Question

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?

      OLS Regression Results                            
   ==============================================================================
   Dep. Variable:                    mpg   R-squared:                       0.822
   Model:                            OLS   Adj. R-squared:                  0.808
   Method:                 Least Squares   F-statistic:                     62.13
   Date:                Fri, 14 Feb 2020   Prob (F-statistic):           7.88e-11
   Time:                        05:00:39   Log-Likelihood:                -69.730
   No. Observations:                  30   AIC:                             145.5
   Df Residuals:                      27   BIC:                             149.7
   Df Model:                           2                                         
   Covariance Type:            nonrobust                                         
   ==============================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
   ------------------------------------------------------------------------------
   Intercept     37.8867      1.748     21.674      0.000      34.300      41.473
   wt            -4.0629      0.694     -5.855      0.000      -5.487      -2.639
   hp            -0.0318      0.009     -3.470      0.002      -0.051      -0.013
   ==============================================================================
   Omnibus:                        5.277   Durbin-Watson:                   1.919
   Prob(Omnibus):                  0.071   Jarque-Bera (JB):                3.980
   Skew:                           0.878   Prob(JB):                        0.137
   Kurtosis:                       3.314   Cond. No.                         620.
   ==============================================================================
   
   Warnings:
   [1] Standard Errors assume that the covariance matrix of the errors is correctly specified

Answer 1