Introduction

Simple linear regression models the relationship between a single explanatory variable \(x\) and a response variable \(y\). The model is:

\[ y = \beta_0 + \beta_1 x + \epsilon \]

Where \(\beta_0\) is the intercept, \(\beta_1\) is the slope, and \(\epsilon\) is the error term.

We’ll use the mtcars dataset to model the relationship between horsepower (hp) and miles per gallon (mpg).

MPG vs Horsepower

Residual vs Horsepower

3D Scatterplot: MPG vs HP and Weight

Model Summary

summary(model)

## 
## Call:
## lm(formula = mpg ~ hp, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.7121 -2.1122 -0.8854  1.5819  8.2360 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 30.09886    1.63392  18.421  < 2e-16 ***
## hp          -0.06823    0.01012  -6.742 1.79e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.863 on 30 degrees of freedom
## Multiple R-squared:  0.6024, Adjusted R-squared:  0.5892 
## F-statistic: 45.46 on 1 and 30 DF,  p-value: 1.788e-07

Confidence Interval for Slope

confint(model, "hp", level = 0.95)

##          2.5 %     97.5 %
## hp -0.08889465 -0.0475619

Conclusion

• Simple linear regression models the linear relationship between different variables.
• Visualization was done using ggplot2 and a 3D plotly plot.
• We examined model fit and statistical errors