Lab - week 5

Based on Applied Statistics with R by David Dalpiaz (https://github.com/daviddalpiaz/appliedstats)

cars Example

We will use the small dataset cars which comes with R and it availiable right away

cars

We want too examine the relationship between the speed of a car (speed) and its stopping distance (dist).

  1. Start by creating a scatter plot of dist and speed. Describe what you see.
plot(dist ~ speed, data = cars)
  1. Fit a simple linear regression model on cars with dist as the response variable and speed as the predictor variable. Plot it on top of the scatter plot. How does it fit?
stop_dist_model <- lm(dist ~ speed, data = cars)
plot(dist ~ speed, data = cars)
abline(stop_dist_model)

  1. Examine the model fit with summary(). Look at the different results from summary() using names().

  2. Verify the value of the \(t\) test statistic for \(\b_1\) and the two-sided p-value associated with that test statistic.

  3. Use the confint() function to obain the confidence interval for \(\beta_0\) and \(\beta_1\).

  4. Verify the calculations that R is performing for the \(\beta_1\) interval.