A Study of Grade Correlation
This is Part 2 of the worksheet on correlation and linear regression.
(1) Make a copy of your ChewGrades.xlsx and work on the new copy.
(2) Our goal is to find the linear relationship between our second scatterplot which
displays Actual Exam Score on the x-axis vs Difference on the y-axis. There appears
to be a good linear relationship here and our correlation coefficient is at least
moderately strong.
We will use linear regression to find the line that best fits this data.
(3) Compute the quantities that we will need for the linear regression.
Σx
Σy
Σxy
Σx2
n
Make an entry for each one in the spreadsheet.
(4) Use these quantities to complete the formula for b and a, the slope and yintercept of our optimal line.
(5) Use the equation of this line to fit an actual drawn line to the scatterplot. Hint:
figure out where the line goes by substituting x=30 and x=100 into the equation to
find the appropriate values for ŷ. Use this line to find the expected residual
difference for a student who scores 50 on the exam. Then compute their expected
exam score.
(7) Use this line to find the expected residual difference for a student who scores 90
on the exam. Then compute their expected exam score.
(8) Now we want to assess how well the data fits the line. Add three columns in
your spreadsheet.
a. The first column is the predicted values for ŷ. Use the x values (actual exam
scores) and your results for b,a to compute the predicted values.
b. The next column is labeled Squares. It computes the squared difference
between each value for y and the average y. See page 254 in our text.
c. The last column is labeled Residuals. It computes the squared difference
between each value and the predicted value you just added. Again see page
254.
(9) Compute SSTO and SSResid as specified in the text. Then compute r2, the
coefficient of determination. Take the square root of this to compare to the
correlation coefficient you found before.