Price vs. Mileage Analysis for Honda Accords

Step 1: Exploratory Data Analysis of All Cars

We begin by loading the required packages and the ThreeCars2017 dataset. We then create two scatterplots: one plain plot of all data points and one categorized by car model (CarType).

# Load libraries
library(Stat2Data)
library(dplyr)
library(ggplot2)

# Load data
data("ThreeCars2017")

# Plain scatterplot of all data
ggplot(ThreeCars2017, aes(x = Mileage, y = Price)) +
  geom_point() +
  labs(
    title = "Price vs. Mileage for Three Cars",
    x = "Mileage (thousands of miles)",
    y = "Price (thousands of dollars)"
  )

# Scatterplot with color and shape mapped to CarType
ggplot(ThreeCars2017, aes(x = Mileage, y = Price, color = CarType, shape = CarType)) +
  geom_point() +
  labs(
    title = "Price vs. Mileage by Car Type",
    x = "Mileage (thousands of miles)",
    y = "Price (thousands of dollars)"
  )

Observation: Accords tend to be more expensive when they have lower mileage compared to the other car types in the dataset.

Step 2: Analysis of Honda Accords

We now filter the dataset to focus strictly on Honda Accords, create a scatterplot, and calculate the correlation coefficient (\(r\)).

# Filter dataset to keep only Accord
my_group <- ThreeCars2017 %>% 
  filter(CarType == "Accord")

# Scatterplot for Accord group
ggplot(my_group, aes(x = Mileage, y = Price)) +
  geom_point(alpha = 0.6) +
  labs(
    title = "Price vs. Mileage for Honda Accords",
    x = "Mileage (thousands of miles)",
    y = "Price (thousands of dollars)"
  )

# Compute correlation coefficient r
cor(my_group$Mileage, my_group$Price, use = "complete.obs")

## [1] -0.8489441

Association & Correlation: The correlation coefficient is \(r = -0.8489441\). This indicates a strong, negative, roughly linear relationship between mileage and price for Honda Accords. As mileage increases, price consistently decreases.

Step 3: Fitting the Simple Linear Regression Model

Next, we fit a simple linear regression model with Price as the response variable and Mileage as the explanatory variable.

# Fit linear model
model <- lm(Price ~ Mileage, data = my_group)

# View coefficients
coef(model)

## (Intercept)     Mileage 
##  20.8096129  -0.1198119

Model Coefficients & Interpretation: - Intercept: 20.8096129 (The predicted price of a brand-new Accord with 0 miles is approximately 20.81 thousand dollars, or $20,810). - Slope: -0.1198119 (For every additional 1,000 miles driven, the predicted price of a Honda Accord decreases by approximately 0.1198 thousand dollars, or about $120).

Step 4: Visualizing the Linear Regression Line

Finally, we overlay the estimated regression line on the scatterplot of Honda Accords using the calculated slope and intercept.

# Scatterplot with regression line overlaid
ggplot(my_group, aes(x = Mileage, y = Price)) +
  geom_point(alpha = 0.6) +
  geom_abline(intercept = 20.8096129, slope = -0.1198119, color = "steelblue", linewidth = 1) +
  labs(
    title = "Price vs. Mileage for Honda Accords with Linear Model",
    subtitle = "Price = 20.8096129 - 0.1198119 * Mileage | r = -0.8489441",
    x = "Mileage (thousands of miles)",
    y = "Price (thousands of dollars)"
  )

Model Verification: The regression line runs smoothly through the middle of the scatterplot points, confirming that the line correctly models the negative linear trend between mileage and price.