Comprehensive Data Analysis Report using mtcars Dataset
Nkudu Uche Victor
2025-07-07
- Introduction The mtcars dataset is a classic dataset from the 1974 Motor Trend US magazine. It comprises fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973–74 models).
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 1- Data Summary and Structure
str(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 ...We observe variables like mpg (miles per gallon), wt (weight), hp (horsepower), and cyl (number of cylinders), which will be key in our regression modeling.
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. :8.000- Descriptive Statistics
mtcars %>%
summarise(
mean_mpg = mean(mpg),
median_hp = median(hp),
sd_wt = sd(wt),
max_qsec = max(qsec)
)## mean_mpg median_hp sd_wt max_qsec
## 1 20.09062 123 0.9784574 22.9- Exploratory Data Visualization
# Histogram
ggplot(mtcars, aes(mpg)) +
geom_histogram(binwidth = 2, fill = "skyblue", color = "black") +
labs(title = "Distribution of MPG", x = "Miles Per Gallon")
# Boxplot
ggplot(mtcars, aes(x = factor(cyl), y = mpg)) +
geom_boxplot(fill = "orange") +
labs(title = "MPG by Number of Cylinders", x = "Cylinders")
# Scatter plot
ggplot(mtcars, aes(x = wt, y = mpg)) +
geom_point() +
geom_smooth(method = "lm", se = TRUE) +
labs(title = "MPG vs Weight")
- Correlation Matrix
cor_matrix <- round(cor(mtcars), 2)
corrplot(cor_matrix, method = "circle", type = "upper", tl.cex = 0.8)
mpg is negatively correlated with wt and hp.
- Simple Linear Regression
model_simple <- lm(mpg ~ wt, data = mtcars)
summary(model_simple)##
## Call:
## lm(formula = mpg ~ wt, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.5432 -2.3647 -0.1252 1.4096 6.8727
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 37.2851 1.8776 19.858 < 2e-16 ***
## wt -5.3445 0.5591 -9.559 1.29e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.046 on 30 degrees of freedom
## Multiple R-squared: 0.7528, Adjusted R-squared: 0.7446
## F-statistic: 91.38 on 1 and 30 DF, p-value: 1.294e-10Diagnostics
par(mfrow = c(2, 2))
plot(model_simple)
- Multiple Linear Regression
model_multi <- lm(mpg ~ wt + hp + qsec + drat, data = mtcars)
summary(model_multi)##
## Call:
## lm(formula = mpg ~ wt + hp + qsec + drat, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5775 -1.6626 -0.3417 1.1317 5.4422
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.25970 10.31545 1.867 0.072785 .
## wt -3.70773 0.88227 -4.202 0.000259 ***
## hp -0.01784 0.01476 -1.209 0.237319
## qsec 0.52754 0.43285 1.219 0.233470
## drat 1.65710 1.21697 1.362 0.184561
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.539 on 27 degrees of freedom
## Multiple R-squared: 0.8454, Adjusted R-squared: 0.8225
## F-statistic: 36.91 on 4 and 27 DF, p-value: 1.408e-10Multicollinearity
vif(model_multi)## wt hp qsec drat
## 3.582683 4.921958 2.876115 2.035473Assumption Checks
# Normality
qqnorm(resid(model_multi))
qqline(resid(model_multi), col = "red")
# Homoscedasticity
plot(model_multi, which = 3)
# Independence
dwtest(model_multi)##
## Durbin-Watson test
##
## data: model_multi
## DW = 1.7876, p-value = 0.1952
## alternative hypothesis: true autocorrelation is greater than 0- Model Evaluation
predicted <- predict(model_multi)
actual <- mtcars$mpg
# RMSE
rmse <- sqrt(mean((predicted - actual)^2))
# MAE
mae <- mean(abs(predicted - actual))
rmse## [1] 2.332538mae## [1] 1.851651- Conclusion Weight and horsepower are strong predictors of fuel efficiency.
The multiple regression model explains a large proportion of variance (R² > 0.8).
Model diagnostics suggest reasonably well-met assumptions.
Recommendations: Consider variable selection or regularization in future models.