Question

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

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

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 \(\hat y = 34.4 + 0.0547x\).

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.

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.