# help(swiss)
summary(swiss)## Fertility Agriculture Examination Education
## Min. :35.00 Min. : 1.20 Min. : 3.00 Min. : 1.00
## 1st Qu.:64.70 1st Qu.:35.90 1st Qu.:12.00 1st Qu.: 6.00
## Median :70.40 Median :54.10 Median :16.00 Median : 8.00
## Mean :70.14 Mean :50.66 Mean :16.49 Mean :10.98
## 3rd Qu.:78.45 3rd Qu.:67.65 3rd Qu.:22.00 3rd Qu.:12.00
## Max. :92.50 Max. :89.70 Max. :37.00 Max. :53.00
## Catholic Infant.Mortality
## Min. : 2.150 Min. :10.80
## 1st Qu.: 5.195 1st Qu.:18.15
## Median : 15.140 Median :20.00
## Mean : 41.144 Mean :19.94
## 3rd Qu.: 93.125 3rd Qu.:21.70
## Max. :100.000 Max. :26.60head(swiss)## Fertility Agriculture Examination Education Catholic
## Courtelary 80.2 17.0 15 12 9.96
## Delemont 83.1 45.1 6 9 84.84
## Franches-Mnt 92.5 39.7 5 5 93.40
## Moutier 85.8 36.5 12 7 33.77
## Neuveville 76.9 43.5 17 15 5.16
## Porrentruy 76.1 35.3 9 7 90.57
## Infant.Mortality
## Courtelary 22.2
## Delemont 22.2
## Franches-Mnt 20.2
## Moutier 20.3
## Neuveville 20.6
## Porrentruy 26.6# number of rows of dataset
nrow(swiss)## [1] 47Histogram plot
hist(swiss$Agriculture, breaks = 5, col = "darkgreen",
xlab = "Percent of males involved in agriculture in an occupation",
main = "Agriculture Distribution")
Explanation: The histogram displays how 47 Swiss provinces are distributed across the proportion of males enforcement employed in agriculture. The X-axis divides these percentage into intervals of 20%, and the y-axis represents how many provinces fall into that percent. The graph is left-skewed. There are 16 provinces that fall into the 60-80% range, while there are 11 provinces fall into the 40 - 60% range
Scatter plot
plot(swiss$Catholic, swiss$Fertility, col="orange",
xlab = "Catholic Percentage",
ylab = "Fertility",
main = "Scatter plot")
Explanation: Each point represents one Swiss province. The plot helps visualize how fertility changes with Catholic percentage. There are 2 obvious clusters: Provinces with very low and high Catholic percentage tend to have higher fertility, while provinces with moderate Catholic percentage tend to have lower fertility.
2 subsets
#set Threshold
threshold <- median(swiss$Education)
threshold## [1] 8#subset lowEdu
lowEdu <- subset(swiss, Education < threshold)
nrow(lowEdu)## [1] 21lowEdu## Fertility Agriculture Examination Education Catholic
## Franches-Mnt 92.5 39.7 5 5 93.40
## Moutier 85.8 36.5 12 7 33.77
## Porrentruy 76.1 35.3 9 7 90.57
## Broye 83.8 70.2 16 7 92.85
## Gruyere 82.4 53.3 12 7 97.67
## Veveyse 87.1 64.5 14 6 98.61
## Aubonne 66.9 67.5 14 7 2.27
## Cossonay 61.7 69.3 22 5 2.82
## Echallens 68.3 72.6 18 2 24.20
## Moudon 65.0 55.1 14 3 4.52
## Orbe 57.4 54.1 20 6 4.20
## Oron 72.5 71.2 12 1 2.40
## Paysd'enhaut 72.0 63.5 6 3 2.56
## Conthey 75.5 85.9 3 2 99.71
## Entremont 69.3 84.9 7 6 99.68
## Herens 77.3 89.7 5 2 100.00
## Martigwy 70.5 78.2 12 6 98.96
## Monthey 79.4 64.9 7 3 98.22
## Sierre 92.2 84.6 3 3 99.46
## Val de Ruz 77.6 37.6 15 7 4.97
## ValdeTravers 67.6 18.7 25 7 8.65
## Infant.Mortality
## Franches-Mnt 20.2
## Moutier 20.3
## Porrentruy 26.6
## Broye 23.6
## Gruyere 21.0
## Veveyse 24.5
## Aubonne 19.1
## Cossonay 18.7
## Echallens 21.2
## Moudon 22.4
## Orbe 15.3
## Oron 21.0
## Paysd'enhaut 18.0
## Conthey 15.1
## Entremont 19.8
## Herens 18.3
## Martigwy 19.4
## Monthey 20.2
## Sierre 16.3
## Val de Ruz 20.0
## ValdeTravers 19.5#subset HighEdu
highEdu <- subset(swiss, Education >= threshold)
nrow(highEdu)## [1] 26highEdu## Fertility Agriculture Examination Education Catholic
## Courtelary 80.2 17.0 15 12 9.96
## Delemont 83.1 45.1 6 9 84.84
## Neuveville 76.9 43.5 17 15 5.16
## Glane 92.4 67.8 14 8 97.16
## Sarine 82.9 45.2 16 13 91.38
## Aigle 64.1 62.0 21 12 8.52
## Avenches 68.9 60.7 19 12 4.43
## Grandson 71.7 34.0 17 8 3.30
## Lausanne 55.7 19.4 26 28 12.11
## La Vallee 54.3 15.2 31 20 2.15
## Lavaux 65.1 73.0 19 9 2.84
## Morges 65.5 59.8 22 10 5.23
## Nyone 56.6 50.9 22 12 15.14
## Payerne 74.2 58.1 14 8 5.23
## Rolle 60.5 60.8 16 10 7.72
## Vevey 58.3 26.8 25 19 18.46
## Yverdon 65.4 49.5 15 8 6.10
## St Maurice 65.0 75.9 9 9 99.06
## Sion 79.3 63.1 13 13 96.83
## Boudry 70.4 38.4 26 12 5.62
## La Chauxdfnd 65.7 7.7 29 11 13.79
## Le Locle 72.7 16.7 22 13 11.22
## Neuchatel 64.4 17.6 35 32 16.92
## V. De Geneve 35.0 1.2 37 53 42.34
## Rive Droite 44.7 46.6 16 29 50.43
## Rive Gauche 42.8 27.7 22 29 58.33
## Infant.Mortality
## Courtelary 22.2
## Delemont 22.2
## Neuveville 20.6
## Glane 24.9
## Sarine 24.4
## Aigle 16.5
## Avenches 22.7
## Grandson 20.0
## Lausanne 20.2
## La Vallee 10.8
## Lavaux 20.0
## Morges 18.0
## Nyone 16.7
## Payerne 23.8
## Rolle 16.3
## Vevey 20.9
## Yverdon 22.5
## St Maurice 17.8
## Sion 18.1
## Boudry 20.3
## La Chauxdfnd 20.5
## Le Locle 18.9
## Neuchatel 23.0
## V. De Geneve 18.0
## Rive Droite 18.2
## Rive Gauche 19.3explanation: I created a threshold using the median value of the Education column of dataset. Then I split the dataset into 2 groups: lowEdu, which contains all rows where Education is below the threshold, and highEdu, which contains all rows where Educaiton is greater than or equal to the threshold. This allows me to compare provinces with lower versus higher educaiton levels.
T-test
t.test(lowEdu$Agriculture, highEdu$Agriculture)##
## Welch Two Sample t-test
##
## data: lowEdu$Agriculture and highEdu$Agriculture
## t = 3.3672, df = 44.395, p-value = 0.001577
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 8.07062 32.12022
## sample estimates:
## mean of x mean of y
## 61.77619 41.68077explanation: Based on the T-test results, the mean Agriculture value in the low-Education group is significantly different from the mean Agriculture value in the high-Education group. The p-value ia 0.0016, which is below the 0.05 significance level. Therefore, I can conclude that the difference between two means is statistically significant.