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Chapter 10: Q8BSC (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.

For 30 recent Academy Award ceremonies, ages of Best Supporting Actors (x) and ages of Best Supporting Actresses (y) are recorded. The 30 paired ages yield\(\bar x = 52.1\)years,\(\bar y = 37.3\)years, r= 0.076, P-value = 0.691, and

\(\hat y = 34.4 + 0.0547x\). Find the best predicted value of\(\hat y\)(age of Best Supporting Actress) in 1982, when the age of the Best Supporting Actor (x) was 46 years.

Short Answer

Expert verified

The predicted value of the\(\hat y\)(age of Best Supporting Actress) for the Best Supporting Actor (x) in the year 1982 then aged 46 years is 37.3 years.

Step by step solution

01

Given information

The sample number of Academy Award ceremonies is\(n = 30\). x represents theages of Best Supporting Actors and y representstheages of Best Supporting Actresses.

The mean ages are \(\bar x = 52.1\) years and \(\bar y = 37.3\)years. The correlation coefficient is \(r = 0.076\) and the P-value is 0.691. The regression equation is \(\hat y = 34.4 + 0.0547x\).

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 (0.691) is greater than the level of significance (0.05). In this case, the null hypothesis fails to be rejected.

Therefore, the correlation coefficient is not significant.

Referring to figure 10-5, the regression model is not a good model and the regression equation cannot be used to predict the value of y.

03

Determine the predicted value

Therefore, thepredicted value is the mean; that is\(\bar y = 37.3\)years.

Thus, the predicted value of the\(\hat y\)(age of Best Supporting Actress) in 1982 for the Best Supporting Actor (x) aged 46 years is 37.3 years.

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Most popular questions from this chapter

Interpreting r For the same two variables described in Exercise 1, if we find that r = 0, does that indicate that there is no association between those two variables?

Prediction Interval Using the heights and weights described in Exercise 1, a height of 180 cm is used to find that the predicted weight is 91.3 kg, and the 95% prediction interval is (59.0 kg, 123.6 kg). Write a statement that interprets that prediction interval. What is the major advantage of using a prediction interval instead of simply using the predicted weight of 91.3 kg? Why is the terminology of prediction interval used instead of confidence interval?

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Manatees Listed below are numbers of registered pleasure boats in Florida (tens of thousands) and the numbers of manatee fatalities from encounters with boats in Florida for each of several recent years. The values are from Data Set 10 鈥淢anatee Deaths鈥� in Appendix B. Is there sufficient evidence to conclude that there is a linear correlation between numbers of registered pleasure boats and numbers of manatee boat fatalities?

Pleasure Boats

99

99

97

95

90

90

87

90

90

Manatee Fatalities

92

73

90

97

83

88

81

73

68

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?
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