Answer :
To find the best predicted value of weight [tex]\(\hat{y}\)[/tex] for an adult male who is 182 cm tall, we can use the provided regression equation:
[tex]\[
\hat{y} = -102 + 1.02x
\][/tex]
Here, [tex]\(x\)[/tex] represents the height in centimeters. Let's go through the steps to find the predicted weight:
1. Identify the given height:
- The height of the adult male, [tex]\(x\)[/tex], is 182 cm.
2. Plug the height into the regression equation:
- Substitute [tex]\(x = 182\)[/tex] into the regression equation.
- [tex]\(\hat{y} = -102 + 1.02 \times 182\)[/tex]
3. Calculate the predicted weight:
- First, multiply 1.02 by 182:
[tex]\[
1.02 \times 182 = 185.64
\][/tex]
- Then, add the result to -102:
[tex]\[
\hat{y} = -102 + 185.64 = 83.64
\][/tex]
4. Round the predicted weight:
- The problem asks us to round the answer to two decimal places. The calculated value is already at two decimal places, so [tex]\(\hat{y} = 83.64\)[/tex].
Thus, the best predicted value of [tex]\(\hat{y}\)[/tex] (the weight) for an adult male who is 182 cm tall is 83.64 kg.
[tex]\[
\hat{y} = -102 + 1.02x
\][/tex]
Here, [tex]\(x\)[/tex] represents the height in centimeters. Let's go through the steps to find the predicted weight:
1. Identify the given height:
- The height of the adult male, [tex]\(x\)[/tex], is 182 cm.
2. Plug the height into the regression equation:
- Substitute [tex]\(x = 182\)[/tex] into the regression equation.
- [tex]\(\hat{y} = -102 + 1.02 \times 182\)[/tex]
3. Calculate the predicted weight:
- First, multiply 1.02 by 182:
[tex]\[
1.02 \times 182 = 185.64
\][/tex]
- Then, add the result to -102:
[tex]\[
\hat{y} = -102 + 185.64 = 83.64
\][/tex]
4. Round the predicted weight:
- The problem asks us to round the answer to two decimal places. The calculated value is already at two decimal places, so [tex]\(\hat{y} = 83.64\)[/tex].
Thus, the best predicted value of [tex]\(\hat{y}\)[/tex] (the weight) for an adult male who is 182 cm tall is 83.64 kg.
