This presentation explores the relationship between horsepower and fuel efficiency (mpg) using the mtcars dataset. We’ll visualize data using ggplot and interactive plots.

# Load and display the first few rows of the dataset
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

library(ggplot2)

# Create a scatter plot
ggplot(mtcars, aes(x = hp, y = mpg)) +
  geom_point(color = "blue") +
  labs(
    title = "Scatter Plot of mpg vs hp",
    x = "Horsepower (hp)",
    y = "Miles per Gallon (mpg)"
  )

# Fit the regression model
model <- lm(mpg ~ hp, data = mtcars)





# Scatter plot with regression line

## `geom_smooth()` using formula = 'y ~ x'

#slide 4

coefficients(model)

#slide 5

library(plotly) plot_ly(data = mtcars, x = ~hp, y = ~mpg, type = ‘scatter’, mode = ‘markers’, marker = list(color = ‘blue’)) %>% add_lines(x = ~hp, y = fitted(model), line = list(color = ‘red’)) %>% layout(title = “Interactive Plot of mpg vs hp”, xaxis = list(title = “Horsepower (hp)”), yaxis = list(title = “Miles per Gallon (mpg)”))

We can represent the regression equation using LaTeX notation:

\[ \hat{y} = \beta_0 + \beta_1 \times \text{hp} \]

Where: - \(\hat{y}\) is the predicted miles per gallon (mpg) - \(\beta_0\) is the intercept - \(\beta_1\) is the slope of horsepower (hp)

Here is the actual regression equation computed using R:

## The actual regression equation is: mpg = 30.1 + -0.07 * hp

Predicted and Mean Values Calculation

# Predicted mpg values
y_pred <- predict(model)

# Mean of actual mpg values
y_mean <- mean(mtcars$mpg)


# Calculate Sum of Squares due to Regression (SSR)
SSR <- sum((y_pred - y_mean)^2)

# Display the SSR value
cat("Sum of squares due to regression (SSR):", round(SSR, 2))

## Sum of squares due to regression (SSR): 678.37