Grades A Statistics instructor created a linear regression equation to predict students’ final exam scores from their midterm exam scores. The regression equation was Fin = 10 + 0.9 Mid.
a) If Susan scored a 70 on the midterm, what did the instructor predict for her score on the final?
b) Susan got an 80 on the final. How big is her residual?
c) If the standard deviation of the final was 12 points and the standard deviation of the midterm was 10 points, what is the correlation between the two tests?
d) How many points would someone need to score on the midterm to have a predicted final score of 100?
e) Suppose someone scored 100 on the final. Explain why you can’t estimate this student’s midterm score from the information given.
f) One of the students in the class scored 100 on the midterm but got overconfident, slacked off, and scored only 15 on the final exam. What is the residual for this student?
g) No other student in the class “achieved” such a dramatic turnaround. If the instructor decides not to include this student’s scores when constructing a new regression model, will the R2
value of the regression increase, decrease, or remain the same? Explain.
h) Will the slope of the new line increase or decrease?