============================================================================== Dep. Variable: mpg R-squared: 0.829 Model: OLS Adj. R-squared: 0.816 Method: Least Squares F-statistic: 65.51 Date: Fri, 02 Dec 2022 Prob (F-statistic): 4.37e-11 Time: 01:00:57 Log-Likelihood: -70.258 No. Observations: 30 AIC: 146.5 Df Residuals: 27 BIC: 150.7 Df Model: 2 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ Intercept 37.2464 1.637 22.755 0.000 33.888 40.605 wt -3.8197 0.652 -5.857 0.000 -5.158 -2.482 hp -0.0327 0.009 -3.517 0.002 -0.052 -0.014 ============================================================================== Omnibus: 4.301 Durbin-Watson: 1.918 Prob(Omnibus): 0.116 Jarque-Bera (JB): 3.210 Skew: 0.797 Prob(JB): 0.201 Kurtosis: 3.166 Cond. No. 571. ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

In your initial post, address the following items:

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:
   1. Define the null and alternative hypothesis in mathematical terms and in words.
   2. Report the level of significance.
   3. Include the test statistic and the P-value. (Hint: F-Statistic and Prob (F-Statistic) in the output).
   4. 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,, 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,, 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.