Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, with heights ranging from 131 to 190 cm and weights from 41 to 150 kg. Let the predictor variable [tex]\( x \)[/tex] be the height. The 100 paired measurements yield:

- [tex]\(\bar{x} = 167.44\)[/tex] cm
- [tex]\(\bar{y} = 81.48\)[/tex] kg
- [tex]\( r = 0.178 \)[/tex]
- [tex]\( P\)-value = 0.076[/tex]
- Regression equation: [tex]\(\hat{y} = -108 + 1.01x\)[/tex]

Find the best predicted value of [tex]\(\hat{y}\)[/tex] (weight) for an adult male who is 143 cm tall. Use a 0.05 significance level.

The best predicted value of [tex]\(\hat{y}\)[/tex] for an adult male who is 143 cm tall is [tex]\(\square\)[/tex] kg. (Round to two decimal places as needed.)

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.