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Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, with heights ranging from 130 to 190 cm and weights from 39 to 150 kg. Let the predictor variable [tex]x[/tex] be the first variable given. The 100 paired measurements yield:

- [tex]\bar{x} = 167.25[/tex] cm
- [tex]\bar{y} = 81.38[/tex] kg
- [tex]r = 0.228[/tex]
- [tex]P\text{-value} = 0.023[/tex]
- [tex]\hat{y} = -102 + 1.06x[/tex]

Find the best-predicted value of [tex]\hat{y}[/tex] (weight) given an adult male who is 159 cm tall. Use a 0.01 significance level.

The best-predicted value of [tex]\hat{y}[/tex] for an adult male who is 159 cm tall is ____ kg. (Round to two decimal places as needed.)

Answer :

Final answer:

The best predicted weight of an adult male who is 159 cm tall, according to the given regression equation, is approximately 66.74 kg.

Explanation:

In this situation, we are equipped with the statistics from a linear regression analysis where the heights (cm) are the predictor variable (x) and the weights (kg) are the response variable (y). The linear regression equation is given as ^y=-102 + 1.06x.

The question is asking us to predict the weight (^y) of an adult male with a height of 159cm using the provided regression equation. To evaluate this, substitute 159 for x in the equation:

^y = -102 + 1.06*(159) ≈ 66.74 kg

Thus, the best predicted weight of an adult male who is 159 cm tall is approximately 66.74 kg, rounded to two decimal places.

Learn more about Linear Regression here:

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