College

Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, ranging from heights of 133 to 193 cm and weights of 40 to 150 kg. Let the predictor variable \( x \) be the first variable given. The 100 paired measurements yield:
\[ \bar{x} = 167.90 \, \text{cm}, \, \bar{y} = 81.47 \, \text{kg}, \, r = 0.228, \, \text{P-value} = 0.023, \, \hat{y} = -105 + 1.13x \]

Find the best predicted value of \(\hat{y}\) (weight) for an adult male who is 172 cm tall. Use a 0.05 significance level.

The best predicted value of \(\hat{y}\) for an adult male who is 172 cm tall is ______ kg. (Round to two decimal places as needed.)

Answer :

The best predicted value of [tex]\hat{y}[/tex] for an adult male who is 172 cm tall is 89.36 kg.

Given the information, we need to find the best predicted value of [tex]\hat{y}\)[/tex] (weight) for an adult male who is 172 cm tall using the regression equation [tex]\hat{y}[/tex] = -105 + 1.13x.

  • The regression equation provided is:

[tex]\hat{y}[/tex] = -105 + 1.13x

We are asked to find [tex]\hat{y}[/tex] for x = 172 cm.

  • Substitute x = 172 into the regression equation:

[tex]\hat{y}[/tex] = -105 + 1.13 (172)

  • Perform the calculation:

[tex]\hat{y}[/tex] = -105 + 1.13 × 172

[tex]\hat{y}[/tex] = -105 + 194.36

[tex]\hat{y}[/tex] = 89.36

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