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Chapter 10: Q7BSC (page 468)

let the predictor variable x be the first variable given. Use the given data to find the regression equation and the best predicted value of the response variable. Be sure to follow the prediction procedure summarized in Figure 10-5 on page 493. Use a 0.05 significance level.

Heights (cm) and weights (kg) are measured for 100 randomly selected

adult males (from Data Set 1 鈥淏ody Data鈥� in Appendix B). The 100 paired measurements yield\(\bar x = 173.79\)cm,\(\bar y = 85.93\)kg, r= 0.418, P-value = 0.000, and\(\hat y = - 106 + 1.10x\). Find the best predicted value of\(\hat y\)(weight) given an adult male who is 180 cm tall.

Short Answer

Expert verified

The predicted value of the \(\hat y\)(weight) for an adult male who is 180 cm tall is 92.0 kg.

Step by step solution

01

Given information

The sample number of adult males is\(n = 100\). x represents theheights of adult males and y represents the weights of adult males.

The mean height and weight are \(\bar x = 173.79\)cm and \(\bar y = 85.93\) kg. The correlation coefficient is \(r = 0.418\) and the P-value is 0.000. The regression equation is \(\hat y = - 106 + 1.10x\).

02

Analyze the model

The statistical hypotheses are formed as,

\({H_0}:\) The correlation coefficient is not significant.

\({H_1}:\)The correlation coefficient is significant.

Since the P-value (0.000) is less than the level of significance (0.05). In this case, the null hypothesis is rejected.

Therefore, the correlation coefficient is significant.

Referring to figure 10-5, the regression model is a good model.

The regression equation can be used to predict the value of y.

03

Compute the predicted value

Thepredicted valueis computed as,

\(\begin{array}{c}\hat y = - 106 + \left( {1.10 \times 180} \right)\\ = - 106 + 198\\ = 92.0\end{array}\).

Thus, the predicted value of the \(\hat y\)(weight) for an adult male who is 180 cm tall is 92.0 kg.

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Most popular questions from this chapter

Exercises 13鈥�28 use the same data sets as Exercises 13鈥�28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493.

Using the listed old/new mpg ratings, find the best predicted new

mpg rating for a car with an old rating of 30 mpg. Is there anything to suggest that the prediction is likely to be quite good?

Testing for a Linear Correlation. In Exercises 13鈥�28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of A = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.)

CPI and the Subway Use CPI>subway data from the preceding exercise to determine whether there is a significant linear correlation between the CPI (Consumer Price Index) and the subway fare.

Cigarette Tar and Nicotine The table below lists measured amounts (mg) of tar, carbonmonoxide (CO), and nicotine in king size cigarettes of different brands (from Data Set 13鈥淐igarette Contents鈥� in Appendix B).

a. Is there is sufficient evidence to support a claim of a linear correlation between tar and nicotine?

b. What percentage of the variation in nicotine can be explained by the linear correlation between nicotine and tar?

c. Letting yrepresent the amount of nicotine and letting xrepresent the amount of tar, identify the regression equation.

d. The Raleigh brand king size cigarette is not included in the table, and it has 23 mg of tar. What is the best predicted amount of nicotine? How does the predicted amount compare to the actual amount of 1.3 mg of nicotine?

Tar

25

27

20

24

20

20

21

24

CO

18

16

16

16

16

16

14

17

Nicotine

1.5

1.7

1.1

1.6

1.1

1.0

1.2

1.4

Exercises 13鈥�28 use the same data sets as Exercises 13鈥�28

in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493.

Find the best predicted temperature at a time when a cricket

chirps 3000 times in 1 minute. What is wrong with this predicted temperature?

Exercises 13鈥�28 use the same data sets as Exercises 13鈥�28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493.

Use the shoe print lengths and heights to find the best predicted height of a male who has a shoe print length of 31.3 cm. Would the result be helpful to police crime scene investigators in trying to describe the male?
See all solutions

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