Chapter 14, Problem 1SE

Predicting Test Scores A professor tells his class that he knows their second exam score without their having to take the test. He tells them that the second exam score can be predicted from the first with this equation:

Predicted second exam score $=5+0.75$ (first exam score)

This tells us that the deterministic part of the regression model that predicts second exam score on the basis of first exam score is a straight line. What factors might contribute to the random component? In other words, why might a student’s score not fall exactly on this line?

To determine

Explain the factors that contribute to the student’s score, to not fall exactly on the regression line.

Explanation of Solution

A professor tells his students that he can predict the scores of the students from their first exam scores using the calculated regression line.

There may be chances that the predicted second exam scores do not fall on the regression line due to some random factors.

The amount of time the student spent on the study.

The level of difficulty of the question paper and familiarity with the type of questions

Psychological and physical condition of the candidate (depression, confidence level, sleeplessness, illness etc.) during exam.

Disturbance in the exam hall.

There may be many such factors, which affect the student’s score in the second exam.