Question

Say, for a given data set, you have the following values in original units:

top enclose x space end enclose = 20.3
top enclose y space end enclose = 4335

std(x) = 3.76
std(y) = 212.3

What is the value of correlation coefficient (r) if the slope of the linear regression line in original units is 29.9?

a. 0.14
b. 0.53
c. 0.82
d. 0.36

Answer 1

To find the correlation coefficient (r), use the formula r = b * (std(x) / std(y)), substituting b with the slope and std(x) and std(y) with their respective values. The calculated correlation coefficient is approximately 0.53, close to the answer option b.

Step-by-step explanation:

The student is asking about the computation of the correlation coefficient (r) given the values in the original units, the standard deviations, and the slope of the linear regression line. To determine which of the provided options for the correlation coefficient is correct, consider the relation of the slope (b) to the standard deviations of x and y and the correlation coefficient:

r = b * (std(x) / std(y))

Given the slope of the regression line in original units is 29.9, and the standard deviations are std(x) = 3.76 and std(y) = 212.3, we calculate:

r = 29.9 * (3.76 / 212.3) = 0.5290 (approx.)

Therefore, the closest answer to 0.5290 provided in the options is b. 0.53.