Simple Linear Regression Example

A college administers for all its courses a student evaluation questionnaire. For a random sample of 12 courses the table below shows both the average student ratings of the instructor (on a scale from 1 to 5), and the average expected grades of the students (on a scale from A=4 to F=0).

Instructor Rating	Expected Grade
2.8	2.6
3.7	2.9
4.4	3.3
3.6	3.2
4.7	3.1
3.5	2.8
4.1	2.7
3.2	2.4
4.9	3.5
4.2	3.0
3.8	3.4
3.3	2.5

a. Find the sample covariance and correlation coefficient between Instructor Ratings and Expected Grades. Is there a strong linear relationship between Instructor Rating and Expected Grade?

b. Use MS Excel to compute the regression coefficients, b₀ and b1. What percentage of variations in Instructor Rating is due to Expected Grade?

c. If a student's expected grade is 3.0, predict this student's rating of the instructor.

d. Plot Instructor Rating against Expected Grade, use MS Excel.