Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, ranging from heights of 134 to 191 cm and weights of 38 to 150 kg. Let the predictor variable [tex]x[/tex] be the first variable given. The 100 paired measurements yield:

- [tex]\bar{x} = 167.42 \, \text{cm}[/tex]
- [tex]\bar{y} = 81.39 \, \text{kg}[/tex]
- [tex]r = 0.401[/tex]
- [tex]\text{P-value} = 0.000[/tex]

The regression equation is [tex]\hat{y} = -108 + 1.17x[/tex].

Find the best-predicted value of [tex]\hat{y}[/tex] (weight) given an adult male who is 181 cm tall. Use a 0.01 significance level.

The best-predicted value of [tex]\hat{y}[/tex] for an adult male who is 181 cm tall is _____ kg. (Round to two decimal places as needed.)

We can conclude that the best predicted value of weight for an adult male who is 181 cm tall is 103.77 kg, and this prediction is statistically significant at the 0.01 significance level.

To find the best predicted value of weight (y) for an adult male who is 181 cm tall, we can use the linear regression equation given:

y = -108 + 1.17x

where x represents the height in centimeters.

Substituting x = 181 into the equation, we get:

y = -108 + 1.17(181)

= -108 + 211.77

= 103.77 kg

So, the best predicted value of weight for an adult male who is 181 cm tall is 103.77 kg.

Now, to determine if this predicted value is statistically significant at a significance level of 0.01, we need to examine the p-value provided. The p-value given in the problem statement is 0.000, which is less than 0.01. This indicates that the relationship between height and weight is statistically significant.

Therefore, we can conclude that the best predicted value of weight for an adult male who is 181 cm tall is 103.77 kg, and this prediction is statistically significant at the 0.01 significance level.

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BenjaminEric BenjaminEric · Answer 2 · 2025-05-16T20:46:25-04:00

In statistics, linear regression involves determining the relationship between two variables x and y, where x is the predictor variable and y is the response variable.

Regression is used to determine the strength of the relationship between two variables, as well as to make predictions.The best predicted value of y^(weight) given an adult male who is 181 cm tall and a significance level of 0.01 can be determined from the regression equation:y^=−108+1.17x. Substituting x=181cm into this equation gives:y^(weight) = -108 + 1.17(181) = 76.27 kgTherefore, the best predicted weight for an adult male who is 181 cm tall is 76.27 kg (rounded to two decimal places).

This is a point estimate that predicts the weight of an adult male who is 181 cm tall, based on the regression equation and the given data. Since the significance level is 0.01, we can say that this estimate is statistically significant and reliable, with a low probability of being due to chance.

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