2. The mean height of American women in their twenties is about 64.3 inches, and the...

2. The mean height of American women in their twenties is about 64.3 inches, and the standard deviation is about 2.7 inches. The mean height of men the same age is about 69.9 inches, with standard deviation about 3.1 inches. Suppose that the correlation between the heights of husbands and wives is about r = 0.5.

What are the slope and intercept of the regression line of the husband’s height on the wife’s height in young couples? Interpret the slope in the context of the problem.
Draw a graph of this regression line for heights of wives between 56 and 72 inches. Predict the height of the husband of a woman who is 67 inches tall, and plot the wife’s height and predicted husband’s height on your graph

Solutions

Expert Solution

What are the slope and intercept of the regression line of the husband’s height on the wife’s height in young couples? Interpret the slope in the context of the problem.

Given: y=husband height and x= wife height

Slope b= r*sy/sx =0.5*3.1/2.7 = 0.5741

=69.9-0.5741*64.3

=32.9854

The estimated regression line is y=32.9854+0.5741*x

When wife height increases by 1 inch, the husband height increases by 0.5741 inches.

Draw a graph of this regression line for heights of wives between 56 and 72 inches. Predict the height of the husband of a woman who is 67 inches tall, and plot the wife’s height and predicted husband’s height on your graph

When x=67, predicted y =32.9854+0.5741*67

=71.45

orchestra answered 1 year ago

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