**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

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.

- Fully interpret the meaning of each coefficient from fitting the model. [
*Hint: Show results from*`summary()`

.] - Fully interpret the meaning of each coefficientâ€™s p-value.
- Fully interpret the meaning of the coefficient of determination.
- Fully interpret the meaning of each coefficientâ€™s confidence interval. [
*Hint: Show results from*`confint()`

.] - 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()`

.] - Interpret the meaning of each mean-square in the ANOVA table, include the mean-square that is usually not presented in the ANOVA table.
- Interpret the F test statistic in the ANOVA table.
- Is there evidence, at the 5% level, for a relationship between mpg and the horsepower of a car? Explain.
- Provide a plot that illustrates your results.