MAT-243 - 7-2 Discussion -Interpreting Multiple Regression Models

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Jan 9, 2024

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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: 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? 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. 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, , for horsepower in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script. 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 from Module Six? Provide appropriate interpretation of this statistic. 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?

2. How do the results of your peers' t-tests compare with yours? 3. Would you recommend this regression model to the car rental company? Why or why not? Hello, This is the evaluation of the significance of my model that used miles per gallon as a response variable. The weight and horsepower were the predictor variables. If we define the null hypothesis in the multiple regression model, the null hypothesis claims that there is no significant correlation at all. In mathematical terms, the null hypothesis is: H0 : β1 = β2 = 0. While the alternative hypothesis is defined as not every variable belongs in the model but at least one of the variables belongs in the model. In mathematical terms, the alternative hypothesis is Ha = At least one β ? ≠ 0 for ? = 1, 2. The level of significance for this test is 0.05 or 5%. The test statistics (F-statistics) is 67.28 and the Prob(F-Statistic) is 3.24e-11 or 0.0000000000324. Since the p-value (0.0000000000324) is lower than the level of significance 0.05, we reject the null hypothesis, in favor of the alternative hypothesis. Therefore at least one of the two variables (weight and horsepower) is significant in the model. The slope coefficient for the weight variable is -3.8944 and the p-value for this slope is 0.000 . Since the p - value (0.000) is less than the significance value of 0.05 this coefficient is significant. The slope coefficient for the horsepower variable is -0.0306 and the p-value for this slope is 0.003 . Since the p - value (0.003) is less than the significance value of 0.05 this coefficient is significant. The F-test determines whether there is a linear relationship with at least one predictor variable, whereas the individual t-test determines whether a single variable has an effect. So the purpose of performing individual t-tests after carrying out the overall F-test is to figure out which variable is significant and which one is not. The coefficient of determination of my multiple regression model which is also known as R- squared is 0.833 or 83.3%. The value of 83.3% gives the percent variance in miles per gallon explained by the predictor of weight and horsepower variables.

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