Evaluate the significance of individual predictors. You will use the given output to perform individual t-tests for each predictor variable. 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. 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>|t|, for weight in Python output. Recall that this is the individual t-test for the beta parameter.)

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>|t|, for horsepower in Python output. Recall that this is the individual t-test for the beta parameter.)

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? Provide appropriate interpretation of this statistic.

MPG against Weight 35 30 25 MPG 20 15 10 15 20 25 3.0 3.5 4.0 4.5 5.0 5.5 Weight (1000s lbs)\f\fOLS Regression Results Dep. Variable: mpg R- squared: 0. 808 Model : OLS Adj. R-squared: 0.794 Method : Least Squares F-statistic: 56.81 Date : Fri, 07 Oct 2022 Prob (F-statistic) : 2. 11e-10 Time : 03:21:47 Log-Likelihood : -70.324 No. Observations : 30 AIC : 146.6 Of Residuals: 27 BIC: 150.9 Of Model : 2 Covariance Type: nonrobust coef std err t P> t [0. 025 0.975] Intercept 36. 8932 1. 744 21.160 0. 000 33.316 40 . 471 wt -3.9027 0. 671 -5.816 0.000 -5.279 -2.526 hp -0.0296 0. 010 - 3. 044 0. 005 - 0. 050 -0. 010 Omnibus : 6.784 Durbin-Watson : 2. 257 Prob (Omnibus ) : 0. 034 Jarque -Bera (JB) : 5.327 Skew: 1.001 Prob (JB) : 0. 0697 Kurtosis : 3.502 Cond. No. 620. Warnings : [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.Cars data frame (showing only the first five observations) Unnamed: 0 mpg cyl disp hp drat wt qsec vs am gear carb 30 Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 5 8 24 Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2 8 Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2 6 Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 4 4 Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 2