• Explore relationship between car weight and fuel efficiency (mpg)
• Demonstrate linear regression in R
• Show results with ggplot2 and plotly

Simple linear regression model:

\[ y_i = \beta_0 + \beta_1 x_i + \varepsilon_i,\quad \varepsilon_i \sim N(0, \sigma^2) \]

Least squares estimate:

\[ \hat\beta_1 = \frac{\sum (x_i-\bar x)(y_i-\bar y)}{\sum (x_i-\bar x)^2} \]

We’ll use the built-in mtcars dataset.

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

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

# Fit linear model
fit <- lm(mpg ~ wt, data=mtcars)

# Summarize results
summary(fit)

• Heavier cars → lower fuel efficiency
• Linear model captures strong negative relationship
• Interactive and static plots confirm same pattern
• Regression formula and visual diagnostics align

• R documentation: ?mtcars, ?lm
• Wickham, ggplot2: Elegant Graphics for Data Analysis
• Plotly R API Docs