Question

A professor would like to conduct a regression analysis to determine whether a student’s final exam score in her class can be predicted from the student’s midterm score. She records the midterm and final exam scores of a sample of students in her class. The midterm scores have a mean of 71.0 and a standard deviation of 9.4. The final exam scores have a mean of 66.2 and a standard deviation of 10.3. The correlation between midterm and final exam score is calculated to be 0.84.

What is the predicted increase in final exam score when a student’s midterm score increases by one?

Answer 1

Let , X : midterm score

Y : Final exam score

The regression equation is ,

Where , 'b' be the regression coefficient or slope of the regression equation.

and 'a' be the constant or intercept of the regression equation.

Now ,

Therefore , The regression equation is ,

Now , For x=1

Therefore , the predicted increase in final exam score when a student’s midterm score increases by one is 1.7720