If the linear correlation between shoe size and height is 0.758 and Dave is 2 standard deviations above the mean in shoe size,what would you predict is Dave's height with respect to the mean height?
A)2.000 standard deviations above the mean height
B)1.516 standard deviations above the mean height
C)0.575 standard deviations above the mean height
D)0.758 standard deviations above the mean height
E)1.149 standard deviations above the mean height

Question

Quizplus · Accepted Answer

First, we need to find the correlation coefficient between shoe size and height using the provided information. The correlation coefficient is 0.758, which indicates a positive relationship between shoe size and height.

Next, we know that Dave is 2 standard deviations above the mean in shoe size. Since we don't know the mean or standard deviation of shoe size or height, we cannot calculate Dave's exact predicted height. However, we can use the correlation coefficient to estimate his predicted height relative to the mean height.

To do this, we use the formula:

predicted change in Y = r * (number of standard deviations that X deviates from its mean)

where Y is the variable we want to predict (height), X is the variable we know (shoe size), r is the correlation coefficient, and the number of standard deviations is based on how many standard deviations Dave is from the mean in shoe size.

In this case, Dave is 2 standard deviations above the mean in shoe size. Therefore, we substitute r = 0.758 and the number of standard deviations = 2 into the formula:

predicted change in Y = 0.758 * 2 = 1.516

This means that Dave's predicted height is 1.516 standard deviations above the mean height. Therefore, the best choice is B.

If the Linear Correlation Between Shoe Size and Height Is