Introduction

This is a simple analysis of the mtcars dataset. The dataset contains information about 32 cars of different brands and models. The data is available from data/mtcars/mtcars.rds. The dataset contains the following variables:

  • mpg: Miles/(US) gallon
  • cyl: Number of cylinders
  • disp: Displacement (cu.in.)
  • hp: Gross horsepower
  • drat: Rear axle ratio
  • wt: Weight (1000 lbs)
  • qsec: 1/4 mile time
  • vs: Engine (0 = V-shaped, 1 = straight)
  • am: Transmission (0 = automatic, 1 = manual)
  • gear: Number of forward gears
  • carb: Number of carburetors

Analysis goals

The analysis goals are:

  • To load the dataset and view it as a table
  • To calculate the correlation of weight and miles per gallon
  • To plot the relationship between weight and miles per gallon with the correlation coefficient

Data analysis

Data loading & viewing

We first load the data from data/mtcars/mtcars.rds and view it as a table.

Correlation calculation

We calculate the correlation of weight and miles per gallon.

corr <- cor.test(mtcars$wt, mtcars$mpg)
corr
## 
##  Pearson's product-moment correlation
## 
## data:  mtcars$wt and mtcars$mpg
## t = -9.559, df = 30, p-value = 1.294e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.9338264 -0.7440872
## sample estimates:
##        cor 
## -0.8676594

Plotting

We plot the relationship between weight and miles per gallon with the correlation coefficient.

mtcars %>%
    ggplot(aes(x = wt, y = mpg)) +
    geom_point() +
    geom_smooth(method = "lm", se = FALSE) +
    labs(
        title = "Relationship between weight and miles per gallon",
        x = "Weight (1000 lbs)",
        y = "Miles/(US) gallon",
        caption = "Source: mtcars dataset"
    ) +
    theme_minimal(base_size = 15) +
    # Add the correlation coefficient
    annotate(
        "text", x = 4.75, y = 25, 
        label = paste0("Correlation coefficient: ", round(corr$estimate, 3))
    )

Conclusion

The correlation between weight and miles per gallon is -0.8677. The relationship between weight and miles per gallon is negative and strong. The significance is 1.294e-10 which is less than 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant correlation between weight and miles per gallon.