Heights $(cm)$ and weights $(kg)$ are measured for 100 randomly selected adult males, and range from heights of 130 to $188 cm$ and weights of 40 to $150 kg$ . Let the predictor variable $x$ be the first variable given. The 100 paired measurements yield $\bar{x} = 167.25 cm, \bar{y} = 81.37 kg, r = 0.405$ , P-value $= 0.000$ , and $\hat{y} = - 106 + 1.02 x$ . Find the best predicted value of $\hat{y}$ (weight) given an adult male who is $166 cm$ tall. Use a 0.01 significance level.
E) Click the icon to view the critical values of the Pearson correlation coefficient $r$ .
The best predicted value of $\hat{y}$ for an adult male who is $166 cm$ tall is $◻ kg$ . (Round to two decimal places as needed.)

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Final Answer: The best predicted value of $\hat{y}$ for an adult male who is 166 cm tall is $63.32 k g$ .

Steps

Step 1 ：Given the equation for the predicted weight, which is $\hat{y} = - 106 + 1.02 x$ , where $x$ is the height in cm.

Step 2 ：Substitute $x = 166$ into the equation to find the predicted weight.

Step 3 ：Calculate $\hat{y} = - 106 + 1.02 \times 166$ to get $\hat{y} = 63.31999999999999$ .

Step 4 ：Round $\hat{y}$ to two decimal places to get $\hat{y} = 63.32$ .

Step 5 ：Final Answer: The best predicted value of $\hat{y}$ for an adult male who is 166 cm tall is $63.32 k g$ .