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

4. Cars data frame (showing only the first five observations) 

   	Unnamed: 0	mpg	cyl	disp	hp	drat	wt	qsec	vs	am	gear	carb
   24	Pontiac Firebird	19.2	8	400.0	175	3.08	3.845	17.05	0	0	3	2
   21	Dodge Challenger	15.5	8	318.0	150	2.76	3.520	16.87	0	0	3	2
   31	Volvo 142E	21.4	4	121.0	109	4.11	2.780	18.60	1	1	4	2
   20	Toyota Corona	21.5	4	120.1	97	3.70	2.465	20.01	1	0	3	1
   30	Maserati Bora	15.0	8	301.0	335	3.54	3.570	14.60	0	1	5

5.  mpg wt hp mpg 1.000000 -0.869762 -0.766450 wt -0.869762 1.000000 0.664804 hp -0.766450 0.664804 1.000000

 OLS Regression Results ============================================================================== Dep. Variable: mpg R-squared: 0.820 Model: OLS Adj. R-squared: 0.807 Method: Least Squares F-statistic: 61.49 Date: Wed, 01 Dec 2021 Prob (F-statistic): 8.85e-11 Time: 23:25:59 Log-Likelihood: -70.448 No. Observations: 30 AIC: 146.9 Df Residuals: 27 BIC: 151.1 Df Model: 2 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ Intercept 37.1674 1.700 21.868 0.000 33.680 40.655 wt -3.9552 0.670 -5.906 0.000 -5.329 -2.581 hp -0.0300 0.010 -3.086 0.005 -0.050 -0.010 ============================================================================== Omnibus: 5.693 Durbin-Watson: 1.730 Prob(Omnibus): 0.058 Jarque-Bera (JB): 4.388 Skew: 0.922 Prob(JB): 0.111 Kurtosis: 3.328 Cond. No. 601. ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.