Homework Heights $$ (\mathrm{cm}) $$ and weights $$ (\mathrm{kg}) $$ are measured for 100 randomly selected adult males, and range from heights of 138 to 192 cm and weights of 39 to 150 kg . Let the predictor variable $$ x $$ be the first variable given. The 100 paired measurements yield $$ \bar{x}=167.53 \mathrm{~cm}, \bar{y}=81.41 \mathrm{~kg}, \mathrm{r}=0.305, \mathrm{P} $$-value $$ =0.002 $$, and $$ \hat{y}=-101+1.02 \mathrm{x} $$. Find the best predicted value of $$ \hat{y} $$ (weight) given an adult male who is 167 cm tall. Use a 0.01 significance level. - 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 167 cm tall is $$ \square \mathrm{kg} $$.

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To find the best predicted value of $$ \hat{y} $$ (weight) given an adult male who is 167 cm tall, we can use the given linear regression equation:

$$ \hat{y} = -101 + 1.02x $$

where $$ x $$ is the height in cm and $$ \hat{y} $$ is the predicted weight in kg.

Given that the adult male is 167 cm tall, we can substitute this value into the equation to find the predicted weight:

$$ \hat{y} = -101 + 1.02(167) $$

Now, let's calculate the predicted weight.
Calculate the value by following steps:
- step0: Calculate:
  $$-101+1.02\times 167$$
- step1: Multiply the numbers:
  $$-101+170.34$$
- step2: Add the numbers:
  $$69.34$$
The best predicted value of $$ \hat{y} $$ (weight) for an adult male who is 167 cm tall is approximately 69.34 kg.
The best predicted weight for a 167 cm tall adult male is approximately 69.34 kg.

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