In this discussion, you will apply the statistical concepts and techniques covered in this week’s reading about multiple regression.

In this discussion, you will apply the statistical concepts and techniques covered in this week’s reading about multiple regression. Last week’s discussion involved a car rental company that wanted to evaluate the premise that heavier cars are less fuel efficient than lighter cars. The company expected fuel efficiency (miles per gallon) and weight of the car (often measured in thousands of pounds) to be correlated. The company also expects cars with higher horsepower to be less fuel efficient than cars with lower horsepower. They would like you to consider this new variable in your analysis.

In this discussion, you will work with a cars data set that includes the three variables used in this discussion:

• Miles per gallon (coded as mpg in the data set)
• Weight of the car (coded as wt in the data set)
• Horsepower (coded as hp in the data set)

The random sample will be drawn from a CSV file. This data will be unique to you, and therefore your answers will be unique as well. Run Step 1 in the Python script to generate your unique sample data.

In your initial post, address the following items:

1. Check to be sure your scatterplots of miles per gallon against horsepower and weight of the car were included in your attachment. Do the plots show any trend? If yes, is the trend what you expected? Why or why not? See Steps 2 and 3 in the Python script.
2. What are the coefficients of correlation between miles per gallon and horsepower? Between miles per gallon and the weight of the car? What are the directions and strengths of these coefficients? Do the coefficients of correlation indicate a strong correlation, weak correlation, or no correlation between these variables? See Step 4 in the Python script.
3. Write the multiple regression equation for miles per gallon as the response variable. Use weight and horsepower as predictor variables. See Step 5 in the Python script. How might the car rental company use this model?

In your follow-up posts to other students, review your peers’ results and provide some analysis and interpretation:

1. Review your peer’s multiple regression model (#3 in their initial post). What is the predicted value of miles per gallon for a car that has 2.78 (2,780 lbs) weight and 225 horsepower? Suppose that this car achieves 18 miles per gallon, what is the residual based on this actual value and the value that is predicted using the regression equation?
2. How do the plots and correlation coefficients of your peers compare with yours?
3. Would you recommend this regression model to the car rental company? Why or why not?

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