Question

In Professor Friedman's economics course the correlation betweenthe students' total scores before the final examination and theirfinal examination scores is r = 0.6. The pre-exam totalsfor all students in the course have mean 280 and standard deviation30. The final exam scores have mean 75 and standard deviation 8.Professor Friedman has lost Julie's final exam but knows that hertotal before the exam was 300. He decides to predict Julie's finalexam score from her pre-exam total.
Question 1. Calculate the slope and interceptof the least squares regression line where the x-variableis pre-exam total score and the y-variable is final examscore.
slope
intercept

Question 2. What is the value of Julie's finalexam score predicted by the least squares regression line?


Question 3. Julie complains to ProfessorFriedman that her final exam score could have been much higher thanwhat is predicted by the least squares regression line. Calculatethe proportion of the variation in final exam scores that isexplained by the linear relationship between pre-exam scores andfinal exam scores. (Express your answer as a decimal, not as apercent).

Answer 1

Answer:

Q1

slope=0.16

intercept=30.2

Q2

78.2

Q3

36%

Step-by-step explanation:

Question 1

We are given that

xbar=280

sx=30

ybar=75

sy=8

r=0.6

The regression line can be written as

y=a+bx

a=intercept

b=slope

where

$b=r\frac{sy}{sx}$

and

$a=ybar-bxbar$

b=0.6*(8/30)

b=0.16

a=75-0.16*280

a=30.2

Thus,

slope=0.16

intercept=30.2

Question 2

The regression line in the given scenario

y=30.2+0.16x

Julie pre exam total before the exam was 300.

y=30.2+0.16*300

y=30.2+48=78.2

So, the predicted final exam score of Julie is 78.2.

Question 3

R² denotes the variation in dependent variable y explained by the linear relationship of x and y.

R²=0.6²=0.36

Thus, the proportion of the variation in final exam scores that is explained by the linear relationship between pre-exam scores and final exam scores is 36%.