Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, with heights ranging from 132 to 194 cm and weights from 40 to 150 kg. Let the predictor variable \( x \) be the first variable given. The 100 paired measurements yield \(\bar{x} = 167.51\) cm, \(\bar{y} = 61.44\) kg, \( r = 0.371 \), \( P\text{-value} = 0.000 \), and the regression equation \( \hat{y} = 100 + 1.18x \).

Find the best predicted value of \( y \) (weight) for an adult male who is 186 cm tall. Use a 0.05 significance level.

The best predicted value of \( y \) for an adult male who is 186 cm tall is \( \boxed{ }\) kg. (Round to two decimal places as needed.)

Question

21-12-2023
Mathematics

High School

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Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, with heights ranging from 132 to 194 cm and weights from 40 to 150 kg. Let the predictor variable \( x \) be the first variable given. The 100 paired measurements yield \(\bar{x} = 167.51\) cm, \(\bar{y} = 61.44\) kg, \( r = 0.371 \), \( P\text{-value} = 0.000 \), and the regression equation \( \hat{y} = 100 + 1.18x \).

Find the best predicted value of \( y \) (weight) for an adult male who is 186 cm tall. Use a 0.05 significance level.

The best predicted value of \( y \) for an adult male who is 186 cm tall is \( \boxed{ }\) kg. (Round to two decimal places as needed.)

Answer :

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Answer 1 · 2023-09-07T18:15:11-04:00

In a study of 100 adult males, heights (x) and weights (y) were measured. The paired measurements resulted in a correlation coefficient of r = 0.371 and a regression equation of y = -167.51 + 1.18x. The task is to find the best predicted value of y (weight) for an adult male who is 186 cm tall, using a significance level of 0.05.

To find the best predicted value of y (weight) for an adult male who is 186 cm tall, we can use the regression equation y = -167.51 + 1.18x, where x represents the height. Substituting x = 186 into the equation, we have y = -167.51 + 1.18 * 186. By calculating this expression, we can obtain the best predicted value of y.

Note that the regression equation provides an estimate of the relationship between height and weight based on the given data. The significance level of 0.05 indicates the level of confidence in the prediction. The predicted value of y represents the expected weight for an adult male with a height of 186 cm, according to the regression model.

To know more about significance level here: brainly.com/question/31519103

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