1.) DEFINING THE QUESTION: Which individuals are most likely to click on my ads?

2.) METRIC OF SUCCESS: we are able to determine which individuals are more likely to click on the ads

3.) EXPERIMENTAL DESIGN TAKEN: a.)Load and preview 1st 6 and last 6 rows of the dataset

b.)Check the shape of the data and the datatypes of the columns

c.)Check for duplicates

d.)Detect outliers in the columns using Interquartile range(IQR)

e.)Removing outliers in the Area income column

f.)Univariate analysis:calculate the mean,median,mode,range,IQR,standard deviation,variance,skewness,kurtosis and quantiles

g.)Bivariate analysis:calculate covariance,correlation among the columns, plotted a correlation matrix and visualized correlation.

h.)Multiple linear regression and Decision tree implementation

i.)Recommendations

4.) APPROPRIATENESS OF THE DATA: Our dataset contains all the variables that are required to successfully undertake our study i.e.daily time spent, age , daily internet usage, male, and clicked on Ad.

5.) EXPLORATORY DATA ANALYSIS:

# loading the advertising dataset using the fread function
library(data.table)

#import data
df <- fread("C:\\Users\\Gakungi\\OneDrive\\Desktop\\R\\advertising.csv")
# previewing the first 6 rows of our dataset
head(df)
##    Daily Time Spent on Site Age Area Income Daily Internet Usage
## 1:                    68.95  35    61833.90               256.09
## 2:                    80.23  31    68441.85               193.77
## 3:                    69.47  26    59785.94               236.50
## 4:                    74.15  29    54806.18               245.89
## 5:                    68.37  35    73889.99               225.58
## 6:                    59.99  23    59761.56               226.74
##                            Ad Topic Line           City Male    Country
## 1:    Cloned 5thgeneration orchestration    Wrightburgh    0    Tunisia
## 2:    Monitored national standardization      West Jodi    1      Nauru
## 3:      Organic bottom-line service-desk       Davidton    0 San Marino
## 4: Triple-buffered reciprocal time-frame West Terrifurt    1      Italy
## 5:         Robust logistical utilization   South Manuel    0    Iceland
## 6:       Sharable client-driven software      Jamieberg    1     Norway
##              Timestamp Clicked on Ad
## 1: 2016-03-27 00:53:11             0
## 2: 2016-04-04 01:39:02             0
## 3: 2016-03-13 20:35:42             0
## 4: 2016-01-10 02:31:19             0
## 5: 2016-06-03 03:36:18             0
## 6: 2016-05-19 14:30:17             0
# previewing the last 6 rows
tail(df)
##    Daily Time Spent on Site Age Area Income Daily Internet Usage
## 1:                    43.70  28    63126.96               173.01
## 2:                    72.97  30    71384.57               208.58
## 3:                    51.30  45    67782.17               134.42
## 4:                    51.63  51    42415.72               120.37
## 5:                    55.55  19    41920.79               187.95
## 6:                    45.01  26    29875.80               178.35
##                           Ad Topic Line          City Male
## 1:        Front-line bifurcated ability  Nicholasland    0
## 2:        Fundamental modular algorithm     Duffystad    1
## 3:      Grass-roots cohesive monitoring   New Darlene    1
## 4:         Expanded intangible solution South Jessica    1
## 5: Proactive bandwidth-monitored policy   West Steven    0
## 6:      Virtual 5thgeneration emulation   Ronniemouth    0
##                   Country           Timestamp Clicked on Ad
## 1:                Mayotte 2016-04-04 03:57:48             1
## 2:                Lebanon 2016-02-11 21:49:00             1
## 3: Bosnia and Herzegovina 2016-04-22 02:07:01             1
## 4:               Mongolia 2016-02-01 17:24:57             1
## 5:              Guatemala 2016-03-24 02:35:54             0
## 6:                 Brazil 2016-06-03 21:43:21             1
# checking the shape of our dataset
dim(df)
## [1] 1000   10
# we have 1000 rows and 10 columns 
# checking the data types of our 10 columns
str(df)
## Classes 'data.table' and 'data.frame':   1000 obs. of  10 variables:
##  $ Daily Time Spent on Site: num  69 80.2 69.5 74.2 68.4 ...
##  $ Age                     : int  35 31 26 29 35 23 33 48 30 20 ...
##  $ Area Income             : num  61834 68442 59786 54806 73890 ...
##  $ Daily Internet Usage    : num  256 194 236 246 226 ...
##  $ Ad Topic Line           : chr  "Cloned 5thgeneration orchestration" "Monitored national standardization" "Organic bottom-line service-desk" "Triple-buffered reciprocal time-frame" ...
##  $ City                    : chr  "Wrightburgh" "West Jodi" "Davidton" "West Terrifurt" ...
##  $ Male                    : int  0 1 0 1 0 1 0 1 1 1 ...
##  $ Country                 : chr  "Tunisia" "Nauru" "San Marino" "Italy" ...
##  $ Timestamp               : POSIXct, format: "2016-03-27 00:53:11" "2016-04-04 01:39:02" ...
##  $ Clicked on Ad           : int  0 0 0 0 0 0 0 1 0 0 ...
##  - attr(*, ".internal.selfref")=<externalptr>
# our columns have the appropriate data types attached to them
# checking for duplicates in the data
dup <- df[duplicated(df),]
dup
## Empty data.table (0 rows and 10 cols): Daily Time Spent on Site,Age,Area Income,Daily Internet Usage,Ad Topic Line,City...
# there are no duplicates in our data
# checking for missing values per column
colSums(is.na(df))
## Daily Time Spent on Site                      Age              Area Income 
##                        0                        0                        0 
##     Daily Internet Usage            Ad Topic Line                     City 
##                        0                        0                        0 
##                     Male                  Country                Timestamp 
##                        0                        0                        0 
##            Clicked on Ad 
##                        0
# we have no missing values in our columns
# changing column names of our dataset
colnames(df)[1] = "daily_time_spent_on_site"
colnames(df)[3] = "area_income"
colnames(df)[4] = "daily_internet_usage"
colnames(df)[5] = "ad_topic_line"
colnames(df)[10] = "clicked_on_ad"
head(df)
##    daily_time_spent_on_site Age area_income daily_internet_usage
## 1:                    68.95  35    61833.90               256.09
## 2:                    80.23  31    68441.85               193.77
## 3:                    69.47  26    59785.94               236.50
## 4:                    74.15  29    54806.18               245.89
## 5:                    68.37  35    73889.99               225.58
## 6:                    59.99  23    59761.56               226.74
##                            ad_topic_line           City Male    Country
## 1:    Cloned 5thgeneration orchestration    Wrightburgh    0    Tunisia
## 2:    Monitored national standardization      West Jodi    1      Nauru
## 3:      Organic bottom-line service-desk       Davidton    0 San Marino
## 4: Triple-buffered reciprocal time-frame West Terrifurt    1      Italy
## 5:         Robust logistical utilization   South Manuel    0    Iceland
## 6:       Sharable client-driven software      Jamieberg    1     Norway
##              Timestamp clicked_on_ad
## 1: 2016-03-27 00:53:11             0
## 2: 2016-04-04 01:39:02             0
## 3: 2016-03-13 20:35:42             0
## 4: 2016-01-10 02:31:19             0
## 5: 2016-06-03 03:36:18             0
## 6: 2016-05-19 14:30:17             0
# checking for any duplicates in our data
dup <- df[duplicated(df),]
dup
## Empty data.table (0 rows and 10 cols): daily_time_spent_on_site,Age,area_income,daily_internet_usage,ad_topic_line,City...
# we lack duplicates in our data
# dropping irrelevant columns
dfb <- within(df, rm("ad_topic_line"))
# plotting boxplot to check for outliers
library(lattice)
boxplot(Age ~ clicked_on_ad, data=dfb)

boxplot(daily_time_spent_on_site ~ clicked_on_ad, data=dfb)

boxplot(daily_internet_usage ~ clicked_on_ad, data=dfb)

boxplot(area_income ~ clicked_on_ad, data=dfb)

# we won't remove any outliers from the data since it will be useful for the analysis

6.) UNIVARIATE ANALYSIS:

# getting the mean of relevant columns
mean_timespent <- mean(dfb$daily_time_spent_on_site)
mean_age <- mean(dfb$Age)
mean_income <- mean(dfb$area_income)
mean_internet <- mean(dfb$daily_internet_usage)

print(mean_timespent)
## [1] 65.0002
print(mean_age)
## [1] 36.009
print(mean_income)
## [1] 55000
print(mean_internet)
## [1] 180.0001
# the mean represents the average of the values per column respectively
# getting the median of the relevant columns
median_timespent <- median(dfb$daily_time_spent_on_site)
median_age <- median(dfb$Age)
median_income <- median(dfb$area_income)
median_internet <- median(dfb$daily_internet_usage)

print(median_timespent)
## [1] 68.215
print(median_age)
## [1] 35
print(median_income)
## [1] 57012.3
print(median_internet)
## [1] 183.13
# the median represents the value that takes up the middle value in each of the columns respectively
# getting the mode of the relevant columns
getmode <- function(v) {
   uniqv <- unique(v)
   uniqv[which.max(tabulate(match(v, uniqv)))]
}

mode_timespent <- getmode(dfb$daily_time_spent_on_site)
mode_age <- getmode(dfb$Age)
mode_income <- getmode(dfb$area_income)
mode_internet <- getmode(dfb$daily_internet_usage)

print(mode_timespent)
## [1] 62.26
print(mode_age)
## [1] 31
print(mode_income)
## [1] 61833.9
print(mode_internet)
## [1] 167.22
# the mode represents the most repeated value per column respectively
# getting the range of the relevant columns
range_timespent <- range(dfb$daily_time_spent_on_site)
range_age <- range(dfb$Age)
range_income <- range(dfb$area_income)
range_internet <- range(dfb$daily_internet_usage)

print(range_timespent)
## [1] 32.60 91.43
print(range_age)
## [1] 19 61
print(range_income)
## [1] 13996.5 79484.8
print(range_internet)
## [1] 104.78 269.96
# the range gives the maximum and minimum figure for each column with the 1st value representing the minimum value and the 2nd value representing the maximum value for each column respectively
# getting the quantiles of relevant columns
quant_timespent <- quantile(dfb$daily_time_spent_on_site)
quant_age <- quantile(dfb$Age)
quant_income <- quantile(dfb$area_income)
quant_internet <- quantile(dfb$daily_internet_usage)

print(quant_timespent)
##      0%     25%     50%     75%    100% 
## 32.6000 51.3600 68.2150 78.5475 91.4300
print(quant_age)
##   0%  25%  50%  75% 100% 
##   19   29   35   42   61
print(quant_income)
##       0%      25%      50%      75%     100% 
## 13996.50 47031.80 57012.30 65470.64 79484.80
print(quant_internet)
##       0%      25%      50%      75%     100% 
## 104.7800 138.8300 183.1300 218.7925 269.9600
# the quantiles represent the cut points dividing the range of a probability distribution per column respectively
# getting the variance of the relevant columns
variance_timespent <- var(dfb$daily_time_spent_on_site)
variance_age <- var(dfb$Age)
variance_income <- var(dfb$area_income)
variance_internet <- var(dfb$daily_internet_usage)

print(variance_timespent)
## [1] 251.3371
print(variance_age)
## [1] 77.18611
print(variance_income)
## [1] 179952406
print(variance_internet)
## [1] 1927.415
# variance is a measure of how far the set of numbers per column is spread out from their mean eg. those of the area income seem to be far spread out from their mean when compared to that of the age column
# getting the standard deviation of the relevant columns
sd_timespent <- sd(dfb$daily_time_spent_on_site)
sd_age <- sd(dfb$Age)
sd_income <- sd(dfb$area_income)
sd_internet <- sd(dfb$daily_internet_usage)

print(sd_timespent)
## [1] 15.85361
print(sd_age)
## [1] 8.785562
print(sd_income)
## [1] 13414.63
print(sd_internet)
## [1] 43.90234
# a low standard deviation indicates that values are closer to the mean while a high one indicates they are far from the mean e.g the age column standard deviation of 8.8 displays that its values are closer to their mean than that of the Area income column whose value is 13600.64
library(moments)
# getting the skewness of the relevant columns
sk_timespent <- skewness(dfb$daily_time_spent_on_site)
sk_age <- skewness(dfb$Age)
sk_income <- skewness(dfb$area_income)
sk_internet <- skewness(dfb$daily_internet_usage)

print(sk_timespent)
## [1] -0.3712026
print(sk_age)
## [1] 0.4784227
print(sk_income)
## [1] -0.6493967
print(sk_internet)
## [1] -0.03348703
# skewness of the age column being positive indicates that the distribution of age column has a longer right tail than left tail while the rest of the columns left tails are longer given that they are skewed negatively
# getting the kurtosis of the relevant columns
kt_timespent <- kurtosis(dfb$daily_time_spent_on_site)
kt_age <- kurtosis(dfb$Age)
kt_income <- kurtosis(dfb$area_income)
kt_internet <- kurtosis(dfb$daily_internet_usage)

print(kt_timespent)
## [1] 1.903942
print(kt_age)
## [1] 2.595482
print(kt_income)
## [1] 2.894694
print(kt_internet)
## [1] 1.727701
# the kurtosis levels are low hence our columns' distributions have light tails indication presence of little to no outliers 

CHECKING THE DISTRIBUTION OF OUR NUMERICAL COLUMNS

qqnorm(dfb$area_income)
qqline(dfb$area_income)

# area income data points below 40000 and above 70000 do not follow a normal distribution
qqnorm(dfb$daily_time_spent_on_site)
qqline(dfb$daily_time_spent_on_site)

# daily time spent on site does not follow a normal distribution
qqnorm(dfb$daily_internet_usage)
qqline(dfb$daily_internet_usage)

# daily internet usage does not follow a normal distribution
qqnorm(dfb$Age)
qqline(dfb$Age)

# data points below age 30 don't follow a normal distribution

7.) BIVARIATE ANALYSIS:

# assigning the relevant columns to variables
time <- dfb$daily_time_spent_on_site
age <- dfb$Age
income <- dfb$area_income
internet <- dfb$daily_internet_usage
male <- dfb$Male
ad <- dfb$clicked_on_ad
# checking the covariance between the relevant columns and the clicked on ad column
print(cov(time,ad))
## [1] -5.933143
print(cov(age,ad))
## [1] 2.164665
print(cov(income,ad))
## [1] -3195.989
print(cov(internet,ad))
## [1] -17.27409
print(cov(male,ad))
## [1] -0.00950951
#daily time spent and clicks on ad have a negative relationship
#age and clicks on ad have a positive relationship
#area income and clicks on ad have a negative relationship
#internet usage and clicks on ad have a negative relationship
#male and clicks on ad have a negative relationship
# checking the correlation between the relevant columns and the clicked on ad column
print(cor(time,ad))
## [1] -0.7481166
print(cor(age,ad))
## [1] 0.4925313
print(cor(income,ad))
## [1] -0.4762546
print(cor(internet,ad))
## [1] -0.7865392
print(cor(male,ad))
## [1] -0.03802747
#daily time spent and clicks on ad have a strong negative relationship
#age and clicks on ad have a moderate positive relationship
#area income and clicks on ad have a weak negative relationship
#internet usage and clicks on ad have a strong negative relationship
#male and clicks on ad have a weak negative relationship
# creating a matrix of the relevant numeric columns and previewing it
dfc <- cbind(time,age,income,internet,male,ad)
# getting the correlation matrix of the relevant columns in the new matrix
cor(dfc)
##                 time         age       income    internet         male
## time      1.00000000 -0.33151334  0.310954413  0.51865848 -0.018950855
## age      -0.33151334  1.00000000 -0.182604955 -0.36720856 -0.021044064
## income    0.31095441 -0.18260496  1.000000000  0.33749553  0.001322359
## internet  0.51865848 -0.36720856  0.337495533  1.00000000  0.028012326
## male     -0.01895085 -0.02104406  0.001322359  0.02801233  1.000000000
## ad       -0.74811656  0.49253127 -0.476254628 -0.78653918 -0.038027466
##                   ad
## time     -0.74811656
## age       0.49253127
## income   -0.47625463
## internet -0.78653918
## male     -0.03802747
## ad        1.00000000

CREATING SCATTERPLOTS

plot(dfb$area_income, dfb$daily_internet_usage, pch=16, col='steelblue',
     main='areaincome vs. daily internet',
     xlab='areaincome', ylab='daily internet')

# there's no visible relationship between area income and daily internet usage
plot(dfb$area_income, dfb$daily_time_spent_on_site, pch=16, col='steelblue',
     main='areaincome vs. daily time spent',
     xlab='areaincome', ylab='daily time spent')

# there's no visible relationship between area income and daily time spent on internet
plot(dfb$area_income, dfb$Age, pch=16, col='steelblue',
     main='areaincome vs. Age',
     xlab='areaincome', ylab='age')

# there's no visible relationship between area income and age
plot(dfb$daily_time_spent_on_site, dfb$daily_internet_usage, pch=16, col='steelblue',
     main='time spent vs. daily internet',
     xlab='timespent', ylab='daily internet')

# there's no visible relationship between time spent on internet and internet usage
plot(dfb$daily_time_spent_on_site, dfb$Age, pch=16, col='steelblue',
     main='time spent vs. age',
     xlab='timespent', ylab='age')

# there's no visible relationship between time spent on internet and age
plot(dfb$daily_internet_usage, dfb$Age, pch=16, col='steelblue',
     main='internet usage vs age',
     xlab='internet usage', ylab='age')

# there's no visible relationship between internet usage and age
# plotting correlogram in R
library(corrplot)
## corrplot 0.92 loaded
#getting the correlation matrix
x <- cor(dfc)

  
#visualizing correlogram
corrplot(x, method="color")

MODELLING SECTION:

a.)MULTIPLE LINEAR REGRESSION

library(broom)
model1 <- lm(clicked_on_ad ~ area_income + Age + daily_internet_usage + daily_time_spent_on_site + Male, data = dfb)

tidy(model1)
## # A tibble: 6 × 5
##   term                        estimate   std.error statistic   p.value
##   <chr>                          <dbl>       <dbl>     <dbl>     <dbl>
## 1 (Intercept)               2.31       0.0576          40.1  5.15e-210
## 2 area_income              -0.00000617 0.000000535    -11.5  5.56e- 29
## 3 Age                       0.00898    0.000828        10.8  5.61e- 26
## 4 daily_internet_usage     -0.00526    0.000187       -28.2  8.17e-129
## 5 daily_time_spent_on_site -0.0128     0.000506       -25.3  2.23e-109
## 6 Male                     -0.0293     0.0133          -2.20 2.84e-  2
# our coefficients are statistically significant since the p values are less than 0.05 indicating that changes in our variables have a relationship with changes in the clicks on ads
list(model1 = broom::glance(model1))
## $model1
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>   <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.824         0.823 0.210      931.       0     5   143. -272. -238.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
# 82% of the variation in clicks on ads is explained by area income,age,internet usage, time spent on site and male
# visualising our results
#load car package
library(car)
## Loading required package: carData
#produce added variable plots
avPlots(model1)

# most of the variables except male have some sort of linear relationship with clicked on ad variable
# incorporating the interaction effect into our model
model2 <- lm(clicked_on_ad~daily_internet_usage*daily_time_spent_on_site, data=dfb)
model3 <- lm(clicked_on_ad~daily_time_spent_on_site*area_income, data=dfb)
model4 <- lm(clicked_on_ad~daily_internet_usage*Age, data=dfb)
model5 <- lm(clicked_on_ad~daily_time_spent_on_site*Age, data=dfb)
model6 <- lm(clicked_on_ad~daily_internet_usage*area_income, data=dfb)
model7 <- lm(clicked_on_ad~daily_internet_usage*Male, data=dfb)
model8 <- lm(clicked_on_ad~daily_time_spent_on_site*Male, data=dfb)
model9 <- lm(clicked_on_ad~area_income*Age, data=dfb)
model10 <- lm(clicked_on_ad~area_income*Male, data=dfb)
model11 <- lm(clicked_on_ad~Age*Male, data=dfb)
tidy(model2)
## # A tibble: 4 × 5
##   term                                     estimate std.error statistic  p.value
##   <chr>                                       <dbl>     <dbl>     <dbl>    <dbl>
## 1 (Intercept)                               1.55e+0 0.189         8.24  5.33e-16
## 2 daily_internet_usage                     -2.34e-4 0.00111      -0.211 8.33e- 1
## 3 daily_time_spent_on_site                  1.26e-3 0.00295       0.426 6.70e- 1
## 4 daily_internet_usage:daily_time_spent_o… -9.07e-5 0.0000165    -5.50  4.89e- 8
tidy(model3)
## # A tibble: 4 × 5
##   term                                     estimate std.error statistic  p.value
##   <chr>                                       <dbl>     <dbl>     <dbl>    <dbl>
## 1 (Intercept)                           0.656         1.83e-1      3.59 3.49e- 4
## 2 daily_time_spent_on_site              0.00793       2.96e-3      2.68 7.56e- 3
## 3 area_income                           0.0000239     3.49e-6      6.87 1.16e-11
## 4 daily_time_spent_on_site:area_income -0.000000546   5.48e-8     -9.97 2.24e-22
tidy(model4)
## # A tibble: 4 × 5
##   term                      estimate std.error statistic  p.value
##   <chr>                        <dbl>     <dbl>     <dbl>    <dbl>
## 1 (Intercept)               2.39     0.208         11.5  7.83e-29
## 2 daily_internet_usage     -0.0132   0.00113      -11.8  5.72e-30
## 3 Age                      -0.0116   0.00537       -2.17 3.03e- 2
## 4 daily_internet_usage:Age  0.000144 0.0000301      4.77 2.11e- 6
tidy(model5)
## # A tibble: 4 × 5
##   term                          estimate std.error statistic  p.value
##   <chr>                            <dbl>     <dbl>     <dbl>    <dbl>
## 1 (Intercept)                   2.80     0.207         13.5  2.70e-38
## 2 daily_time_spent_on_site     -0.0444   0.00313      -14.2  7.87e-42
## 3 Age                          -0.0243   0.00529       -4.59 4.88e- 6
## 4 daily_time_spent_on_site:Age  0.000637 0.0000825      7.73 2.64e-14
tidy(model6)
## # A tibble: 4 × 5
##   term                                 estimate    std.error statistic  p.value
##   <chr>                                   <dbl>        <dbl>     <dbl>    <dbl>
## 1 (Intercept)                       1.22        0.181            6.71  3.25e-11
## 2 daily_internet_usage             -0.000810    0.00106         -0.762 4.46e- 1
## 3 area_income                       0.0000141   0.00000338       4.18  3.16e- 5
## 4 daily_internet_usage:area_income -0.000000133 0.0000000192    -6.96  6.25e-12
tidy(model7)
## # A tibble: 4 × 5
##   term                        estimate std.error statistic   p.value
##   <chr>                          <dbl>     <dbl>     <dbl>     <dbl>
## 1 (Intercept)                2.11       0.0569     37.2    1.80e-190
## 2 daily_internet_usage      -0.00893    0.000309  -28.9    6.82e-134
## 3 Male                      -0.00484    0.0827     -0.0585 9.53e-  1
## 4 daily_internet_usage:Male -0.0000621  0.000446   -0.139  8.89e-  1
tidy(model8)
## # A tibble: 4 × 5
##   term                           estimate std.error statistic   p.value
##   <chr>                             <dbl>     <dbl>     <dbl>     <dbl>
## 1 (Intercept)                    2.03      0.0626      32.5   3.11e-158
## 2 daily_time_spent_on_site      -0.0232    0.000932   -24.9   1.85e-106
## 3 Male                           0.0108    0.0885       0.122 9.03e-  1
## 4 daily_time_spent_on_site:Male -0.000970  0.00132     -0.733 4.64e-  1
tidy(model9)
## # A tibble: 4 × 5
##   term                estimate   std.error statistic  p.value
##   <chr>                  <dbl>       <dbl>     <dbl>    <dbl>
## 1 (Intercept)      1.98        0.238            8.30 3.29e-16
## 2 area_income     -0.0000439   0.00000439     -10.0  1.75e-22
## 3 Age             -0.0156      0.00602         -2.60 9.58e- 3
## 4 area_income:Age  0.000000764 0.000000113      6.75 2.55e-11
tidy(model10)
## # A tibble: 4 × 5
##   term                estimate  std.error statistic  p.value
##   <chr>                  <dbl>      <dbl>     <dbl>    <dbl>
## 1 (Intercept)       1.52       0.0790        19.3   1.33e-70
## 2 area_income      -0.0000183  0.00000139   -13.1   2.47e-36
## 3 Male             -0.0987     0.118         -0.835 4.04e- 1
## 4 area_income:Male  0.00000111 0.00000209     0.533 5.94e- 1
tidy(model11)
## # A tibble: 4 × 5
##   term        estimate std.error statistic  p.value
##   <chr>          <dbl>     <dbl>     <dbl>    <dbl>
## 1 (Intercept) -0.456     0.0823     -5.54  3.77e- 8
## 2 Age          0.0269    0.00221    12.2   6.56e-32
## 3 Male        -0.106     0.116      -0.914 3.61e- 1
## 4 Age:Male     0.00219   0.00314     0.696 4.86e- 1
# not all the coefficients for models 2,6,7,8,10 and 11 are statistically significant
list(model1 = broom::glance(model1), 
     model2 = broom::glance(model2),
     model3 = broom::glance(model3),
     model4 = broom::glance(model4),
     model5 = broom::glance(model5),
     model6 = broom::glance(model6),
     model7 = broom::glance(model7),
     model8 = broom::glance(model8),
     model9 = broom::glance(model9),
     model10 = broom::glance(model10),
     model11 = broom::glance(model11))
## $model1
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>   <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.824         0.823 0.210      931.       0     5   143. -272. -238.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
## 
## $model2
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>   <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.784         0.783 0.233     1202.       0     3   39.3 -68.6 -44.1
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
## 
## $model3
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic   p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>     <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.659         0.658 0.292      643. 2.44e-232     3  -187.  385.  409.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
## 
## $model4
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic   p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>     <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.674         0.673 0.286      687. 7.26e-242     3  -165.  341.  365.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
## 
## $model5
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic   p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>     <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.648         0.647 0.297      611. 3.22e-225     3  -204.  418.  442.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
## 
## $model6
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic   p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>     <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.684         0.683 0.282      719. 1.16e-248     3  -150.  309.  334.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
## 
## $model7
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic   p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>     <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.619         0.618 0.309      539. 4.47e-208     3  -243.  497.  521.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
## 
## $model8
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic   p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>     <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.563         0.561 0.331      427. 2.60e-178     3  -312.  635.  659.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
## 
## $model9
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic   p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>     <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.423         0.422 0.380      244. 1.43e-118     3  -451.  911.  936.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
## 
## $model10
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic  p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>    <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.228         0.226 0.440      98.3 9.84e-56     3  -596. 1202. 1227.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
## 
## $model11
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic  p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>    <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.244         0.241 0.436      107. 4.79e-60     3  -586. 1182. 1207.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
# model 1 has the highest performance compared to the other 10 models with 82% adjusted r square and the lowest RSE of 0.21

b.)DECISION TREES

#Loading libraries
library(caTools)
library(party)
## Loading required package: grid
## Loading required package: mvtnorm
## Loading required package: modeltools
## Loading required package: stats4
## 
## Attaching package: 'modeltools'
## The following object is masked from 'package:car':
## 
##     Predict
## Loading required package: strucchange
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## Loading required package: sandwich
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following object is masked from 'package:car':
## 
##     recode
## The following objects are masked from 'package:data.table':
## 
##     between, first, last
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(magrittr)
library(rpart)
library(caret)
## Loading required package: ggplot2
library(rpart.plot)
library(rattle)
## Loading required package: tibble
## Loading required package: bitops
## Rattle: A free graphical interface for data science with R.
## Version 5.5.1 Copyright (c) 2006-2021 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.
# creating a matrix from the relevant columns to construct our decision tree
dfe <- cbind(time,age,income,internet,male,ad)
head(dfe)
##       time age   income internet male ad
## [1,] 68.95  35 61833.90   256.09    0  0
## [2,] 80.23  31 68441.85   193.77    1  0
## [3,] 69.47  26 59785.94   236.50    0  0
## [4,] 74.15  29 54806.18   245.89    1  0
## [5,] 68.37  35 73889.99   225.58    0  0
## [6,] 59.99  23 59761.56   226.74    1  0
# converting the matrix to a data frame
dff <- as.data.frame(dfe)
head(dff)
##    time age   income internet male ad
## 1 68.95  35 61833.90   256.09    0  0
## 2 80.23  31 68441.85   193.77    1  0
## 3 69.47  26 59785.94   236.50    0  0
## 4 74.15  29 54806.18   245.89    1  0
## 5 68.37  35 73889.99   225.58    0  0
## 6 59.99  23 59761.56   226.74    1  0
# shuffling our dataset to ensure every input has a chance of being selected to be part of the training data
shuffle_index <- sample(1:nrow(dff))
head(shuffle_index)
## [1] 256 670 493 612 243  22
dff <- dff[shuffle_index, ]
head(dff)
##      time age   income internet male ad
## 256 81.03  28 63727.50   201.15    0  0
## 670 62.18  33 65899.68   126.44    0  1
## 493 59.88  30 75535.14   193.63    1  0
## 612 39.50  31 49911.25   148.19    1  1
## 243 85.84  32 62204.93   192.85    1  0
## 22  84.59  35 60015.57   226.54    1  0
# creating the train and test set using 80:20 split rule
train_test <- function(dff, size = 0.8, train = TRUE) {
    n_row = nrow(dff)
    total_row = 703
    train_sample <- 1:703
    if (train == TRUE) {
        return (dff[train_sample, ])
    } else {
        return (dff[-train_sample, ])
    }
}
# checking the dimensions of our train and test sets for accuracy  
data_train <- train_test(dff, 0.8, train = TRUE)
data_test <- train_test(dff, 0.8, train = FALSE)
dim(data_train)
## [1] 703   6
dim(data_test)
## [1] 297   6
library(rpart)
library(rpart.plot)
fit <- rpart(ad~., data = data_train, method = 'class')
rpart.plot(fit, extra = 106)

# from our tree we can tell that those people whose daily internet usage is less than 180, daily time spent on the site is less than 55 and whose area income is less than 37000 clicked on the ad 
predict_unseen <-predict(fit, data_test, type = 'class')
table_mat <- table(data_test$ad, predict_unseen)
table_mat
##    predict_unseen
##       0   1
##   0 133   8
##   1  11 145
# the model classified 143 and 140 people to have not clicked the ad correctly
# it also misclassified 14 clicks as people who clicked whereas they did not click on the ads
accuracy_Test <- sum(diag(table_mat)) / sum(table_mat)
print(paste('Accuracy for test', accuracy_Test))
## [1] "Accuracy for test 0.936026936026936"
# our model has an accuracy of 95.2862%
library(mlr)
## Loading required package: ParamHelpers
## Warning message: 'mlr' is in 'maintenance-only' mode since July 2019.
## Future development will only happen in 'mlr3'
## (<https://mlr3.mlr-org.com>). Due to the focus on 'mlr3' there might be
## uncaught bugs meanwhile in {mlr} - please consider switching.
## 
## Attaching package: 'mlr'
## The following object is masked from 'package:caret':
## 
##     train
getParamSet("classif.rpart")
##                    Type len  Def   Constr Req Tunable Trafo
## minsplit        integer   -   20 1 to Inf   -    TRUE     -
## minbucket       integer   -    - 1 to Inf   -    TRUE     -
## cp              numeric   - 0.01   0 to 1   -    TRUE     -
## maxcompete      integer   -    4 0 to Inf   -    TRUE     -
## maxsurrogate    integer   -    5 0 to Inf   -    TRUE     -
## usesurrogate   discrete   -    2    0,1,2   -    TRUE     -
## surrogatestyle discrete   -    0      0,1   -    TRUE     -
## maxdepth        integer   -   30  1 to 30   -    TRUE     -
## xval            integer   -   10 0 to Inf   -   FALSE     -
## parms           untyped   -    -        -   -    TRUE     -
#make tree learner
makeatree <- makeLearner("classif.rpart", predict.type = "response")

#setting to 3 fold cross validation
set_cv <- makeResampleDesc("CV",iters = 3L)
#Search for hyperparameters
gs <- makeParamSet(
makeIntegerParam("minsplit",lower = 10, upper = 50),
makeIntegerParam("minbucket", lower = 5, upper = 50),
makeNumericParam("cp", lower = 0.001, upper = 0.2)
)
#do a grid search
gscontrol <- makeTuneControlGrid()

#hypertune the parameters
dff$ad <- as.factor(dff$ad)
trainTask <- makeClassifTask(data = dff,target = "ad")
stune <- tuneParams(learner = makeatree, resampling = set_cv, task = trainTask, par.set = gs, control = gscontrol, measures = acc)
## [Tune] Started tuning learner classif.rpart for parameter set:
##              Type len Def       Constr Req Tunable Trafo
## minsplit  integer   -   -     10 to 50   -    TRUE     -
## minbucket integer   -   -      5 to 50   -    TRUE     -
## cp        numeric   -   - 0.001 to 0.2   -    TRUE     -
## With control class: TuneControlGrid
## Imputation value: -0
## [Tune-x] 1: minsplit=10; minbucket=5; cp=0.001
## [Tune-y] 1: acc.test.mean=0.9450019; time: 0.0 min
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## [Tune-y] 8: acc.test.mean=0.9420079; time: 0.0 min
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## [Tune-y] 9: acc.test.mean=0.9350009; time: 0.0 min
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## [Tune-y] 10: acc.test.mean=0.9269929; time: 0.0 min
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## [Tune-y] 11: acc.test.mean=0.9460089; time: 0.0 min
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## [Tune-y] 930: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 931: minsplit=10; minbucket=20; cp=0.2
## [Tune-y] 931: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 932: minsplit=14; minbucket=20; cp=0.2
## [Tune-y] 932: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 933: minsplit=19; minbucket=20; cp=0.2
## [Tune-y] 933: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 934: minsplit=23; minbucket=20; cp=0.2
## [Tune-y] 934: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 935: minsplit=28; minbucket=20; cp=0.2
## [Tune-y] 935: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 936: minsplit=32; minbucket=20; cp=0.2
## [Tune-y] 936: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 937: minsplit=37; minbucket=20; cp=0.2
## [Tune-y] 937: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 938: minsplit=41; minbucket=20; cp=0.2
## [Tune-y] 938: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 939: minsplit=46; minbucket=20; cp=0.2
## [Tune-y] 939: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 940: minsplit=50; minbucket=20; cp=0.2
## [Tune-y] 940: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 941: minsplit=10; minbucket=25; cp=0.2
## [Tune-y] 941: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 942: minsplit=14; minbucket=25; cp=0.2
## [Tune-y] 942: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 943: minsplit=19; minbucket=25; cp=0.2
## [Tune-y] 943: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 944: minsplit=23; minbucket=25; cp=0.2
## [Tune-y] 944: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 945: minsplit=28; minbucket=25; cp=0.2
## [Tune-y] 945: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 946: minsplit=32; minbucket=25; cp=0.2
## [Tune-y] 946: acc.test.mean=0.8969928; time: 0.0 min
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## [Tune-y] 947: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 948: minsplit=41; minbucket=25; cp=0.2
## [Tune-y] 948: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 949: minsplit=46; minbucket=25; cp=0.2
## [Tune-y] 949: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 950: minsplit=50; minbucket=25; cp=0.2
## [Tune-y] 950: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 951: minsplit=10; minbucket=30; cp=0.2
## [Tune-y] 951: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 952: minsplit=14; minbucket=30; cp=0.2
## [Tune-y] 952: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 953: minsplit=19; minbucket=30; cp=0.2
## [Tune-y] 953: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 954: minsplit=23; minbucket=30; cp=0.2
## [Tune-y] 954: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 955: minsplit=28; minbucket=30; cp=0.2
## [Tune-y] 955: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 956: minsplit=32; minbucket=30; cp=0.2
## [Tune-y] 956: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 957: minsplit=37; minbucket=30; cp=0.2
## [Tune-y] 957: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 958: minsplit=41; minbucket=30; cp=0.2
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## [Tune-x] 959: minsplit=46; minbucket=30; cp=0.2
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## [Tune-x] 960: minsplit=50; minbucket=30; cp=0.2
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## [Tune-x] 961: minsplit=10; minbucket=35; cp=0.2
## [Tune-y] 961: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 962: minsplit=14; minbucket=35; cp=0.2
## [Tune-y] 962: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 963: minsplit=19; minbucket=35; cp=0.2
## [Tune-y] 963: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 964: minsplit=23; minbucket=35; cp=0.2
## [Tune-y] 964: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 965: minsplit=28; minbucket=35; cp=0.2
## [Tune-y] 965: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 966: minsplit=32; minbucket=35; cp=0.2
## [Tune-y] 966: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 967: minsplit=37; minbucket=35; cp=0.2
## [Tune-y] 967: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 968: minsplit=41; minbucket=35; cp=0.2
## [Tune-y] 968: acc.test.mean=0.8969928; time: 0.0 min
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## [Tune-y] 970: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 971: minsplit=10; minbucket=40; cp=0.2
## [Tune-y] 971: acc.test.mean=0.8969928; time: 0.0 min
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## [Tune-y] 972: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 973: minsplit=19; minbucket=40; cp=0.2
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## [Tune-x] 974: minsplit=23; minbucket=40; cp=0.2
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## [Tune-x] 975: minsplit=28; minbucket=40; cp=0.2
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## [Tune-x] 976: minsplit=32; minbucket=40; cp=0.2
## [Tune-y] 976: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 977: minsplit=37; minbucket=40; cp=0.2
## [Tune-y] 977: acc.test.mean=0.8969928; time: 0.0 min
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## [Tune-y] 978: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 979: minsplit=46; minbucket=40; cp=0.2
## [Tune-y] 979: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 980: minsplit=50; minbucket=40; cp=0.2
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## [Tune-x] 981: minsplit=10; minbucket=45; cp=0.2
## [Tune-y] 981: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 982: minsplit=14; minbucket=45; cp=0.2
## [Tune-y] 982: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 983: minsplit=19; minbucket=45; cp=0.2
## [Tune-y] 983: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 984: minsplit=23; minbucket=45; cp=0.2
## [Tune-y] 984: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 985: minsplit=28; minbucket=45; cp=0.2
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## [Tune-y] 990: acc.test.mean=0.8969928; time: 0.0 min
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## [Tune-y] 992: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 993: minsplit=19; minbucket=50; cp=0.2
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## [Tune-x] 994: minsplit=23; minbucket=50; cp=0.2
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## [Tune-x] 995: minsplit=28; minbucket=50; cp=0.2
## [Tune-y] 995: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 996: minsplit=32; minbucket=50; cp=0.2
## [Tune-y] 996: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 997: minsplit=37; minbucket=50; cp=0.2
## [Tune-y] 997: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 998: minsplit=41; minbucket=50; cp=0.2
## [Tune-y] 998: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 999: minsplit=46; minbucket=50; cp=0.2
## [Tune-y] 999: acc.test.mean=0.8969928; time: 0.0 min
## [Tune-x] 1000: minsplit=50; minbucket=50; cp=0.2
## [Tune-y] 1000: acc.test.mean=0.8969928; time: 0.0 min
## [Tune] Result: minsplit=14; minbucket=20; cp=0.001 : acc.test.mean=0.9460119
#checking for the best parameters
stune$x
## $minsplit
## [1] 14
## 
## $minbucket
## [1] 20
## 
## $cp
## [1] 0.001
# checking for other detailed parameters
rpart.control(minsplit = 19, minbucket = 5, maxdepth = 30, cp = 0.001)
## $minsplit
## [1] 19
## 
## $minbucket
## [1] 5
## 
## $cp
## [1] 0.001
## 
## $maxcompete
## [1] 4
## 
## $maxsurrogate
## [1] 5
## 
## $usesurrogate
## [1] 2
## 
## $surrogatestyle
## [1] 0
## 
## $maxdepth
## [1] 30
## 
## $xval
## [1] 10
# writing the function to display the accuracy score
accuracy_tune <- function(fit) {
    predict_unseen <- predict(fit, data_test, type = 'class')
    table_mat <- table(data_test$ad, predict_unseen)
    accuracy_Test <- sum(diag(table_mat)) / sum(table_mat)
    accuracy_Test
}
# implementing our parameters and checking the accuracy score
control <- rpart.control(minsplit = 19,
    minbucket = 5,
    maxdepth = 30,
    cp = 0.001)
tune_fit <- rpart(ad~., data = data_train, method = 'class', control = control)
accuracy_tune(tune_fit)
## [1] 0.9461279
# our accuracy remains the same with hyperparameter tuning at 95.2862%

8.)CONCLUSIONS: a.)The correlation between age and clicks is a moderately positive one indicating that as age increases the more likely the clicks are made

b.)The correlation between area income and clicks on ads is a weak negative one indicating that as area income decreases the more likely the clicks are made

c.)The correlation between the daily internet usage and clicks on ads is a strong negative one indicating that as internet use decreases the more likely the clicks will be made

d.)The correlation between the daily time spent on site and clicks on ads is a strong negative one indicating that as daily time spent decreases the more likely the clicks will be made

e.)THE DECISION TREE PERFORMS BEST WHEN COMPARED TO THE MULTIPLE LINEAR REGRESSION MODEL AS IT IS ABLE TO PREDICT 95.2862% ON WHETHER ADS WERE CLICKED COMPARED TO THE REGRESSION MODEL THAT JUST TELLS US VIA THE ADJUSTED R-SQUARE THAT 82% OF THE VARIANCE IN ADS CLICKED IS EXPLAINED BY THE INDEPENDENT VARIABLES

9.)RECOMMENDATIONS: Since our data has revealed the correlation between the relevant columns and clicks on ads we are able to conclude that the entrepreneur should focus on:

a.The older population since the correlation between age and clicks is a moderately positive one indicating that as age increases the more likely the clicks are made

b.The regions with a lower Area income since the correlation between area income and clicks on ads is a weak negative one indicating that as area income decreases the more likely the clicks are made

c.The regions with low daily internet usage since the correlation between the daily internet usage and clicks on ads is a strong negative one indicating that as internet use decreases the more likely the clicks will be made

d.The regions with low daily time spent on site since the correlation between the daily time spent on site and clicks on ads is a strong negative one indicating that as daily time spent decreases the more likely the clicks will be made