Question

 A Statistics professor assigned 10 quizzes over the course of the semester. He wanted to see if there was a relationship between the total mark of all 10 quizzes and the final exam mark. There were 203 students who completed all the quizzes and wrote the final exam. The standard deviation of the total quiz marks was 15, and that of the final exam was 16. The correlation between the total quiz mark and the final exam was 0.8. 

Based on the least squares regression line fitted to the data of the 203 students, if a student scored 22 points above the mean of total quiz marks, then how many points above the mean on the final would you predict her final exam grade to be? above the mean on the final. Round your answer to one decimal place, but do not 

The predicted final exam grade is round in intermediate steps.

Answer 1

Answer:

Given,

Let us assume that X be the final exam grade

Let the total marks of all 10 quizzes be Y

So now the standard deviation of total quiz marks = $\sigma y$ = 15

Standard deviation of final exam = $\sigma x$ = 16

The correlation between the total quiz mark and the final exam = r = 0.8

Here it is given,

student scored 22 points above the mean of total quiz marks

So now consider,

Regression co-efficient = r * $\sigma x$ / $\sigma y$

substitute values

= 0.8 * 16/15

= 0.8*1.0667

= 0.8534

Regression co-efficient = 0.8534

So now if a student scored 22 points above the mean on the midterm then we expect her to score =

= Regression co-efficient * 22

= 0.8534 * 22

= 18.7748 above the mean on the final

The predicted final exam grade is 18.8 above the mean on the final.