The cases that make up this dataset are types of cars. The data include the engine size (in liters) and horsepower (HP) of 319 vehicles sold in the United States in 2011.
(a) Create a scatterplot of the horse power on the engine displacement of the car. Does the trend in the average horsepower seem linear?
(b) Estimate the linear equation using least squares. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate rep-resents a large extrapolation and is consequently not reliable.
(c) Interpret r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate.
(d) If a manufacturer increases the size of the engine by 0.5 liters, should it use 0.5b1 to get a sense of how much more power the engine will generate?
(e) A car with a 3-liter engine among these produces 333 HP. What is the residual for this case? Does the data point representing this car lie above or below the fitted line?
(f) How would you describe cars with positive residuals? Those with negative residuals?
(g) Do you find patterns in the residuals from this regression? Does it make sense to interpret se as the standard deviation of the errors of the ft? Use the plot of the residuals on the predictor to help decide.