EBK PRACTICE OF STAT.F/AP EXAM,UPDATED
EBK PRACTICE OF STAT.F/AP EXAM,UPDATED
6th Edition
ISBN: 9781319287573
Author: Starnes
Publisher: MPS PUB
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Chapter 3.2, Problem 65E

(a)

To determine

To state the equation of the least squares regression line if each student scored the same on the midterm and final.

(a)

Expert Solution
Check Mark

Answer to Problem 65E

  y^=x .

Explanation of Solution

Let x be midterm score and y be the final score.

If each student scores the same on the midterm and the final then the data of the explanatory variable x will be the same as the data for the response variable y . If the data of the two variables are the same then the linear model will predict that the two variables are equal and thus the linear model will assume that the predicted y -variable is equal to the x -variable. Thus, we have the least square regression line as:

  y^=x .

(b)

To determine

To predict the score of a student who scored 50 on the midterm and a student who scored 100 on the midterm.

(b)

Expert Solution
Check Mark

Answer to Problem 65E

The predicted score of a student who scored 50 on the midterm is 67.10 .

The predicted score of a student who scored 100 on the midterm is 87.60 .

Explanation of Solution

It is given in the question the least square regression line be as:

  y^=46.6+0.41x

To predict the score of a student who scored 50 on the midterm, then we have,

  y^=46.6+0.41x=46.6+0.41(50)=67.10

Thus the predicted score of a student who scored 50 on the midterm is 67.10 .

Now, to predict the score of a student who scored 100 on the midterm, we have,

  y^=46.6+0.41x=46.6+0.41(100)=87.60

Thus the predicted score of a student who scored 100 on the midterm is 87.60 .

(c)

To determine

To explain how your answer to part (b) illustrate regression to the mean.

(c)

Expert Solution
Check Mark

Explanation of Solution

We have from part (b) as:

The predicted score of a student who scored 50 on the midterm is 67.10 .

The predicted score of a student who scored 100 on the midterm is 87.60 .

Thus, we estimate that the mean of the midterm will be somewhere between 50 and 100 ,assuming that most students pass the midterm. Similarly, this is for the score of the final. The student who score 50 on the midterm then scored lower that the mean. And the student who scored 100 on the midterm then scored higher than the mean. Finally, we also note that the student who scored 50 has the higher predicted score on the final, while the student who scored 100 has a lower predicted score on the final, which indicates that the prediction on the final exam appears to be closer to the mean.

Chapter 3 Solutions

EBK PRACTICE OF STAT.F/AP EXAM,UPDATED

Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.2 - Prob. 65ECh. 3.2 - Prob. 66ECh. 3.2 - Prob. 67ECh. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - Prob. 70ECh. 3.2 - Prob. 71ECh. 3.2 - Prob. 72ECh. 3.2 - Prob. 73ECh. 3.2 - Prob. 74ECh. 3.2 - Prob. 75ECh. 3.2 - Prob. 76ECh. 3.2 - Prob. 77ECh. 3.2 - Prob. 78ECh. 3.2 - Prob. 79ECh. 3.2 - Prob. 80ECh. 3 - Prob. R3.1RECh. 3 - Prob. R3.2RECh. 3 - Prob. R3.3RECh. 3 - Prob. R3.4RECh. 3 - Prob. R3.5RECh. 3 - Prob. R3.6RECh. 3 - Prob. T3.1SPTCh. 3 - Prob. T3.2SPTCh. 3 - Prob. T3.3SPTCh. 3 - Prob. T3.4SPTCh. 3 - Prob. T3.5SPTCh. 3 - Prob. T3.6SPTCh. 3 - Prob. T3.7SPTCh. 3 - Prob. T3.8SPTCh. 3 - Prob. T3.9SPTCh. 3 - Prob. T3.10SPTCh. 3 - Prob. T3.11SPTCh. 3 - Prob. T3.12SPTCh. 3 - Prob. T3.13SPT
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