# regression study

MAT 273 — Applied Statistics

PROJECT II

50 points

Passing Rate for the 12th Grade Proficiency Examination – c. 1995

This project may be done in groups of up to 3 Students

This project is a regression study done on the rate at which students in schools in northwest Ohio passed the 12th grade proficiency examinations about the year 1995. (This is the year for which I have data.) The data comprises 8 variables for 88 districts. 6 additional school districts’ data has been placed at the right of the sheet. These have been removed from the data because they are outliers. A detailed description of the variables in the data set is below, and the data file is in the web portal. Your job is to do a regression analysis, and then think about the results and draw conclusions.

This project will contain 7 pages and only 7 pages

Use the “Project 2 Data Schools file to complete the following:

Using the data in the *Income Data* sheet, produce a scatter plot with the passing rate as the response variable and the ‘Mean Family Income in the District’ as the explanatory variable. Print as page 2.

Repeat Step 2. using the ‘Mean Salary for Classroom Teachers’ as the explanatory variable in the *Salary Data* sheet. Print as page 3.

Repeat Step 2. using the ‘Average Daily Attendance Rate’ as the explanatory variable in the *Attendance Data* sheet. Print as page 4.

Run 3 simple regressions with the passing rate as the response variable and each of ‘Mean Family Income in the District,’ ‘Mean Salary for Classroom Teachers’ and ‘Average Daily Attendance Rate’ as the explanatory variable. For *each one*:

Indicate the correlation coefficient (R)

*I**nterpret* the coefficient of determination (R²)

*I**nterpret* the significance

Give the linear regression equation

Use the regression equation to predict one passing rate value.

Note: These can be written by hand on the printouts, or typed into the sheet before printing. Print these as pages 5, 6, and 7.

**Report your findings: **

Submit a typewritten 6-paragraph summary of the assignment and your findings. The summary should be formatted with one paragraph each for the introduction and conclusion and one paragraph of ANALYSIS/INTERPRETATION for *each* of the four questions below. Attach a copy of the EXCEL printouts to the report.

The questions you are asked to consider are:

Which of the three possible explanatory variables in Part 4 is significantly tied to the passing rate? Justify your answer using significance.

Which of the three possible explanatory variables in Part 4 is the best predictor of the passing rate? Justify your answer using correlation.

Do any of the relationships look nonlinear? Which one or ones?

Are any of the regression equations surprising? Which one or ones?