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Answer :
To find the best predicted value of the weight ([tex]\(\hat{y}\)[/tex]) for an adult male who is 187 cm tall, we use the linear regression equation [tex]\(\hat{y} = -101 + 1.19x\)[/tex], where [tex]\(x\)[/tex] is the height in centimeters.
Here's how to solve the problem step-by-step:
1. Identify the Variables:
- Predictor variable ([tex]\(x\)[/tex]): Height of the adult male, which is 187 cm.
- Intercept of the regression line: [tex]\(-101\)[/tex].
- Slope of the regression line: [tex]\(1.19\)[/tex].
2. Use the Regression Equation:
The linear regression equation is [tex]\(\hat{y} = -101 + 1.19x\)[/tex]. Our goal is to plug in the given height into this equation to find the predicted weight.
3. Perform the Calculation:
Substitute the height ([tex]\(x = 187\)[/tex]) into the equation:
[tex]\[
\hat{y} = -101 + 1.19 \times 187
\][/tex]
4. Calculate Step-by-Step:
- First, multiply the slope ([tex]\(1.19\)[/tex]) by the height ([tex]\(187\)[/tex]):
[tex]\[
1.19 \times 187 = 222.53
\][/tex]
- Next, add the intercept ([tex]\(-101\)[/tex]) to this product:
[tex]\[
\hat{y} = -101 + 222.53 = 121.53
\][/tex]
5. Round the Result:
The predicted value [tex]\(\hat{y}\)[/tex] is already rounded to two decimal places, which gives us:
[tex]\[
\hat{y} = 121.53 \text{ kg}
\][/tex]
Therefore, the best predicted value of the weight for an adult male who is 187 cm tall is 121.53 kg.
Here's how to solve the problem step-by-step:
1. Identify the Variables:
- Predictor variable ([tex]\(x\)[/tex]): Height of the adult male, which is 187 cm.
- Intercept of the regression line: [tex]\(-101\)[/tex].
- Slope of the regression line: [tex]\(1.19\)[/tex].
2. Use the Regression Equation:
The linear regression equation is [tex]\(\hat{y} = -101 + 1.19x\)[/tex]. Our goal is to plug in the given height into this equation to find the predicted weight.
3. Perform the Calculation:
Substitute the height ([tex]\(x = 187\)[/tex]) into the equation:
[tex]\[
\hat{y} = -101 + 1.19 \times 187
\][/tex]
4. Calculate Step-by-Step:
- First, multiply the slope ([tex]\(1.19\)[/tex]) by the height ([tex]\(187\)[/tex]):
[tex]\[
1.19 \times 187 = 222.53
\][/tex]
- Next, add the intercept ([tex]\(-101\)[/tex]) to this product:
[tex]\[
\hat{y} = -101 + 222.53 = 121.53
\][/tex]
5. Round the Result:
The predicted value [tex]\(\hat{y}\)[/tex] is already rounded to two decimal places, which gives us:
[tex]\[
\hat{y} = 121.53 \text{ kg}
\][/tex]
Therefore, the best predicted value of the weight for an adult male who is 187 cm tall is 121.53 kg.
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