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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

Outlier Refer to the accompanying Minitab-generated scatterplot. a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a correlation between x and y. b. After identifying the 10 pairs of coordinates corresponding to the 10 points, find the value of the correlation coefficient r and determine whether there is a linear correlation. c. Now remove the point with coordinates (10, 10) and repeat parts (a) and (b). d. What do you conclude about the possible effect from a single pair of values?

In Exercises 5鈥�8, use a significance level of A = 0.05 and refer to the

accompanying displays.

Casino Size and Revenue The New York Times published the sizes (square feet) and revenues (dollars) of seven different casinos in Atlantic City. Is there sufficient evidence to support the claim that there is a linear correlation between size and revenue? Do the results suggest that a casino can increase its revenue by expanding its size?

In Exercises 5鈥�8, use a significance level of A = 0.05 and refer to theaccompanying displays.Garbage Data Set 31 鈥淕arbage Weight鈥� in Appendix B includes weights of garbage discarded in one week from 62 different households. The paired weights of paper and glass were used to obtain the XLSTAT results shown here. Is there sufficient evidence to support the claim that there is a linear correlation between weights of discarded paper and glass?

In Exercises 9 and 10, use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.

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?
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