Tutorial Week 4
Tan Wenling Megan
2025-09-02
Load Motor Trend Car Road Tests dataset
library(ggplot2)
library(dplyr)
data(mtcars)head(mtcars)## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1str(mtcars)## 'data.frame': 32 obs. of 11 variables:
## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ cyl : num 6 6 4 6 8 6 8 4 4 6 ...
## $ disp: num 160 160 108 258 360 ...
## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...
## $ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...
## $ qsec: num 16.5 17 18.6 19.4 17 ...
## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...
## $ am : num 1 1 1 0 0 0 0 0 0 0 ...
## $ gear: num 4 4 4 3 3 3 3 4 4 4 ...
## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...Summmary of dataset
summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000Is there a linear relationship between horsepower (hp) and miles per gallon (mpg)?
L1 <-
lm(mpg ~ hp, data = mtcars)
summary(L1)##
## Call:
## lm(formula = mpg ~ hp, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.7121 -2.1122 -0.8854 1.5819 8.2360
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30.09886 1.63392 18.421 < 2e-16 ***
## hp -0.06823 0.01012 -6.742 1.79e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.863 on 30 degrees of freedom
## Multiple R-squared: 0.6024, Adjusted R-squared: 0.5892
## F-statistic: 45.46 on 1 and 30 DF, p-value: 1.788e-07plot(mpg ~ hp,
data = mtcars,
pch = 16,
col = "aquamarine4",
ylab = "Miles per gallon",
xlab = "Horsepower")
abline(
a = 30.09886,
b = -0.06823,
lwd = 1.5,
col = "aquamarine4"
)
cor(mtcars$hp, mtcars$mpg)## [1] -0.7761684There is a negative linear relationship between horsepower and miles per gallon where horsepower increases as miles per gallon decreases, indicating a negative relationship.
Which test would you use to compare mpg across 3+ cylinder groups?
MPG is a continuous data. We need to check if mpg is normally distributed by plotting a histogram.
ggplot(mtcars, aes(x = mpg)) +
geom_histogram(aes(y = ..density..), bins = 10, fill = "lightblue", color = "black") +
geom_density(color = "red", size = 1) +
labs(title = "Distribution of mpg")## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(density)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
Since mpg is not normally distributed, we cannot use the 1 way ANOVA
test. Hence, we will use the Kruskal-Wallis test
#kruskal.test(dependent_variable ~ independent_variable, data = your_data_frame)
kruskal.test(mpg ~ factor(cyl), data=mtcars)##
## Kruskal-Wallis rank sum test
##
## data: mpg by factor(cyl)
## Kruskal-Wallis chi-squared = 25.746, df = 2, p-value = 2.566e-06Since the p value is < 0.05, we can conclude that there is a statistically significant difference in mpg across the 3+ cylinder groups.
Conducting the Pairwise wilcoxon test to determine between which group of cylinder has different MPG
pairwise.wilcox.test(mtcars$mpg, mtcars$cyl,
p.adjust.method = "BH")## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: mtcars$mpg and mtcars$cyl
##
## 4 6
## 6 0.001 -
## 8 8.3e-05 0.001
##
## P value adjustment method: BHSince p value < 0.05 between 4 and 6 cylinders and 4 and 8 cylinders, there is a statistically significant difference in mpg across 4 and 6 cylinders and 4 and 8 cylinders.