EPS 625 – INTERMEDIATE STATISTICS
SIMPLE LINEAR REGRESSION – SAMPLE QUESTIONS – KEY
Professor Stats has collected data (Exam 1, Exam 2, and Final Exam) on students in
her previous semester’s statistics class. She now wants to use that data to predict the
performance of her current semester’s statistics class students. Using the simple linear
regression output from SPSS, answer the following questions…
1.
Professor Stats has decided to use Simple Linear Regression (1 predictor or independent
variable and 1 criterion or dependent variable), and determined that Exam 2 would be the
better predictor (between Exam 1 and Exam 2) for the Final Exam. Do you agree with
her? Yes or No, and indicate why or why not.
Yes
2.

because it is significantly different from zero (r = .428**).
What is the relationship between Exam 2 and the Final Exam?
r = .701
4.
because the relationship (correlation) between Exam 2 and the
Final (r = .701), is stronger than the relationship between Exam 1
and the Final (r = .428). Additionally, the relationship between
Exam 2 and the Final is significantly different from zero.
Based on your knowledge of a “good” predictor, would you agree that Exam 1 would
also be a good predictor of the Final Exam? Yes or No, and indicate why or why not.
Yes
3.

Positive (Direct), Imperfect
What proportion of total variance in the Final Exam is being accounted for by the
variance in Exam 2?
r2 = .491 (or) approximately 49.1%
5.
In preparation for using the given information to predict a Final Exam score for a student
in the current semester:
5a.
Write the formula used in predicating a student’s Final Exam score. Use the
appropriate symbols as indicated in your text.
Yˆ = bX + a
EPS 625 – INTERMEDIATE STATISTICS
SIMPLE LINEAR REGRESSION – SAMPLE QUESTIONS – KEY
5b.
What is the numeric value of the regression constant?
a = 47.432
5c.
What is the numeric value of the regression coefficient?
b = .518
6.
Using the formula from question 4a. – and knowing that a current student has made an 80
on Exam 2, what would you predict their score to be on the Final Exam?
Y’ = bX + a

Y’ = .518(80) + 47.432
Y’ = 41.44 + 47.432
Y’ = 88.892 (89)
7.
What is the degree of error associated with this regression analysis?
7.565 standard deviations