1. Is at least one of the two variables (weight and horsepower) significant in the model? Run the overall F-test and provide your interpretation at 5% level of significance. See Step 5 in the Python script. Include the following in your analysis:

Define the null and alternative hypothesis in mathematical terms and in words. Report the level of significance. Include the test statistic and the P-value. (Hint: F-Statistic and Prob (F-Statistic) in the output). Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?

2. What is the slope coefficient for the weight variable? Is this coefficient significant at 5% level of significance (alpha=0.05)? (Hint: Check the P-value, P is greater than the absolute value of t, for weight in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script.

3. What is the slope coefficient for the horsepower variable? Is this coefficient significant at 5% level of significance (alpha=0.05)? (Hint: Check the P-value, P is greater than the absolute value of t, for horsepower in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script.

4. What is the purpose of performing individual t-tests after carrying out the overall F-test? What are the differences in the interpretation of the two tests?

5. What is the coefficient of determination of your multiple regression model from Module Six? Provide appropriate interpretation of this statistic.

Step 5: Multiple regression model to predict miles per gallon using weight and horsepower This block of code produces a multiple regression model with "miles per gallon" as the response variable, and "weight" and "horsepower" as predictor variables. The ols method in statsmodels.formula.api submodule returns all statistics for this multiple regression model. Click the block of code below and hit the Run button above. In [5]: from statsmodels . formula. api import ols # create the multiple regression model with mpg as the response variable; weight and horsepower as predictor variables. model = ols ('mpg ~ wt+hp', data=cars_df) .fit( ) print (model . summary ( ) ) OLS Regression Results Dep. Variable: mpg R - squared : 0. 832 Model : OLS Adj . R-squared: 0. 819 Method : Least Squares F-statistic : 66. 78 Date: Thu, 11 Aug 2022 Prob (F-statistic) : 3. 52e-11 Time : 22:23:49 Log-Likelihood : -69 . 864 No. Observations: 30 AIC : 145.7 Of Residuals: 27 BIC: 149.9 Df Model : 2 Covariance Type: nonrobust coef std err t P> t [0. 025 0.975] Intercept 37.4359 1. 636 22. 882 0.000 34 . 079 40. 793 wt -3. 8924 0. 641 -6. 070 0.000 -5. 208 -2.577 hp - 0. 0319 0. 009 - 3. 498 0. 002 - 0. 051 -0. 013 EEEE Omnibus : 4. 148 Durbin-Watson: 1. 666Step 5: Multiple regression model to predict miles per gallon using weight and horsepower This block of code produces a multiple regression model with "miles per gallon" as the response variable, and "weight" and "horsepower" as predictor variables. The ols method in statsmodels.formula.api submodule returns all statistics for this multiple regression model. Click the block of code below and hit the Run button above. In [5]: from statsmodels. formula . api import ols # create the multiple regression model with mpg as the response variable; weight and horsepower as predictor variables. model = ols ('mpg ~ wt+hp', data=cars_df) . fit( ) print (model . summary ( ) ) No. Observations : 30 AIC : 145 .7 Of Residuals : 27 BIC : 149.9 Df Model: 2 Covariance Type: nonrobust coef std err t P> |t| [0 . 025 0.975] Intercept 37.4359 1. 636 22. 882 0. 000 34. 079 40 . 793 wt -3. 8924 0. 641 -6. 070 0.000 -5 . 208 - 2.577 hp -0. 0319 0. 009 - 3. 498 0. 002 -0 . 051 - 0. 013 Omnibus : 4. 148 Durbin-Watson : 1. 666 Prob (Omnibus ) : 0. 126 Jarque -Bera (JB) : 2.999 Skew: 0. 767 Prob ( JB) : 0. 223 Kurtosis : 3.217 Cond. No. 579 Warnings : [1] Standard Errors assume that the covariance matrix of the errors is correctly specified