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 50 randomly selected speed dates, attractiveness ratings by males of their

female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings are from Data Set 18 “Speed Dating” in Appendix B. The 50 paired ratings yield\(\bar x = 6.5\),\(\bar y = 5.9\), r= -0.277, P-value = 0.051, and\(\hat y = 8.18 - 0.345x\). Find the best predicted value of\(\hat y\)(attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x= 8.

Short answer

The regression equation is\(\hat y = 8.18 - 0.345x\).

The predicted value of \(\hat y\) , that is, attractiveness rating by a female of male for a date in which the attractiveness rating by the male of the female is x= 8 is 5.9.

Step-by-step solution

Given information

The sample number of speed dates is\(n = 20\). Variable x represents theattractiveness ratings by males of their female date partners and y represents the attractiveness ratings by females of their male date partners.

The mean ratings are \(\bar x = 6.5\) and \(\bar y = 5.9\). The correlation coefficient is \(r = - 0.277\) and the P-value is 0.051. The regression equation is \(\hat y = 8.18 - 0.345x\).

Analyse the regression 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 (0.051) is greater than the level of significance (0.05), in this case, the null hypothesis fails to be rejected.

Therefore, there is enough evidence that the correlation coefficient is not significant.

Refer to Figure 10-5 for the description of a good model.

As the correlation coefficient is not significant, the regression model is a bad model.

Therefore, the regression equation cannot be used to predict the value of y.

Determine the predicted value

Resultant to conclusion, the bestpredicted valuefor a bad model is equal to its mean; that is \(\bar y = 5.9\).

Thus, the predicted value of the\(\hat y\)(attractiveness rating by the female of male) for a date in which the attractiveness rating by the male of the female is x= 8 is 5.9.