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Husbands and wives The mean height of American women in their early twenties is 64.5inches and the standard deviation is 2.5inches. The mean height of men the same age is 68.5inches, with standard deviation2.7inches. The correlation between the heights of husbands and wives is about r=0.5

(a) Find r2and interpret this value in context.

(b) For these data, s=1.2. Explain what this value mean

Short Answer

Expert verified

(a) r2=0.25r2=0.25

(b) s=1.2shows too much prediction error.

Step by step solution

01

Part (a) Step 1:  Given Information

Given in the question that The correlation between the heights of husbands and wives is about r=0.5we have to find out r2

02

Part (a) Step 2: Explanation 

For these data:

r2=(0.5)2 =0.25

In regression, r2is a statistic that provides information on a model's goodness of fit. A statistical measure of how well the regression line approximates the real data points is the r2coefficient of determination. An r2of 1.0indicates that the regression line fully fits the data, but its value is 0.25, indicating that the regression line does not precisely fit the data, and that the straight-line relationship between Yand Xaccounts for around 25%of the variation in Y.

03

Part (b) Step 1:  Given Information

Given in the problem that s=1.2we have to explain the what this value means.

04

Part (b) Step 2:  Explanation

For these data the standard deviation of the residuals is s=1.2

The standard deviation of the residuals smeasures the average size of the prediction errors (residuals) when using the regression line. s=1.2shows too much prediction error.

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