Lab 4: Linear Regression Extensions Overview The ISLR2 library contains a dataset called Auto. This dataset contains a list of American cars, with variables for the mpg, horsepower, weight, and acceleration. If you are unfamiliar with car terminology. MPG is a measure of fuel efficiency (more mpg, more efficient) and horsepower is a measurement of how much "power" an engine produces (more horsepower, more power). The car weights are measured in pounds. The "origin" variable is a categorical variable for where the car was made. 1 Is American, 2 is European, 3 is Japanese. To complete this lab: create a Word document (or similar document) with results for all questions in the Lab Steps section Include photos of plots. Set-up 1. Load the Auto dataset Lab Steps 1. Write coefficients from a linear model with response = mpg, and explanatory variables horsepower and origin, with an interaction between horsepower and origin 2. Predict the average mpg for four cars: (100 horsepower, American), (100 horsepower, Japanese), (170 horsepower, American), (170 horsepower, Japanese) 3. What do you notice about how the predictions change as horsepower increases? 4. Plot a scatter plot with x = horsepower, y = mpg 5. Based on the plot, do you think a simple linear regression will work well here? 6. Write coefficients from a linear model with response = mpg and explanatory = horsepower, with a suitable transformation for the horsepower variable (for example, square it) 7. Predict the average mpg for 3 cars: 80 horsepower, 100 horsepower, 120 horsepower 8. What do you notice about these predictions