Note Your answers to the questions below should follow the expectations for homework found here. Due date is on the Dates page.

Car Horsepower and Gas Mileage I

1993 Car Students in the Introduction to Environmental Studies course were interested in what characteristics of cars affected the gas mileage (miles per gallon) of a car. Using an internet search they recorded several variables on a sample of makes of cars (note that these data are industry-reported summaries for the make of a car, not measurements on an individual car). Two of the variables that they recorded were mpg (miles per gallon of gasoline for the car) and hp (horsepower of the car engine). These data, along with many other variables are in CarMPG.csv (download, meta). Use these data to compute a model that can be used to predict the mpg of a car from its horsepower.

  1. Fully interpret the meaning of each coefficient from fitting the model. [Hint: Show results from summary().]
  2. Fully interpret the meaning of each coefficient’s p-value.
  3. Fully interpret the meaning of the coefficient of determination.
  4. Fully interpret the meaning of each coefficient’s confidence interval. [Hint: Show results from confint().]
  5. Show how each degrees-of-freedom in the ANOVA table was calculated. Include the degrees-of-freedom that R does not report. [Note: Make sure to show the ANOVA table produced by anova().]
  6. Interpret the meaning of each mean-square in the ANOVA table, include the mean-square that is usually not presented in the ANOVA table.
  7. Interpret the F test statistic in the ANOVA table.
  8. Is there evidence, at the 5% level, for a relationship between mpg and the horsepower of a car? Explain.
  9. Provide a plot that illustrates your results.