High School

Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, with heights ranging from 139 to 191 cm and weights from 40 to 150 kg. Let the predictor variable \( x \) be the first variable given. The 100 paired measurements yield:

- \( \bar{x} = 167.80 \) cm
- \( \bar{y} = 81.46 \) kg
- \( r = 0.168 \)
- P-value = 0.095
- Regression equation: \( \hat{y} = -102 + 1.11x \)

Find the best-predicted value of \( y \) (weight) given an adult male who is 182 cm tall. Use a 0.05 significance level.

The best-predicted value of \( \hat{y} \) for an adult male who is 182 cm tall is ___ kg. (Round to two decimal places as needed.)

Answer :

To find the best predicted value of y (weight) for an adult male who is 182 cm tall, we will use the regression equation:

ŷ = -102 + 1.11x

Substituting x = 182 into the equation, we get:

ŷ = -102 + 1.11(182)

ŷ = -102 + 201.02

ŷ ≈ 99.02

The best predicted value of ŷ (weight) for an adult male who is 182 cm tall is approximately 99.02 kg.

Note: The given information includes the regression equation, which represents the linear relationship between the predictor variable x (height) and the response variable y (weight). By plugging in the value of x = 182 into the equation, we can estimate the corresponding value of y. The significance level mentioned (0.05) is not directly relevant to predicting the value of ŷ.

Learn more about regression equation here:

https://brainly.com/question/31969332

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