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 “Body Data” 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.

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 \(\hat y = - 106 + 1.10x\).

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.

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.