisics
##
##
## Table: summary statistics
##
## | | Seasons | Holiday |Rented.Bike.Count | Visibility | Humidity | Snowfall |
## |:--|:----------------|:----------------|:-----------------|:------------|:-------------|:---------------|
## | |Length:4380 |Length:4380 |Min. : 0.0 |Min. : 53 |Min. : 0.00 |Min. :0.00000 |
## | |Class :character |Class :character |1st Qu.: 202.0 |1st Qu.: 955 |1st Qu.:42.00 |1st Qu.:0.00000 |
## | |Mode :character |Mode :character |Median : 518.0 |Median :1715 |Median :57.00 |Median :0.00000 |
## | |NA |NA |Mean : 720.8 |Mean :1447 |Mean :57.96 |Mean :0.07048 |
## | |NA |NA |3rd Qu.:1088.0 |3rd Qu.:2000 |3rd Qu.:74.00 |3rd Qu.:0.00000 |
## | |NA |NA |Max. :3418.0 |Max. :2000 |Max. :98.00 |Max. :6.00000 |
## ### Subsample 5 summary statisics
##
##
## Table: summary statistics
##
## | | Seasons | Holiday |Rented.Bike.Count | Visibility | Humidity | Snowfall |
## |:--|:----------------|:----------------|:-----------------|:--------------|:-------------|:---------------|
## | |Length:4380 |Length:4380 |Min. : 0.0 |Min. : 33.0 |Min. : 0.00 |Min. :0.00000 |
## | |Class :character |Class :character |1st Qu.: 193.0 |1st Qu.: 954.2 |1st Qu.:43.00 |1st Qu.:0.00000 |
## | |Mode :character |Mode :character |Median : 499.0 |Median :1700.0 |Median :57.00 |Median :0.00000 |
## | |NA |NA |Mean : 704.4 |Mean :1444.2 |Mean :58.23 |Mean :0.07781 |
## | |NA |NA |3rd Qu.:1058.0 |3rd Qu.:2000.0 |3rd Qu.:74.00 |3rd Qu.:0.00000 |
## | |NA |NA |Max. :3404.0 |Max. :2000.0 |Max. :98.00 |Max. :7.10000 |
## ### Subsample 6 summary statisics
##
##
## Table: summary statistics
##
## | | Seasons | Holiday |Rented.Bike.Count | Visibility | Humidity | Snowfall |
## |:--|:----------------|:----------------|:-----------------|:------------|:-------------|:---------------|
## | |Length:4380 |Length:4380 |Min. : 0.0 |Min. : 27 |Min. : 0.00 |Min. :0.00000 |
## | |Class :character |Class :character |1st Qu.: 189.8 |1st Qu.: 906 |1st Qu.:43.00 |1st Qu.:0.00000 |
## | |Mode :character |Mode :character |Median : 489.5 |Median :1686 |Median :58.00 |Median :0.00000 |
## | |NA |NA |Mean : 698.4 |Mean :1424 |Mean :58.69 |Mean :0.08171 |
## | |NA |NA |3rd Qu.:1059.0 |3rd Qu.:2000 |3rd Qu.:75.00 |3rd Qu.:0.00000 |
## | |NA |NA |Max. :3404.0 |Max. :2000 |Max. :98.00 |Max. :5.00000 |Scrutinizing subsamples
# summary statistics for each subsamples
summary_stats <-lapply(subsample_list, summary)
# plot histogram
histograms <- lapply(subsample_list, function(subsample) {
ggplot(subsample, aes(x = Humidity)) +
geom_histogram(binwidth = 1, fill = 'blue', color = 'black') +
labs(title = "Histogram for humidity", x = 'Value', y = 'Frequency')
})
# display histograms and summary
for (i in 1:num) {
cat("Subsample", i, "summary statistics:\n")
print(summary_stats[[i]])
print(histograms[[i]])
}## Subsample 1 summary statistics:
## Seasons Holiday Rented.Bike.Count Visibility
## Length:4380 Length:4380 Min. : 0.0 Min. : 33.0
## Class :character Class :character 1st Qu.: 192.0 1st Qu.: 951.5
## Mode :character Mode :character Median : 490.5 Median :1681.0
## Mean : 704.9 Mean :1435.9
## 3rd Qu.:1062.0 3rd Qu.:1999.0
## Max. :3556.0 Max. :2000.0
## Humidity Snowfall
## Min. : 0.00 Min. :0.00000
## 1st Qu.:42.00 1st Qu.:0.00000
## Median :57.00 Median :0.00000
## Mean :58.12 Mean :0.07011
## 3rd Qu.:74.00 3rd Qu.:0.00000
## Max. :98.00 Max. :8.80000
## Subsample 2 summary statistics:
## Seasons Holiday Rented.Bike.Count Visibility
## Length:4380 Length:4380 Min. : 0.0 Min. : 27
## Class :character Class :character 1st Qu.: 193.0 1st Qu.: 946
## Mode :character Mode :character Median : 479.5 Median :1674
## Mean : 704.7 Mean :1435
## 3rd Qu.:1071.2 3rd Qu.:2000
## Max. :3298.0 Max. :2000
## Humidity Snowfall
## Min. : 0.00 Min. :0.00000
## 1st Qu.:42.00 1st Qu.:0.00000
## Median :57.00 Median :0.00000
## Mean :58.24 Mean :0.07023
## 3rd Qu.:74.00 3rd Qu.:0.00000
## Max. :98.00 Max. :8.80000
## Subsample 3 summary statistics:
## Seasons Holiday Rented.Bike.Count Visibility
## Length:4380 Length:4380 Min. : 0.0 Min. : 27
## Class :character Class :character 1st Qu.: 185.0 1st Qu.: 895
## Mode :character Mode :character Median : 479.5 Median :1662
## Mean : 692.7 Mean :1420
## 3rd Qu.:1044.0 3rd Qu.:2000
## Max. :3556.0 Max. :2000
## Humidity Snowfall
## Min. : 0.00 Min. :0.00000
## 1st Qu.:43.00 1st Qu.:0.00000
## Median :57.00 Median :0.00000
## Mean :58.52 Mean :0.07888
## 3rd Qu.:75.00 3rd Qu.:0.00000
## Max. :98.00 Max. :8.80000
## Subsample 4 summary statistics:
## Seasons Holiday Rented.Bike.Count Visibility
## Length:4380 Length:4380 Min. : 0.0 Min. : 53
## Class :character Class :character 1st Qu.: 202.0 1st Qu.: 955
## Mode :character Mode :character Median : 518.0 Median :1715
## Mean : 720.8 Mean :1447
## 3rd Qu.:1088.0 3rd Qu.:2000
## Max. :3418.0 Max. :2000
## Humidity Snowfall
## Min. : 0.00 Min. :0.00000
## 1st Qu.:42.00 1st Qu.:0.00000
## Median :57.00 Median :0.00000
## Mean :57.96 Mean :0.07048
## 3rd Qu.:74.00 3rd Qu.:0.00000
## Max. :98.00 Max. :6.00000
## Subsample 5 summary statistics:
## Seasons Holiday Rented.Bike.Count Visibility
## Length:4380 Length:4380 Min. : 0.0 Min. : 33.0
## Class :character Class :character 1st Qu.: 193.0 1st Qu.: 954.2
## Mode :character Mode :character Median : 499.0 Median :1700.0
## Mean : 704.4 Mean :1444.2
## 3rd Qu.:1058.0 3rd Qu.:2000.0
## Max. :3404.0 Max. :2000.0
## Humidity Snowfall
## Min. : 0.00 Min. :0.00000
## 1st Qu.:43.00 1st Qu.:0.00000
## Median :57.00 Median :0.00000
## Mean :58.23 Mean :0.07781
## 3rd Qu.:74.00 3rd Qu.:0.00000
## Max. :98.00 Max. :7.10000
## Subsample 6 summary statistics:
## Seasons Holiday Rented.Bike.Count Visibility
## Length:4380 Length:4380 Min. : 0.0 Min. : 27
## Class :character Class :character 1st Qu.: 189.8 1st Qu.: 906
## Mode :character Mode :character Median : 489.5 Median :1686
## Mean : 698.4 Mean :1424
## 3rd Qu.:1059.0 3rd Qu.:2000
## Max. :3404.0 Max. :2000
## Humidity Snowfall
## Min. : 0.00 Min. :0.00000
## 1st Qu.:43.00 1st Qu.:0.00000
## Median :58.00 Median :0.00000
## Mean :58.69 Mean :0.08171
## 3rd Qu.:75.00 3rd Qu.:0.00000
## Max. :98.00 Max. :5.00000
Anomalies and consistency
means <- lapply(subsample_list, function(subsample) {
mean(subsample$Humidity)})
print(means)## [[1]]
## [1] 58.11849
##
## [[2]]
## [1] 58.23653
##
## [[3]]
## [1] 58.51553
##
## [[4]]
## [1] 57.96096
##
## [[5]]
## [1] 58.23333
##
## [[6]]
## [1] 58.68721sds <- lapply(subsample_list, function(subsample) {
sd(subsample$Visibility)})
print(sds)## [[1]]
## [1] 607.5581
##
## [[2]]
## [1] 610.8125
##
## [[3]]
## [1] 614.9329
##
## [[4]]
## [1] 602.7616
##
## [[5]]
## [1] 602.0797
##
## [[6]]
## [1] 615.1279for (i in 1:num) {
cat("Subsample", i, "Humidity", means[[i]],"\n")
cat("Subsample", i, "Visibility", sds[[i]],"\n")
}## Subsample 1 Humidity 58.11849
## Subsample 1 Visibility 607.5581
## Subsample 2 Humidity 58.23653
## Subsample 2 Visibility 610.8125
## Subsample 3 Humidity 58.51553
## Subsample 3 Visibility 614.9329
## Subsample 4 Humidity 57.96096
## Subsample 4 Visibility 602.7616
## Subsample 5 Humidity 58.23333
## Subsample 5 Visibility 602.0797
## Subsample 6 Humidity 58.68721
## Subsample 6 Visibility 615.1279ANALYSIS: 1. As we divided the dataset into subsamples and applied various aggregations, we can observe there is no significant variation between subsamples. 2. As there is no huge deviation, possibility of anamoly occurence is less. That is what we can observe from one of the column “Humidity”. 3. I can conclude there is prominent consistency among the columns across all the subsamples.