Core Module 3 Week 1 IP
Jane Ngala
2022-05-28
1. Defining the Question
(a) Specifying the Question
To identify which individuals are most likely to click on the advertisements
(b) Metric of Success
The project will be considered a success if individuals most likely to click on the ads.can be identified
(c) Understanding the context
A Kenyan entrepreneur has created an online cryptography course and would want to advertise it on her blog. She currently targets audiences originating from various countries. In the past, she ran ads to advertise a related course on the same blog and collected data in the process. She would now like to employ your services as a Data Science Consultant to help her identify which individuals are most likely to click on her ads.
(d) Experimental Design
Load the dataset
Find and deal with outliers, anomalies, and missing data within the dataset.
Perform univariate and bivariate analysis.
Provide a conclusion and recommendation.
(e) Appropriateness of Data
The data is appropriate and reliable.
# Loading data set
url<-"http://bit.ly/IPAdvertisingData"
Advert_data<-read.csv(url)
head(Advert_data)## 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 the dimensions of dataset
dim(Advert_data)## [1] 1000 10-The dataset contains 1000 rows and 10 columns
# Checking for number of missing data
length(which(is.na(Advert_data)))## [1] 0-No Missing values in the dataset
# Checking class of columns in dataset
sapply(Advert_data, class)## Daily.Time.Spent.on.Site Age Area.Income
## "numeric" "integer" "numeric"
## Daily.Internet.Usage Ad.Topic.Line City
## "numeric" "character" "character"
## Male Country Timestamp
## "integer" "character" "character"
## Clicked.on.Ad
## "integer"# Selecting the Numerical columns
num_cols<-unlist(lapply(Advert_data,is.numeric))
data_num<-Advert_data[ , num_cols]
data_num## Daily.Time.Spent.on.Site Age Area.Income Daily.Internet.Usage Male
## 1 68.95 35 61833.90 256.09 0
## 2 80.23 31 68441.85 193.77 1
## 3 69.47 26 59785.94 236.50 0
## 4 74.15 29 54806.18 245.89 1
## 5 68.37 35 73889.99 225.58 0
## 6 59.99 23 59761.56 226.74 1
## 7 88.91 33 53852.85 208.36 0
## 8 66.00 48 24593.33 131.76 1
## 9 74.53 30 68862.00 221.51 1
## 10 69.88 20 55642.32 183.82 1
## 11 47.64 49 45632.51 122.02 0
## 12 83.07 37 62491.01 230.87 1
## 13 69.57 48 51636.92 113.12 1
## 14 79.52 24 51739.63 214.23 0
## 15 42.95 33 30976.00 143.56 0
## 16 63.45 23 52182.23 140.64 1
## 17 55.39 37 23936.86 129.41 0
## 18 82.03 41 71511.08 187.53 0
## 19 54.70 36 31087.54 118.39 1
## 20 74.58 40 23821.72 135.51 1
## 21 77.22 30 64802.33 224.44 1
## 22 84.59 35 60015.57 226.54 1
## 23 41.49 52 32635.70 164.83 0
## 24 87.29 36 61628.72 209.93 1
## 25 41.39 41 68962.32 167.22 0
## 26 78.74 28 64828.00 204.79 1
## 27 48.53 28 38067.08 134.14 1
## 28 51.95 52 58295.82 129.23 0
## 29 70.20 34 32708.94 119.20 0
## 30 76.02 22 46179.97 209.82 0
## 31 67.64 35 51473.28 267.01 1
## 32 86.41 28 45593.93 207.48 1
## 33 59.05 57 25583.29 169.23 1
## 34 55.60 23 30227.98 212.58 0
## 35 57.64 57 45580.92 133.81 1
## 36 84.37 30 61389.50 201.58 0
## 37 62.26 53 56770.79 125.45 1
## 38 65.82 39 76435.30 221.94 0
## 39 50.43 46 57425.87 119.32 1
## 40 38.93 39 27508.41 162.08 0
## 41 84.98 29 57691.95 202.61 0
## 42 64.24 30 59784.18 252.36 0
## 43 82.52 32 66572.39 198.11 1
## 44 81.38 31 64929.61 212.30 0
## 45 80.47 25 57519.64 204.86 0
## 46 37.68 52 53575.48 172.83 1
## 47 69.62 20 50983.75 202.25 1
## 48 85.40 43 67058.72 198.72 0
## 49 44.33 37 52723.34 123.72 1
## 50 48.01 46 54286.10 119.93 0
## 51 73.18 23 61526.25 196.71 1
## 52 79.94 28 58526.04 225.29 0
## 53 33.33 45 53350.11 193.58 1
## 54 50.33 50 62657.53 133.20 1
## 55 62.31 47 62722.57 119.30 0
## 56 80.60 31 67479.62 177.55 0
## 57 65.19 36 75254.88 150.61 0
## 58 44.98 49 52336.64 129.31 0
## 59 77.63 29 56113.37 239.22 0
## 60 41.82 41 24852.90 156.36 0
## 61 85.61 27 47708.42 183.43 0
## 62 85.84 34 64654.66 192.93 1
## 63 72.08 29 71228.44 169.50 0
## 64 86.06 32 61601.05 178.92 1
## 65 45.96 45 66281.46 141.22 0
## 66 62.42 29 73910.90 198.50 1
## 67 63.89 40 51317.33 105.22 0
## 68 35.33 32 51510.18 200.22 0
## 69 75.74 25 61005.87 215.25 1
## 70 78.53 34 32536.98 131.72 0
## 71 46.13 31 60248.97 139.01 0
## 72 69.01 46 74543.81 222.63 0
## 73 55.35 39 75509.61 153.17 1
## 74 33.21 43 42650.32 167.07 1
## 75 38.46 42 58183.04 145.98 1
## 76 64.10 22 60465.72 215.93 0
## 77 49.81 35 57009.76 120.06 1
## 78 82.73 33 54541.56 238.99 1
## 79 56.14 38 32689.04 113.53 1
## 80 55.13 45 55605.92 111.71 0
## 81 78.11 27 63296.87 209.25 1
## 82 73.46 28 65653.47 222.75 1
## 83 56.64 38 61652.53 115.91 0
## 84 68.94 54 30726.26 138.71 0
## 85 70.79 31 74535.94 184.10 0
## 86 57.76 41 47861.93 105.15 0
## 87 77.51 36 73600.28 200.55 0
## 88 52.70 34 58543.94 118.60 1
## 89 57.70 34 42696.67 109.07 0
## 90 56.89 37 37334.78 109.29 1
## 91 69.90 43 71392.53 138.35 0
## 92 55.79 24 59550.05 149.67 0
## 93 70.03 26 64264.25 227.72 1
## 94 50.08 40 64147.86 125.85 1
## 95 43.67 31 25686.34 166.29 1
## 96 72.84 26 52968.22 238.63 0
## 97 45.72 36 22473.08 154.02 1
## 98 39.94 41 64927.19 156.30 0
## 99 35.61 46 51868.85 158.22 0
## 100 79.71 34 69456.83 211.65 1
## 101 41.49 53 31947.65 169.18 0
## 102 63.60 23 51864.77 235.28 1
## 103 89.91 40 59593.56 194.23 0
## 104 68.18 21 48376.14 218.17 1
## 105 66.49 20 56884.74 202.16 0
## 106 80.49 40 67186.54 229.12 1
## 107 72.23 25 46557.92 241.03 1
## 108 42.39 42 66541.05 150.99 0
## 109 47.53 30 33258.09 135.18 0
## 110 74.02 32 72272.90 210.54 0
## 111 66.63 60 60333.38 176.98 0
## 112 63.24 53 65229.13 235.78 1
## 113 71.00 22 56067.38 211.87 0
## 114 46.13 46 37838.72 123.64 1
## 115 69.00 32 72683.35 221.21 1
## 116 76.99 31 56729.78 244.34 1
## 117 72.60 55 66815.54 162.95 0
## 118 61.88 42 60223.52 112.19 1
## 119 84.45 50 29727.79 207.18 0
## 120 88.97 45 49269.98 152.49 0
## 121 86.19 31 57669.41 210.26 1
## 122 49.58 26 56791.75 231.94 0
## 123 77.65 27 63274.88 212.79 0
## 124 37.75 36 35466.80 225.24 0
## 125 62.33 43 68787.09 127.11 0
## 126 79.57 31 61227.59 230.93 0
## 127 80.31 44 56366.88 127.07 0
## 128 89.05 45 57868.44 206.98 0
## 129 70.41 27 66618.21 223.03 0
## 130 67.36 37 73104.47 233.56 0
## 131 46.98 50 21644.91 175.37 0
## 132 41.67 36 53817.02 132.55 0
## 133 51.24 36 76368.31 176.73 0
## 134 75.70 29 67633.44 215.44 0
## 135 43.49 47 50335.46 127.83 0
## 136 49.89 39 17709.98 160.03 1
## 137 38.37 36 41229.16 140.46 0
## 138 38.52 38 42581.23 137.28 1
## 139 71.89 23 61617.98 172.81 1
## 140 75.80 38 70575.60 146.19 1
## 141 83.86 31 64122.36 190.25 0
## 142 37.51 30 52097.32 163.00 1
## 143 55.60 44 65953.76 124.38 1
## 144 83.67 44 60192.72 234.26 1
## 145 69.08 41 77460.07 210.60 0
## 146 37.47 44 45716.48 141.89 1
## 147 56.04 49 65120.86 128.95 1
## 148 70.92 41 49995.63 108.16 1
## 149 49.78 46 71718.51 152.24 0
## 150 68.61 57 61770.34 150.29 0
## 151 58.18 25 69112.84 176.28 1
## 152 78.54 35 72524.86 172.10 0
## 153 37.00 48 36782.38 158.22 1
## 154 65.40 33 66699.12 247.31 0
## 155 79.52 27 64287.78 183.48 1
## 156 87.98 38 56637.59 222.11 1
## 157 44.64 36 55787.58 127.01 0
## 158 41.73 28 61142.33 202.18 1
## 159 80.46 27 61625.87 207.96 1
## 160 75.55 36 73234.87 159.24 0
## 161 76.32 35 74166.24 195.31 1
## 162 82.68 33 62669.59 222.77 1
## 163 72.01 31 57756.89 251.00 0
## 164 75.83 24 58019.64 162.44 0
## 165 41.28 50 50960.08 140.39 0
## 166 34.66 32 48246.60 194.83 0
## 167 66.18 55 28271.84 143.42 0
## 168 86.06 31 53767.12 219.72 1
## 169 59.59 42 43662.10 104.78 1
## 170 86.69 34 62238.58 198.56 0
## 171 43.77 52 49030.03 138.55 1
## 172 71.84 47 76003.47 199.79 1
## 173 80.23 31 68094.85 196.23 0
## 174 74.41 26 64395.85 163.05 0
## 175 63.36 48 70053.27 137.43 0
## 176 71.74 35 72423.97 227.56 0
## 177 60.72 44 42995.80 105.69 0
## 178 72.04 22 60309.58 199.43 0
## 179 44.57 31 38349.78 133.17 1
## 180 85.86 34 63115.34 208.23 0
## 181 39.85 38 31343.39 145.96 0
## 182 84.53 27 40763.13 168.34 0
## 183 62.95 60 36752.24 157.04 0
## 184 67.58 41 65044.59 255.61 1
## 185 85.56 29 53673.08 210.46 0
## 186 46.88 54 43444.86 136.64 0
## 187 46.31 57 44248.52 153.98 1
## 188 77.95 31 62572.88 233.65 1
## 189 84.73 30 39840.55 153.76 0
## 190 39.86 36 32593.59 145.85 0
## 191 50.08 30 41629.86 123.91 0
## 192 60.23 35 43313.73 106.86 0
## 193 60.70 49 42993.48 110.57 1
## 194 43.67 53 46004.31 143.79 1
## 195 77.20 33 49325.48 254.05 1
## 196 71.86 32 51633.34 116.53 0
## 197 44.78 45 63363.04 137.24 1
## 198 78.57 36 64045.93 239.32 1
## 199 73.41 31 73049.30 201.26 1
## 200 77.05 27 66624.60 191.14 0
## 201 66.40 40 77567.85 214.42 0
## 202 69.35 29 53431.35 252.77 1
## 203 35.65 40 31265.75 172.58 1
## 204 70.04 31 74780.74 183.85 1
## 205 69.78 29 70410.11 218.79 0
## 206 58.22 29 37345.24 120.90 0
## 207 76.90 28 66107.84 212.67 0
## 208 84.08 30 62336.39 187.36 1
## 209 59.51 58 39132.64 140.83 0
## 210 40.15 38 38745.29 134.88 1
## 211 76.81 28 65172.22 217.85 1
## 212 41.89 38 68519.96 163.38 0
## 213 76.87 27 54774.77 235.35 1
## 214 67.28 43 76246.96 155.80 1
## 215 81.98 40 65461.92 229.22 0
## 216 66.01 23 34127.21 151.95 0
## 217 61.57 53 35253.98 125.94 1
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## 220 43.60 38 20856.54 170.49 0
## 221 77.88 37 55353.41 254.57 0
## 222 75.83 27 67516.07 200.59 0
## 223 49.95 39 68737.75 136.59 0
## 224 60.94 41 76893.84 154.97 0
## 225 89.15 42 59886.58 171.07 0
## 226 78.70 30 53441.69 133.99 0
## 227 57.35 29 41356.31 119.84 0
## 228 34.86 38 49942.66 154.75 0
## 229 70.68 31 74430.08 199.08 0
## 230 76.06 23 58633.63 201.04 0
## 231 66.67 33 72707.87 228.03 1
## 232 46.77 32 31092.93 136.40 1
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## 235 37.32 50 56735.14 199.25 1
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## 252 61.22 45 63883.81 119.03 1
## 253 84.54 33 64902.47 204.02 1
## 254 46.08 30 66784.81 164.63 1
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## 257 80.91 32 61608.23 231.42 0
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## 266 70.66 43 63450.96 120.95 1
## 267 70.58 26 56694.12 136.94 0
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## 271 44.49 53 63100.13 168.00 1
## 272 73.04 37 73687.50 221.79 1
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## 939 32.60 38 40159.20 190.05 0
## 940 60.83 19 40478.83 185.46 1
## 941 44.72 46 40468.53 123.86 1
## 942 78.76 51 66980.27 162.05 0
## 943 79.51 39 34942.26 125.11 1
## 944 39.30 32 48335.20 145.73 0
## 945 64.79 30 42251.59 116.07 0
## 946 89.80 36 57330.43 198.24 0
## 947 72.82 34 75769.82 191.82 1
## 948 38.65 31 51812.71 154.77 1
## 949 59.01 30 75265.96 178.75 1
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## 951 63.99 43 72802.42 138.46 0
## 952 41.35 27 39193.45 162.46 1
## 953 62.79 36 18368.57 231.87 1
## 954 45.53 29 56129.89 141.58 0
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## 960 85.35 37 64235.51 161.42 1
## 961 56.78 28 39939.39 124.32 0
## 962 78.67 26 63319.99 195.56 0
## 963 70.09 21 54725.87 211.17 0
## 964 60.75 42 69775.75 247.05 1
## 965 65.07 24 57545.56 233.85 0
## 966 35.25 50 47051.02 194.44 0
## 967 37.58 52 51600.47 176.70 1
## 968 68.01 25 68357.96 188.32 1
## 969 45.08 38 35349.26 125.27 0
## 970 63.04 27 69784.85 159.05 0
## 971 40.18 29 50760.23 151.96 0
## 972 45.17 48 34418.09 132.07 1
## 973 50.48 50 20592.99 162.43 0
## 974 80.87 28 63528.80 203.30 0
## 975 41.88 40 44217.68 126.11 1
## 976 39.87 48 47929.83 139.34 1
## 977 61.84 45 46024.29 105.63 1
## 978 54.97 31 51900.03 116.38 1
## 979 71.40 30 72188.90 166.31 0
## 980 70.29 31 56974.51 254.65 1
## 981 67.26 57 25682.65 168.41 1
## 982 76.58 46 41884.64 258.26 0
## 983 54.37 38 72196.29 140.77 0
## 984 82.79 32 54429.17 234.81 1
## 985 66.47 31 58037.66 256.39 1
## 986 72.88 44 64011.26 125.12 0
## 987 76.44 28 59967.19 232.68 1
## 988 63.37 43 43155.19 105.04 1
## 989 89.71 48 51501.38 204.40 1
## 990 70.96 31 55187.85 256.40 0
## 991 35.79 44 33813.08 165.62 1
## 992 38.96 38 36497.22 140.67 1
## 993 69.17 40 66193.81 123.62 0
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## 995 43.70 28 63126.96 173.01 0
## 996 72.97 30 71384.57 208.58 1
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## 998 51.63 51 42415.72 120.37 1
## 999 55.55 19 41920.79 187.95 0
## 1000 45.01 26 29875.80 178.35 0
## Clicked.on.Ad
## 1 0
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## 986 1
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## 996 1
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## 999 0
## 1000 1# Checking for outliers
boxplot(data_num)
-Outliers are present in the Area.Income column.
# Listing the outliers
boxplot.stats(data_num$Area.Income)$out## [1] 17709.98 18819.34 15598.29 15879.10 14548.06 13996.50 14775.50 18368.57- The outliers are valid, as income betwen different regions and different people can vary with a wide range _ We shall keep the outliers
# Statistical description of the numerical columns
summary(data_num)## Daily.Time.Spent.on.Site Age Area.Income Daily.Internet.Usage
## Min. :32.60 Min. :19.00 Min. :13996 Min. :104.8
## 1st Qu.:51.36 1st Qu.:29.00 1st Qu.:47032 1st Qu.:138.8
## Median :68.22 Median :35.00 Median :57012 Median :183.1
## Mean :65.00 Mean :36.01 Mean :55000 Mean :180.0
## 3rd Qu.:78.55 3rd Qu.:42.00 3rd Qu.:65471 3rd Qu.:218.8
## Max. :91.43 Max. :61.00 Max. :79485 Max. :270.0
## Male Clicked.on.Ad
## Min. :0.000 Min. :0.0
## 1st Qu.:0.000 1st Qu.:0.0
## Median :0.000 Median :0.5
## Mean :0.481 Mean :0.5
## 3rd Qu.:1.000 3rd Qu.:1.0
## Max. :1.000 Max. :1.0# Calculating Range in the numerical columns
# Daily.Time.Spent.on.Site
range_DTS<-91.43-32.60
range_DTS## [1] 58.83# Age
range_age<-61.00-19.00
range_age## [1] 42# Area.Income
range_Income<-79485-13996
range_Income## [1] 65489# Daily.Internet.Usage
range_DIU<-270.0-104.8
range_DIU## [1] 165.2# Univariate Analysis
# Measures of Central Tendency:Mode
getmode <- function(d) {
uniqd <- unique(d)
uniqd[which.max(tabulate(match(d, uniqd)))]
}
getmode(data_num$Daily.Time.Spent.on.Site)## [1] 62.26- Majority of the people spend 62.26 mins on the site
getmode(data_num$Area.Income)## [1] 61833.9-The most popular area income is 61833.9
getmode(data_num$Age)## [1] 31-Majority of people that visit the site are aged 31
getmode(data_num$Daily.Internet.Usage)## [1] 167.22-Most people had a daily internet usage of 167.22
getmode(data_num$Male)## [1] 0-Majority of the site visitors were Female
getmode(data_num$Clicked.on.Ad)## [1] 0-Majority of those that visted the site did not click on the Ad.
# Measures of Dispresion : Variance
var(data_num$Age)## [1] 77.18611- The age data is highly spread from its mean
# Frequency distribution for sex
sex_col<-data_num$Male
sex_freq<-table(sex_col)
sex_freq## sex_col
## 0 1
## 519 481- Out of those that visited the site 519 were Female and 481 Male
# Frequency distribution for age
age_col<-data_num$Age
age_freq<-table(age_col)
age_freq## age_col
## 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
## 6 6 6 13 19 21 27 37 33 48 48 39 60 38 43 39 39 50 36 37 30 36 32 26 23 21
## 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
## 30 18 13 16 18 20 12 15 10 9 7 2 6 4 2 4 1# Frequency distribution on clicks on te ad.
clicks<-data_num$Clicked.on.Ad
clicks_freq<-table(clicks)
clicks_freq## clicks
## 0 1
## 500 500- There was an equal number of people that clicked on the ad. and those who did not
# Histogram visualization of age
hist(data_num$Age)
# Bivariate Analysis
# correlation between the age and Male columns
age<-data_num$Age
sex<-data_num$Male
cor(age,sex)## [1] -0.02104406- Indicates a negative linear realtionship between sex and age
# Relationship between sex and Daily.Time.Spent.on.Site
DTSS<-data_num$Daily.Time.Spent.on.Site
cor(sex,DTSS)## [1] -0.01895085- Indicates a negative linear realtionship between sex and Daily time spent on Site
# Relationship between sex and Clicks
cor(sex,clicks)## [1] -0.03802747- Indicates a negative linear realtionship between sex and clicks on the ad.
# Relationship between age and clicks
cor(age,clicks)## [1] 0.4925313- Indicates a positive linear relationship between age and clicks on the ad.
# Correlation matrix
corr_matrix <- cor(data_num, method = c("pearson"))
round(corr_matrix, 2)## Daily.Time.Spent.on.Site Age Area.Income
## Daily.Time.Spent.on.Site 1.00 -0.33 0.31
## Age -0.33 1.00 -0.18
## Area.Income 0.31 -0.18 1.00
## Daily.Internet.Usage 0.52 -0.37 0.34
## Male -0.02 -0.02 0.00
## Clicked.on.Ad -0.75 0.49 -0.48
## Daily.Internet.Usage Male Clicked.on.Ad
## Daily.Time.Spent.on.Site 0.52 -0.02 -0.75
## Age -0.37 -0.02 0.49
## Area.Income 0.34 0.00 -0.48
## Daily.Internet.Usage 1.00 0.03 -0.79
## Male 0.03 1.00 -0.04
## Clicked.on.Ad -0.79 -0.04 1.00# Graphical Visualization
# Scatterplot showing relationship of age and Clicked on Ad.
plot(data_num$Age, data_num$Clicked.on.Ad, xlab = 'Age', ylab = 'Clicks')
# Scatter plot showing relationship of sex and Clicked on Ad.
plot(data_num$Male, data_num$Clicked.on.Ad, xlab = 'Sex', ylab = 'Clicks')
Conclusion:
- Females are more likely to click on the advertisement.
- Individuals of ages between 22-53 were the most active on the site and are more likely to click on the ad.
Recommendation:
- Work on the advert to attract more males
2. Modelling (i) Linear Regression
library(caTools)# Splitting data into train and test
split <- sample.split(data_num$Clicked.on.Ad, SplitRatio = 0.7)
train_set <- subset(data_num, split == "TRUE")
test_set <- subset(data_num, split == "FALSE")# Feature Scaling
train_scale<-scale(train_set)
test_scale<-scale(test_set)# Fitting Linear Regression Algorithm
regressor = lm(formula = Clicked.on.Ad ~ Daily.Time.Spent.on.Site + Daily.Internet.Usage + Age + Male, data = train_set)# Making Prediction
y_pred<-predict(regressor, data = test_set)
y_pred## 1 2 3 4 5 6
## 0.024263396 0.141398734 0.045669836 -0.078733968 0.200987492 0.173185561
## 7 8 9 10 11 13
## -0.010387763 0.834311228 0.059456871 0.244734341 1.188365369 0.887093808
## 14 15 21 22 23 24
## 0.009712411 0.993948981 0.005440249 -0.065628105 1.064830251 -0.002991737
## 25 26 27 28 29 30
## 0.955845790 0.074961214 0.890133419 1.114425609 0.754167519 0.065626557
## 32 35 36 37 38 40
## -0.047761107 1.020064021 0.064410643 0.965943514 0.292298455 1.001168094
## 41 44 46 47 49 50
## 0.041306624 0.056064861 1.040992327 0.146564838 1.086282604 1.168204200
## 51 54 55 56 58 59
## 0.153615788 1.064386191 0.979424998 0.259027481 1.185494599 -0.057603641
## 61 62 64 65 68 69
## 0.120746544 0.093653868 0.150295192 1.070570142 0.779224249 0.032852206
## 70 71 72 74 75 76
## 0.567853123 0.956698524 0.305472156 1.056160323 1.090018916 0.199494875
## 77 78 79 81 82 83
## 1.011770939 -0.125928131 0.985338266 0.050344052 0.049982665 0.998373849
## 85 88 90 91 93 94
## 0.360792733 0.970361467 0.989382241 0.732098309 0.053087917 1.020159721
## 97 98 100 102 103 105
## 0.890492972 1.036569562 0.076429519 0.075236097 0.115463533 0.224294378
## 106 107 109 113 114 115
## 0.021949451 -0.060222639 0.949336566 0.124894507 1.140927733 0.156550671
## 117 118 119 121 122 123
## 0.664235334 0.947362851 0.209047386 -0.033521578 0.350568764 0.070470720
## 125 126 128 130 131 132
## 0.900653134 -0.021412628 0.101289031 0.188771373 0.911722940 1.099284626
## 133 138 139 140 141 142
## 0.720611073 1.101902322 0.303804065 0.528421193 0.143015919 0.903321798
## 143 145 146 147 148 149
## 0.985996326 0.326778102 1.144208312 0.998734969 0.833667703 0.964800619
## 151 152 153 154 155 156
## 0.495100598 0.353448027 1.095934808 0.105024928 0.172895087 -0.062319266
## 157 160 161 162 163 164
## 1.088127241 0.475381778 0.223215312 -0.035609478 -0.025986224 0.347743194
## 165 167 169 170 171 172
## 1.185144255 0.862420442 1.020506443 0.083811290 1.144748202 0.367484764
## 173 174 175 177 179 181
## 0.161023613 0.382011997 0.873326090 1.050474523 0.977685792 1.068458446
## 182 184 186 188 189 190
## 0.219306413 0.065975291 1.162452856 -0.046875618 0.323553680 1.051255395
## 192 193 195 196 197 201
## 0.971385149 1.034752825 -0.131368529 0.727905197 1.075937122 0.334525251
## 202 203 204 205 206 209
## -0.049245545 0.964899581 0.339504544 0.165663473 0.869069408 0.997032936
## 210 211 212 213 215 216
## 1.092240303 0.029945495 0.943525237 -0.076420874 0.033660073 0.534960008
## 217 218 219 221 222 226
## 0.972939451 1.031936805 0.856318493 -0.075247357 0.163469652 0.517580378
## 227 228 229 233 234 235
## 0.887160363 1.090066009 0.279575096 0.762226287 -0.077799416 0.882414145
## 238 239 240 244 245 246
## 0.568165646 0.637835296 0.021694891 0.038885829 0.300211400 0.159855661
## 247 248 249 250 251 252
## 1.094601544 0.134770595 1.067805137 0.555323389 0.111079458 0.945358414
## 254 256 257 258 259 261
## 0.773799647 0.096085270 -0.034128662 1.072510931 0.021054480 0.122764329
## 262 264 265 266 267 269
## 0.955026143 1.191479092 -0.097677311 0.784329383 0.580129505 0.784662194
## 270 271 273 274 275 277
## 0.093360761 0.980746932 -0.086816814 0.465635814 -0.020138949 -0.017094579
## 278 279 280 281 282 283
## 0.110468398 0.287219246 0.078123586 1.109798840 0.718765230 1.101031377
## 285 287 288 289 290 291
## 1.128292538 0.838503460 0.082265627 1.056088335 0.536491318 0.714793456
## 292 293 294 296 297 298
## 0.029508276 0.753628872 -0.020440883 0.015828316 0.050693220 0.108808806
## 299 301 305 306 307 309
## 0.056505821 -0.018278803 1.093360054 0.167892429 0.013460850 0.158336420
## 310 311 312 313 315 317
## 0.913916595 0.066139664 0.207123198 0.295556533 -0.008332428 0.185513769
## 319 320 321 322 323 324
## 0.208609458 1.035442903 0.928130183 0.148418443 0.171064714 0.132168789
## 326 327 329 330 333 334
## 0.816720967 0.850958936 0.156945740 0.575920578 0.960326436 -0.107216874
## 335 336 337 339 340 341
## 0.164817103 1.092721540 0.164908972 0.157983640 0.199265719 1.070901774
## 342 343 344 345 347 348
## 0.870582946 -0.079691660 -0.002508884 0.709428613 0.071569584 0.951412162
## 349 350 352 354 355 356
## 0.368609405 0.389069069 0.065110844 0.133855279 0.804597543 -0.066755487
## 357 358 361 362 363 364
## 1.060726922 1.126702557 0.977544453 0.941832991 0.121899642 0.603754258
## 365 366 367 368 371 372
## 0.186612900 0.757997710 0.224350759 -0.072987655 1.089042480 1.119660887
## 373 374 375 376 377 378
## 0.069613604 1.128442819 0.132304578 0.096868726 -0.086326946 0.813495805
## 379 380 381 385 386 388
## 0.730256234 -0.100966221 -0.004304640 0.790469582 0.054271567 1.079236394
## 389 390 391 392 395 397
## 0.203864696 0.780867165 -0.020545009 0.170306750 0.851997186 0.961200717
## 398 399 400 401 402 403
## 0.422701372 0.251885504 0.106130637 1.061111051 -0.067414849 1.103396552
## 405 408 409 411 412 413
## 1.072455141 0.868054684 0.376837307 0.718015713 0.099844935 0.139085156
## 415 416 417 418 419 420
## 0.034397087 1.153037033 0.715709140 0.097627810 0.172123786 0.528526429
## 421 422 424 426 427 428
## 1.058135183 0.068579362 0.842835714 0.925522127 0.772864897 -0.037608171
## 429 431 432 433 434 435
## 0.823435321 -0.069160096 -0.083333732 0.091720169 0.009457445 0.013951348
## 436 437 438 441 442 443
## 0.903540165 0.141026706 0.081293220 0.917571482 -0.016500145 1.082748583
## 444 445 446 447 448 449
## 1.052554293 1.042383343 -0.104249556 0.646490647 0.242979292 1.150809954
## 450 452 453 454 455 456
## 0.229594207 0.723643391 -0.059161976 0.100712309 0.259582773 0.143148247
## 457 459 460 463 464 465
## 1.100225174 0.807879805 -0.060053836 0.284058268 0.926342275 0.169626138
## 467 468 472 473 475 477
## 0.368510198 0.704391708 0.278000493 0.064338399 0.924840774 -0.044585161
## 479 481 482 483 484 485
## 1.081461233 0.312975011 0.211510135 0.165275912 0.902230539 1.117622449
## 486 487 488 489 491 493
## 0.774982274 0.363629239 0.107000206 1.141821949 1.099067980 0.419510859
## 495 496 497 498 499 500
## 0.727372254 0.028450552 -0.014033928 1.156308020 0.339775487 0.873113708
## 503 504 505 506 507 509
## 0.135171396 1.022544759 0.973904213 0.116919398 -0.017522659 0.524556637
## 511 513 514 517 519 520
## 0.629037962 -0.019690509 1.037683909 -0.136056900 1.021170463 1.091888545
## 521 524 525 526 527 530
## 1.062770202 0.815960751 -0.046431452 0.618570433 1.063027951 0.214735469
## 531 533 535 536 538 539
## 0.931274167 0.078612113 0.156616603 0.092174559 0.254160187 -0.085436732
## 541 543 544 545 547 548
## 0.063388381 0.218220479 0.904304581 0.109400993 0.068859708 -0.027133652
## 551 552 553 554 555 556
## 0.109094536 0.034391307 0.966873199 1.041771387 1.014812511 0.169273545
## 557 561 562 563 564 565
## 1.074387475 0.932955013 1.089857965 0.230853288 0.632709931 0.856987314
## 566 567 569 570 571 572
## 0.146847580 1.164245742 0.476555125 0.027720618 1.051106081 0.005214892
## 573 574 575 576 581 582
## 0.006311183 0.345726592 1.188132862 1.146653431 0.910756302 0.829755097
## 583 584 586 587 588 590
## 0.882300065 0.680095552 -0.039183513 -0.058365428 1.167983727 0.895544919
## 592 594 598 599 600 601
## 1.054845408 0.085789335 -0.020795203 0.112769242 0.753236825 0.556598346
## 602 605 606 608 609 610
## 1.121561800 0.963693769 0.843109977 0.087725059 0.904619403 0.260225578
## 611 612 613 617 619 620
## 0.963511184 0.965997603 -0.074970636 1.083368596 1.108922165 0.049246102
## 621 625 628 630 631 632
## 0.078565237 0.143314821 1.087099281 -0.048472574 0.122515513 -0.141104540
## 633 635 636 637 638 639
## 0.144211983 0.997894855 0.969497762 1.085321328 0.043965163 0.779021167
## 640 641 642 646 647 648
## 0.012685049 0.677675674 -0.010170281 0.902582254 1.171911592 0.902758354
## 650 651 652 653 655 656
## -0.077782974 0.291156824 -0.013179473 -0.087908551 -0.017605282 1.060627122
## 657 659 660 661 662 663
## 0.131333423 0.165497563 -0.011578029 0.935118538 0.381217934 1.152889519
## 664 665 666 667 668 669
## 0.753608118 0.058737158 0.452362822 -0.004883897 -0.049821139 0.217850775
## 670 671 672 673 674 675
## 0.818113394 0.120416877 0.658145537 -0.026595793 1.010226262 0.095518955
## 676 678 681 686 687 689
## -0.003619283 0.910244142 0.090098735 -0.020136807 -0.016149778 0.095200388
## 690 692 693 694 695 698
## -0.021139954 -0.113989044 0.560597798 0.791505663 0.299416484 0.008251566
## 700 701 702 705 708 709
## 0.026126331 0.316567501 0.864704421 0.170899875 0.064338923 0.854311763
## 711 712 714 715 717 718
## 1.181486295 0.173719257 1.132418420 0.056062132 1.048295927 0.096742511
## 719 720 721 723 724 725
## 0.520484522 0.918499604 -0.024219038 0.987963263 0.590680392 -0.067239658
## 727 728 732 734 736 737
## 0.086169726 -0.091378744 0.123152412 1.138418729 -0.055582934 -0.078567418
## 739 740 741 742 743 744
## 0.617007743 0.060159315 1.041258239 0.294894324 0.243521936 0.934785649
## 745 746 747 748 749 750
## 0.752888212 1.037508644 0.043366949 1.025668868 0.896432657 0.800109713
## 751 753 754 755 756 757
## 0.878839543 0.303558226 0.216673037 0.162060332 0.194568818 1.008168366
## 758 759 760 762 764 765
## 0.979217638 0.759345255 0.327150142 0.293319654 0.735487291 1.102179944
## 768 769 770 771 773 775
## 1.072446726 0.516399572 0.132714555 0.122057679 0.021361600 1.013965034
## 776 777 778 779 780 781
## 1.004513951 0.697531009 0.106327585 0.690904001 0.061031901 0.354506218
## 783 785 788 789 790 791
## -0.050769759 1.064906559 0.455841741 0.070594826 1.030616671 0.892703302
## 792 793 794 795 796 797
## 1.076245096 0.370967291 0.936601680 1.176252343 0.127224582 0.092526092
## 799 802 804 805 807 808
## 0.449103759 1.000011296 1.174345868 0.977149212 0.996248391 1.138484945
## 810 812 813 814 815 816
## 0.827311666 -0.125700392 0.220058992 0.177386009 -0.092457303 0.029267951
## 819 821 822 823 824 825
## 0.070928069 1.042494410 -0.066875501 -0.093752805 0.078141402 0.131879117
## 826 827 829 830 831 832
## 0.176763995 -0.064253476 0.872750564 1.086378648 0.933729623 1.033024713
## 834 835 837 838 839 841
## 1.022681102 0.123230132 1.175252348 1.066732385 1.089301379 0.806723350
## 842 843 845 846 848 849
## 1.029239752 0.101420960 -0.098526965 1.079256170 0.234294691 -0.085709138
## 851 854 855 857 858 859
## -0.129006398 -0.031593229 -0.067199240 -0.066178003 0.046607345 1.096337633
## 860 862 863 864 865 866
## -0.073655050 0.180051984 0.261639406 -0.001144183 0.105858510 1.016285409
## 868 871 872 873 874 875
## -0.019390825 0.714430397 -0.045339236 0.282015697 -0.049141784 0.388088428
## 876 877 878 879 883 884
## 0.828512196 0.948389543 0.367565425 -0.048371047 -0.001124544 1.009177378
## 886 887 888 889 890 891
## 1.157645088 1.131463854 1.084011274 0.057555607 1.010504779 -0.021787375
## 892 893 894 895 896 900
## 0.528421882 0.867230872 0.004498831 0.108927709 0.010511706 1.157402306
## 901 902 904 906 907 909
## 1.161768512 0.739621056 0.185393516 -0.072237917 0.827390906 0.931919710
## 910 911 912 913 914 915
## 0.002163779 0.916660097 0.957089413 1.059070211 -0.005553042 1.111614871
## 916 917 920 921 922 924
## 0.921822320 1.036056973 0.363859425 -0.096219269 0.988130343 1.107218253
## 925 926 927 929 930 931
## 0.832240535 1.158040529 0.155750756 0.186594422 0.614213234 -0.046283200
## 932 940 947 948 949 952
## 0.897773537 0.354104693 0.282881545 0.941596295 0.513957334 0.825799688
## 953 955 956 957 958 959
## 0.220323193 0.265908365 1.118731950 0.962690235 -0.001477796 -0.094187964
## 960 962 963 964 966 967
## 0.301142596 0.142487565 0.132723878 0.218151883 0.971315346 1.021016830
## 968 971 972 973 974 975
## 0.290344318 0.951151992 1.125522233 0.933997392 0.086456531 1.134036461
## 976 977 979 980 981 982
## 1.159887201 1.010674628 0.441669240 -0.055181207 0.693616852 0.002162546
## 984 986 990 991 992 993
## -0.112512468 0.772122647 -0.041055513 1.036725180 1.076985027 0.797242007
## 995 997 998 999
## 0.776515306 0.999829537 1.125825680 0.447814298# Evaluating the Algorithm
error <- y_pred - data_num$Clicked.on.Ad## Warning in y_pred - data_num$Clicked.on.Ad: longer object length is not a
## multiple of shorter object lengthrmse <- sqrt(mean(error^2))
rmse## [1] 0.6554185The algorithm is a good fit
(ii) KNN
# Finding value of k to use
round(sqrt(1000), digits = 0)## [1] 32library(caret)## Loading required package: ggplot2## Loading required package: latticelibrary(class)# Fitting the model
knn_classifier <- knn(train_scale, test_scale, cl = train_set$Clicked.on.Ad, k = 32)# Evaluating the algorithm
conf_matrix<-table(test_set$Clicked.on.Ad, knn_classifier)
confusionMatrix(conf_matrix)## Confusion Matrix and Statistics
##
## knn_classifier
## 0 1
## 0 150 0
## 1 2 148
##
## Accuracy : 0.9933
## 95% CI : (0.9761, 0.9992)
## No Information Rate : 0.5067
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9867
##
## Mcnemar's Test P-Value : 0.4795
##
## Sensitivity : 0.9868
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9867
## Prevalence : 0.5067
## Detection Rate : 0.5000
## Detection Prevalence : 0.5000
## Balanced Accuracy : 0.9934
##
## 'Positive' Class : 0
## _ The accuracy score is 99.3%, the model could be subject to overfitting.
(iii) Decision Trees
library(rpart)
library(e1071)# Fitting the model
classifier = rpart(Clicked.on.Ad ~ Daily.Time.Spent.on.Site + Age + Area.Income + Daily.Internet.Usage, data = data_num)# Plotting the tree
plot(classifier)
text(classifier)
(iii)SVM
# Splitting data into train and test sets
intrain <- createDataPartition(y = data_num$Clicked.on.Ad, p= 0.7, list = FALSE)
train_svm <- data_num[intrain,]
test_svm <- data_num[-intrain,]# Previewing size of train and test sets
dim(train_svm)## [1] 700 6dim(test_svm)## [1] 300 6# Fitting the Model
svm_linear = svm(formula = Clicked.on.Ad ~ .,data = test_svm,type = 'C-classification',kernel = 'linear')# Making Prediction
pred = predict(svm_linear, data = test_svm)
pred## 1 3 4 5 10 13 17 18 19 20 30 36 38 39 41 45 51 52 54 56
## 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 0
## 58 62 63 69 72 74 78 81 82 84 85 88 89 92 94 102 111 115 116 118
## 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1
## 120 124 125 133 137 138 139 140 141 142 149 156 157 158 173 179 181 184 188 190
## 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 1
## 193 194 204 206 207 208 209 210 211 218 226 229 238 239 241 244 246 248 257 258
## 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1
## 262 263 265 266 267 271 272 274 275 281 286 287 291 301 302 307 308 315 317 322
## 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0
## 324 325 326 328 329 334 335 339 341 342 344 345 347 352 359 360 361 362 365 366
## 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1
## 371 385 388 393 398 399 405 411 417 424 429 434 438 439 443 446 448 453 455 461
## 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 1 1
## 465 467 469 472 475 481 483 484 487 494 499 504 505 507 509 513 518 519 526 527
## 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1
## 528 530 532 535 538 540 546 547 552 554 558 564 575 579 584 588 592 593 596 605
## 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1
## 610 611 619 621 623 625 627 630 631 633 634 635 640 644 645 647 649 660 662 663
## 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1
## 667 674 683 689 690 691 692 696 706 716 719 722 728 733 734 738 739 741 742 747
## 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0
## 748 754 759 760 765 766 767 775 776 778 780 781 794 797 798 801 802 803 809 816
## 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0
## 820 825 826 827 829 834 836 839 842 843 845 851 852 856 859 866 868 869 870 872
## 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0
## 878 879 885 890 895 897 902 909 915 916 920 924 929 934 935 937 938 939 940 944
## 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1
## 945 946 950 953 956 958 960 965 966 976 977 978 979 982 983 984 987 994 997 999
## 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1
## Levels: 0 1# Evaluating Algorithm
conf_mat<-table(test_svm$Clicked.on.Ad, pred)
confusionMatrix(conf_mat)## Confusion Matrix and Statistics
##
## pred
## 0 1
## 0 143 7
## 1 7 143
##
## Accuracy : 0.9533
## 95% CI : (0.9229, 0.9743)
## No Information Rate : 0.5
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9067
##
## Mcnemar's Test P-Value : 1
##
## Sensitivity : 0.9533
## Specificity : 0.9533
## Pos Pred Value : 0.9533
## Neg Pred Value : 0.9533
## Prevalence : 0.5000
## Detection Rate : 0.4767
## Detection Prevalence : 0.5000
## Balanced Accuracy : 0.9533
##
## 'Positive' Class : 0
## The model has an accuracy score of 96.7%
(v) Naive Bayes
# Splitting data into train and test sets
indxTrain <- createDataPartition(y = data_num$Clicked.on.Ad,p = 0.7,list = FALSE)
train_naive <- data_num[indxTrain,]
test_naive <- data_num[-indxTrain,]# Training the model
naive_model <- naiveBayes(Clicked.on.Ad ~ ., data = train_naive)# Making Prediction
Predict <- predict(naive_model,newdata = test_naive)
Predict## [1] 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0
## [38] 1 1 0 0 1 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1
## [75] 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0
## [112] 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1
## [149] 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 1
## [186] 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0
## [223] 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0
## [260] 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1
## [297] 0 1 1 1
## Levels: 0 1# Evaluating Algorithm
conf_mat2<- table(test_naive$Clicked.on.Ad, Predict)
confusionMatrix(conf_mat2)## Confusion Matrix and Statistics
##
## Predict
## 0 1
## 0 144 6
## 1 6 144
##
## Accuracy : 0.96
## 95% CI : (0.9312, 0.9792)
## No Information Rate : 0.5
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.92
##
## Mcnemar's Test P-Value : 1
##
## Sensitivity : 0.96
## Specificity : 0.96
## Pos Pred Value : 0.96
## Neg Pred Value : 0.96
## Prevalence : 0.50
## Detection Rate : 0.48
## Detection Prevalence : 0.50
## Balanced Accuracy : 0.96
##
## 'Positive' Class : 0
## - The model has an accuracy score of 97.7%
- The best model to use for prediction would be the Naive Bayes