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Answer :
To find the best predicted weight [tex]\(\hat{y}\)[/tex] for an adult male who is 143 cm tall, we can use the provided linear regression equation:
[tex]\[
\hat{y} = -108 + 1.01x
\][/tex]
In this equation:
- [tex]\(-108\)[/tex] is the intercept.
- [tex]\(1.01\)[/tex] is the slope of the line.
- [tex]\(x\)[/tex] represents the height in centimeters.
Let's calculate the predicted weight by substituting [tex]\(x = 143\)[/tex] cm into the equation.
1. Start with the linear equation:
[tex]\[
\hat{y} = -108 + 1.01x
\][/tex]
2. Substitute [tex]\(x = 143\)[/tex] into the equation:
[tex]\[
\hat{y} = -108 + 1.01 \times 143
\][/tex]
3. Calculate the value:
- First, compute [tex]\(1.01 \times 143 = 144.43\)[/tex].
- Then add [tex]\(-108\)[/tex] to [tex]\(144.43\)[/tex]:
[tex]\[
-108 + 144.43 = 36.43
\][/tex]
Therefore, the best predicted weight [tex]\(\hat{y}\)[/tex] for an adult male who is 143 cm tall is [tex]\(36.43\)[/tex] kg.
[tex]\[
\hat{y} = -108 + 1.01x
\][/tex]
In this equation:
- [tex]\(-108\)[/tex] is the intercept.
- [tex]\(1.01\)[/tex] is the slope of the line.
- [tex]\(x\)[/tex] represents the height in centimeters.
Let's calculate the predicted weight by substituting [tex]\(x = 143\)[/tex] cm into the equation.
1. Start with the linear equation:
[tex]\[
\hat{y} = -108 + 1.01x
\][/tex]
2. Substitute [tex]\(x = 143\)[/tex] into the equation:
[tex]\[
\hat{y} = -108 + 1.01 \times 143
\][/tex]
3. Calculate the value:
- First, compute [tex]\(1.01 \times 143 = 144.43\)[/tex].
- Then add [tex]\(-108\)[/tex] to [tex]\(144.43\)[/tex]:
[tex]\[
-108 + 144.43 = 36.43
\][/tex]
Therefore, the best predicted weight [tex]\(\hat{y}\)[/tex] for an adult male who is 143 cm tall is [tex]\(36.43\)[/tex] kg.
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