# discussion And project

I’m working on a Mathematics question and need guidance to help me study.

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.

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?

Remember to attach your Python output and respond to all questions in your initial and follow-up posts. Be sure to clearly communicate your ideas using appropriate terminology. Finally, be sure to review the Discussion Rubric to understand how you will be graded on this assignment.

PART 2 :

For this project, you will submit the Python script you used to make your calculations and a summary report explaining your findings.

1. Python Script: To complete the tasks listed below, open the Project Three Jupyter Notebook link in the Assignment Information module. This notebook contains your data set and the Python scripts for your project. In the notebook, you will find step-by-step instructions and code blocks that will help you complete the following tasks:
• Simple Linear Regression
• Create scatterplots
• Compute the correlation coefficient
• Conduct a linear regression
• Multiple Regression
• Create scatterplots
• Compute the correlation matrix
• Conduct a multiple regression analysis
1. Summary Report: Once you have completed all the steps in your Python script, you will create a summary report to present your findings. Use the provided template to create your report. You must complete each of the following sections:
• Introduction: Set the context for your scenario and the analyses you will be performing.
• Scatterplots and Correlation: Discuss relationships between variables using scatterplots and correlation coefficients.
• Simple Linear Regression: Create a simple linear regression model to predict the response variable.
• Multiple Regression: Create a multiple regression model to predict the response variable.
• Conclusion: Summarize your findings and explain their practical implications.