Case Study, Statistics The Prescott High School Regression Case Study

Project description
For this case study the dependent variable is the college GPA and all other variables are the independent variables. 
 
You are to do the following tests including explaining/analyzing the results of these statistical tests: 
 
1. A one variable summary for all variables (single output with all 4 on it). 
2. A scatterplot with the college GPA and the high school GPA, add a trend line and show the R2 value on the plot. 
3. A correlation coefficient showing all variables – analyze the results. 
4. Histograms for all variables – 4 different histograms. 
5. A multiple regression with all 4 coefficients calculated correctly. Explain the r-squared value, what it means, the F-value and what it means, and the T-test values and what they mean. 
a. Are there any variables that could be deleted from the regression? If there are rerun the regression without this variable(s). 
b. If you remove one or more variable then calculate the college GPA for all variables, and then for those variables less that the alpha. Which way better predicts the college GPA? 
6. Predict the college GPA for the following three students and complete and include Table One found below in your written report: 
a. Susie Smart who has a high school GPA of 3.54; an SAT score of 1410; and who has letters of recommendation that rank at level 8. 
b. Burt Passer who has a high school GPA of 2.75, an SAT score of 1235; and who has letters of recommendation that rank at level 5. 
c. Johnny Goofoff who has a high school GPA of 2.10, an SAT score of 1460; and who has letters of recommendation that rank at level 9. 
7. Support or attack gently Brenda Miller’s contention that she can predict college GPA better than the FCAT test can by using the final high school GPA, SAT total score, and the quality of the letters of recommendation for graduating students. 
 
Table One. Predicted College GPA 
 
Student Predicted College GPA 
Susie Smart 
Bert Passer 
Johnny Goofoff 
 
Your Tasks 
 
1. Carry out the various statistical tests as indicated above. 
2. Predict the possible college GPAs for the three students listed and decide if the regression can actually predict college GPAs (not a yes or no answer, be specific). 
3. Analyze the resulting data, and determine if Ms. Miller is correct or not. 
4. Submit your individual report on time. 
 
Write a management report (using the required format) suggesting and justifying an appropriate decision regarding the use of the three variables to predict college GPA. In your report, analyze the patterns of the interplay of college GPA, high school GPA, SAT scores and the quality of the letters of recommendation. Independent outside research is encouraged to provide relevant background information and/ or to provide more support for your arguments.

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