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 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 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 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 What is the coefficient of determination of your multiple regression model from Module Six Provide appropriate interpretation of this statistic This is step 5 OL5 Regression Results Dep Variable mpg R squared 0 835 Model OLS Adj R squared 0 823 Method Least Squares F statistic 68 39 Date Fri, 10 Jun 2022 Prob (F statistic) 2 70e 11 Time 02 14 02 Log Likelihood 69 855 No Observations 30 AIC 145 7 Of Residuals 27 BIC 149 9 Of Model 2 Covariance Type nonrobust coef std err t P t 0 025 0 975 Intercept 37 5934 1 644 22 860 0 000 34 219 40 968 wt 3 9334 0 642 6 123 0 090 5 252 2 615 hp 0 0324 0 009 3 515 0 002 0 051 0 013 Omnibus 4 567 Durbin Watson 2 063 Prob (Omnibus ) 0 102 Jarque Bera (JB) 3 422 Skew 0 821 Prob (JB) 9 181 Kurtosis 3 201 Cond No 590 Warnings 1 Standard Errors assume that the covariance matrix of the errors is correctly specified

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jun 26, 2024

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%

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

OL5 Regression Results Dep. Variable: mpg R-squared: 0.835 Model : OLS Adj. R-squared: 0. 823 Method: Least Squares F-statistic: 68.39 Date: Fri, 10 Jun 2022 Prob (F-statistic) : 2.70e-11 Time: 02 :14:02 Log-Likelihood: -69.855 No. Observations: 30 AIC: 145.7 Of Residuals: 27 BIC: 149.9 Of Model: 2 Covariance Type: nonrobust coef std err t P> t [0. 025 0.975] Intercept 37 .5934 1. 644 22.860 0.000 34.219 40.968 wt -3.9334 0.642 -6.123 0.090 -5.252 -2. 615 hp -0. 0324 0.009 -3.515 0. 002 -0.051 -0.013 Omnibus : 4.567 Durbin-Watson: 2.063 Prob (Omnibus ) : 0.102 Jarque-Bera (JB): 3.422 Skew: 0. 821 Prob (JB) : 9.181 Kurtosis: 3. 201 Cond. No. 590. Warnings : [1] Standard Errors assume that the covariance matrix of the errors is correctly specified