7-2 Discussion

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Southern New Hampshire University *

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Mathematics

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Apr 29, 2024

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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: A. Define the null and alternative hypothesis in mathematical terms and in words. H0: B1 = B2 = 0 Ha: Bn ≠ 0 for n =1 B. Report the level of significance. 0.05 or 5% level of significance C. Include the test statistic and the P-value. (Hint: F- Statistic and Prob (F-Statistic) in the output). Test Statistic = 71.04 P-Value = 1.76e-11 D. Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not? 1.76e-11 = 0.0000000000176 which is less than the level of significance so the null hypotheses should be rejected. 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.) See Step 5 in the Python script. -3.8630 Since the slope coefficient for the weight is less than the significance level of 0.05 it is statically significant.
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.) See Step 5 in the Python script. -0.0325 Since the slope coefficient for the horsepower variable is less than the significance level of 0.05 it is also statically significant. 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? The purpose of performing individual t-tests after carrying out F-tests is that the F-test will determine if a linear relationship exists with one predictor variable. Then once we are done checking with the F-test we proceed with the t-test to determine if the single variable makes any changes. 5. What is the coefficient of determination of your multiple regression model from Module Six? Provide appropriate interpretation of this statistic. The value of the coefficient determination (R^2) = 0.840 which means that 84.0% of the total variation data in MPG is explained by the variances with weight and HP as the predictors.
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