In a particular college math class, students begin the semester taking a pre-test (Pre). At the end of the
semester, students receive a final class percentage (Final). Both scores are recorded as percentages out of 100. It was desired to know if performance on the pre-test was predictive of final class percentage. There were 9 students in the class. The results are below:
For all of the parts below, please perform the calculations by hand, and show your work. You may use R to make plots and check your answers.
- (a) Make a scatterplot of the data. Does it seem like a straight line model is reasonable?
- (b) Assuming a straight-line model, compute estimates of the intercept (β0) and slope (β1).
- Perform a test of
H0 :β1 =0 vs.HA :β1 ̸=0,
a. using a T -test at α = 0.05. Make a conclusion in the context of the problem.
b. Compute R2 for this regression and interpret it.
c. If a student scores 80 on the pre-test, what does the model predict their final score will be? Compute the SE of this estimate assuming it is for an individual future test taker.