PRACTICE OF STATISTICS F/AP EXAM
PRACTICE OF STATISTICS F/AP EXAM
6th Edition
ISBN: 9781319113339
Author: Starnes
Publisher: MAC HIGHER
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Chapter 3.2, Problem 58E

(a)

To determine

To calculate and interpret the residual for the student who was 141 cm tall at age 10 .

(a)

Expert Solution
Check Mark

Answer to Problem 58E

The residual is 7.2 .

Explanation of Solution

The relationship between the height and age of the students is given in the question. And the regression line is as:

  y^=106.1+4.21x

And also given that the student who was 141 cm tall at age 10 . Thus, we have,

  x=10y=141

Thus the predicted height of the student is as:

  y^=106.1+4.21x=106.1+4.21(10)=148.2

Thus, the residual will be calculated as:

  Residual=yy^=141148.2=7.2

This then implies that we overestimated the height of the student at age 10 by 7.2 cm, when making a prediction using the regression line.

(b)

To determine

To interpret the slope of the least square regression line.

(b)

Expert Solution
Check Mark

Explanation of Solution

The relationship between the height and age of the students is given in the question. And the regression line is as:

  y^=106.1+4.21x

And also given that the student who was 141 cm tall at age 10 . Thus, we have,

  x=10y=141

As we know that the slope is coefficient of x in the least square regression equation and represents the average increase or decrease of y per unit of x . Thus,

  b1=4.21

This then implies that on average, the height increases by 4.21 cm per year.

(c)

To determine

To interpret the value of s .

(c)

Expert Solution
Check Mark

Explanation of Solution

The relationship between the height and age of the students is given in the question. And the regression line is as:

  y^=106.1+4.21x

And also given that the student who was 141 cm tall at age 10 . Thus, we have,

  x=10y=141

And the value of s is, s=8.61 . As we know that the standard error of the estimate s represents the average error of predictions thus the average deviation between actual and the predicted values. Thus the predicted height of a student using the equation of least square regression line deviates on average by 8.61 cm from the actual height of the student.

(d)

To determine

To interpret the value of r2 .

(d)

Expert Solution
Check Mark

Explanation of Solution

The relationship between the height and age of the students is given in the question. And the regression line is as:

  y^=106.1+4.21x

And also given that the student who was 141 cm tall at age 10 . Thus, we have,

  x=10y=141

And the value of r2 is,

  r2=0.274=27.4%

As we know that the coefficient of determination measures the proportion of variation in the responses y variable that is explained by the least square regression model using the explanatory x variable. Thus, we can say that 27.4% of the variation in the height is explained by the least square regression line using the age as explanatory variable.

Chapter 3 Solutions

PRACTICE OF STATISTICS F/AP EXAM

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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