Directions

Read the information below. Then, using the data in the Excel file named RegressionAssignmentData.xlsx, answer the questions below. I recommend that you put your answers here before putting them into the Blackboard submission.

For Questions 2 and 10, copy your graphs from your Excel work and paste them in this document. Unless otherwise specified, round final calculated values to 4 decimal places. (You will then upload your graphs to Blackboard).

Fuel Economy and Carbon Footprint

Sources: fueleconomy.gov and epa.gov

A typical passenger vehicle emits about 4.6 metric tons of carbon dioxide per year. This assumes the average gasoline vehicle on the road today has a fuel economy of about 22.0miles per gallon and drives around 11,500 miles per year. Every gallon of gasoline burned creates about 8,887 grams of CO₂. This number can vary based on a vehicle's fuel, fuel economy, and the number of miles driven per year.

The data provided contains the highway fuel economy and corresponding carbon footprint (in C02 emitted in grams per mile) for 69 cars.

(Data are given in the RegressionAssignmentData.xlsx Excel file.)

Questions

In the data given, which variable is the independent variable? Which is the dependent variable? (4pt)

Construct a scatter plot of the data. Be sure to use a descriptive title and axis labels. (6 pt)

Calculate the coefficient of correlation, r. (10 pt)

What does the correlation coefficient say about the relationship between highway fuel economy and carbon

(Updated 12/3/2019)

footprint? Specify strength and direction. (12 pt)

Find the linear regression equation. Give the slope and the vertical intercept. Round both answers to two decimal places. (20 pt)

Calculate the coefficient of determination, r². Round your answer to 4 decimal places. (10pt)

how to Create a residual plot. (6 pt)

How well does your linear model fit the data? Explain your answer based on the scatter plot, the value of r², and the residual plot. (12 pt)

Using the linear regression equation you found in question 5, predict the carbon footprint for a vehicle with a highway fuel economy of 42 mpg. (10pt)

Does your regression model over-predict or under-predict the carbon footprint for a vehicle with a highway fuel economy of 42 mpg? (4 pt)

Can we use this linear regression model to predict carbon footprint for a car with a highway fuel economy of 59 mpg? Briefly explain your answer. (6 pt)