A researcher is interested in determining the relationship between the number of hours of sleep a student gets the night before an exam (X) and the number of errors he or she makes on that exam (Y). Compute the Pearson’s r to determine the direction and strength of this relationship. Then use the linear regression equation to predict the number of errors for a student who gets three hours of sleep. Include in your answer the standard error of the estimate as well as the proportion of variance accounted for. Round to two decimal places for all of your answers.

Hours of Sleep (X) Number of Errors (Y)
0 9
1 8
1 8
0 7
1 6
3 5
2 6
3 5
5 3
6 3
7 2
9 0