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7-2 Discussion: Interpreting Multiple Regression Models In this discussion, you will apply the statistical concepts and techniques covered in this week's reading about multiple regression. You will not be completing work in Jupyter Notebook this week. Instead, you will be interpreting output from your Python scripts for the Module Six discussion. If you did not complete the Module Six discussion, please complete that before working on this assignment. Last week’s discussion involved development of a multiple regression model that used miles per gallon as a response variable. Weight and horsepower were predictor variables. You performed an overall F-test to evaluate the significance of your model. This week, you will evaluate the significance of individual predictors. You will use output of Python script from Module Six to perform individual t-tests for each predictor variable. Specifically, you will look at Step 5 of the Python script to answer all questions in the discussion this week. 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: a. Define the null and alternative hypothesis in mathematical terms and in words. H0: β1 = β2 = 0 Ha: at least one βn ≠ 0 for n = 1, 2. b. Report the level of significance. 0.05. 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 = 64.36 P-value = 5.33 ∙10−11 d. Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not? Since this p-value is less than the level of significance, reject the null hypothesis. Significant linear relationship exists between Y and the set {X1, X2} when X1= wt(weight)and X2 = hp(horsepower).

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. -0.877244 Since P-value 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 Pvalue, , for horsepower in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script. -0.768871 Since P-value is less than the significance level of 0.05, it is 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? F-test determines whether a linear relationship exists with at least one predictor variable. So after we check if any linear relationship exists, we conduct t-test to determine whether a single variable has an effect.

5. What is the coefficient of determination of your multiple regression model from Module Six? Provide appropriate interpretation of this statistic. 0.844 The value for R2 means that 82.7% of the data fit the regression model. In other word, approximately 82.7% of the total variation in MPG is accounted for by the linear regression model with HP(horsepower) and WT(weight) as predictors.

In your follow-up posts to other students, review your peers' results and provide some analysis and interpretation: 1. Interpret your peer’s coefficient of determination. How does it compare with yours? 0.827 2. How do the results of your peers’ t-tests compare with yours? 64.36

3. Would you recommend this regression model to the car rental company? Why or why not?

Your R-squared is 0.819 while mine was 0.827. there is not much difference. And your t-test is 60.99 while mine was 64.36. mine is slightly higher than yours. I would recommend this regression model to the car company because your R-squared suggests that your model is a good predictor. Your coefficient of determination and the t-test both are little bit higher than mine. I would recommend this model to the rental car company since the high value of R-squared indicates good fit for the regression model....