Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, with heights ranging from 130 to 188 cm and weights from 41 to 150 kg. Let the predictor variable \(x\) be the height.

The 100 paired measurements yield:
- \(\bar{x} = 166.99\) cm
- \(\bar{y} = 81.21\) kg
- \(r = 0.208\)
- P-value = 0.038
- Regression equation: \(y = -102 + 1.13x\)

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 139.80 kg. (Round to two decimal places as needed.)

The predicted weight for an adult male who is 186 cm tall, using the given linear regression formula, is 108.58 kg. However, the relationship between height and weight is statistically significant with a p-value of 0.038 and a correlation coefficient of 0.208.

Explanation:

The information given provides us with a linear regression formula y = -102 + 1.13x, where y is the weight in kg, and x is the height in cm. To find the expected weight of an adult male with a height of 186 cm, we simply substitute x = 186 into the formula.

Using the provided formula, we find: y = -102 + (1.13 * 186) which results in y = 108.58 kg. However, the provided answer seems to suggest a different value, which could be the result of a typo, rounding error or an extraneous variable not mentioned in the problem statement. In any case,

we must also consider the p-value of 0.038, which is less than the significance level of 0.05, indicating that the relationship between height and weight is statistically significant and the correlation is not due to random chance. Meanwhile, the positive value r = 0.208, albeit small, indicates a weak positive relationship between height and weight.

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