MAT 243 Project Three Summary Report Template

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Southern New Hampshire University *

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Mathematics

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Feb 20, 2024

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MAT 243 Project Three Summary Report [Full Name] [SNHU Email] Southern New Hampshire University

Notes:  Replace the bracketed text on page one (the cover page) with your personal information.  You will use your selected team for all three projects 1. Introduction Discuss the statement of the problem in terms of the statistical analyses that are being performed. Be sure to address the following:  What is the data set that you are exploring?  How will your results be used?  What type of analyses will you be running in this project? Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include Python code in your report. 2. Data Preparation There are some important variables that are used in this project. Identify and explain these variables. See the introductory section and Step 1 of the Python script to address the following:  What does the variable avg_pts_differential represent? How would you explain it to someone who does not understand the data?  What does the variable avg_elo_n represent? How would you explain it to someone who does not understand the data? Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include Python code in your report. 3. Simple Linear Regression: Scatterplot and Correlation for the Total Number of Wins and Average Relative Skill You constructed a scatterplot of the total number of wins and the average relative skill to study their correlation. You also calculated the Pearson correlation coefficient along with its P-value. See Step 2 in the Python script to address the following items:  In general, how are data visualization techniques used to study relationship trends between two variables?  How is the correlation coefficient used to get the strength and direction of the association between two variables?  In this activity, you generated a scatterplot of the total number of wins and the average relative skill. Include a screenshot of this plot in your report.  What do the scatterplot and the Pearson correlation coefficient tell you about the association between total number of wins and average relative skill?

 Is the correlation coefficient statistically significant based on the P-value? Use a 1% level of significance. Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include Python code in your report. 4. Simple Linear Regression: Predicting the Total Number of Wins using Average Relative Skill You created a simple linear regression model for the total number of wins in a regular season using the average relative skill as the predictor variable. See Step 3 in the Python script to address the following items:  In general, how is a simple linear regression model used to predict the response variable using the predictor variable?  What is the equation for your model?  What are the results of the overall F-test? Summarize all important steps of this hypothesis test. This includes: a. Null Hypothesis (statistical notation and its description in words) b. Alternative Hypothesis (statistical notation and its description in words) c. Level of Significance d. Report the test statistic and the P-value in a formatted table as shown below: Table 1: Hypothesis Test for the Overall F-Test Statistic Value Test Statistic X.XX *Round off to 2 decimal places. P-value X.XXXX *Round off to 4 decimal places. e. Conclusion of the hypothesis test and its interpretation based on the P-value  Based on the results of the overall F-test, can average relative skill predict the total number of wins in the regular season?  What is the predicted total number of wins in a regular season for a team that has an average relative skill of 1550? Round your answer down to the nearest integer.  What is the predicted number of wins in a regular season for a team that has an average relative skill of 1450? Round your answer down to the nearest integer. Answer the questions in a paragraph response. Remove all questions and this note (but not the table) before submitting! Do not include Python code in your report. 5. Multiple Regression: Scatterplot and Correlation for the Total Number of Wins and Average Points Scored You will now add a second predictor to the model from section 3 and create a multiple regression model for the total number of wins.

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