In a certain country the mean height of women in their twenties is about 62.3 in
ID: 3241787 • Letter: I
Question
In a certain country the mean height of women in their twenties is about 62.3 inches, and the standard deviation is about 2.9 inches. The mean height of men the same age is about 69.9 inches, with standard deviation about 3 inches. Suppose that the correlation between the heights of husbands and wives is about r = 0.4 (a) What are the slope and intercept of the regression line of the husband's height on the wife's height in young couples? (Round your answers to four decimal places.) Slope = 0.413 Intercept 44.1701 Interpret the slope in the context of the problem. For every inch of a wife's height, her husband is about 44.1207 inches taller. For every inch of a wife's height, her husband is about 0.4138 inches taller. For every inch of a wife's height, her husband is about 44.1207 inches shorter. For every inch of a wife's height, her husband is about 0.4138 inches shorter. (b) 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. 0.43 inches (c) You don't expect this prediction for a single couple to be very accurate. Why not? The r^2 = 0.16, so the linear regression explains 16% of the variation in men's heights. Because the heights of men having wives 67 inches tall vary only by a little. The r^2 = 0.84, so the linear regression explains 84% of the variation inExplanation / Answer
Answer to part a)
Formula of Slope b is as follows
b = r * Sy / Sx
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We got : r = 0.4
Sy = 3
Sx = 2.9
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On plugging the values we get
b = 0.4 * 3 /2.9
b = 0.41379
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The question states to round your answer to 4 decimal places , thus
b = 0.4138
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The formula of intercept is :
Ymean = a + b * X mean
We got Y mean = 69.9
X mean = 62.3
b = 0.4138
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On plugging the values we get:
69.9 = a + 0.4138 * 62.3
a = 44.1207
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Slope value is 0.4138. This means for every inch of wife's height , the height of husband is increased 0.4138 times. Thus husband is 0.4138 times taller.
Thus the correct option is seond statement
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Answer to part b)
Predicted height of husband for a height of 67 of wife is :
Predicted Y = 44.1207 + 0.4138 * 67
Predicted Y = 71.8453
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We need to round this answer to two decimal places;
we get Predicted Y = 71.85 inches
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Answer to part c)
Yes we do not expect to explain the relation of wife and hisband's height with complete accuracy because the value of r = 0.4
this means r square = 0.4 *0.4 = 0.16
this implies this model helps explain only 16% of the variation in the height of the husband.
Thus the first statement is the correct answer choice