Simple linear regression is a method to predict a dependent variable (Y) based on an independent variable (X). It assumes a linear relationship between X and Y.

The simple linear regression equation is: \[ Y = \beta_0 + \beta_1 X + \epsilon \] where \(Y\) is the dependent variable, \(X\) is the independent variable, \(\beta_0\) is the intercept, \(\beta_1\) is the slope, and \(\epsilon\) is the error term.

We will use the cars dataset to demonstrate linear regression.

ggplot(cars, aes(x = speed, y = dist)) +
  geom_point() +
  labs(title = "Speed vs Stopping Distance", x = "Speed", y = "Distance")

model <- lm(dist ~ speed, data = cars)
summary(model)

## 
## Call:
## lm(formula = dist ~ speed, data = cars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.069  -9.525  -2.272   9.215  43.201 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -17.5791     6.7584  -2.601   0.0123 *  
## speed         3.9324     0.4155   9.464 1.49e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.38 on 48 degrees of freedom
## Multiple R-squared:  0.6511, Adjusted R-squared:  0.6438 
## F-statistic: 89.57 on 1 and 48 DF,  p-value: 1.49e-12

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