Question

g You run a regression analysis on a bivariate set of data ( n = 14 ). With ¯ x = 27.7 and ¯ y = 26.5 , you obtain the regression equation y = 0.495 x − 14.914 with a correlation coefficient of r = 0.39 . You want to predict what value (on average) for the response variable will be obtained from a value of 110 as the explanatory variable. What is the predicted response value?

Answer 1

Predicted response value = 39.536

Note that this predicted response value will most likely be far from the actual response value because the correlation coefficient of the regression equation used (r = 0.39) is too far away from 1.

Explanation:

The response variable is the dependent variable (y) whose value is obtained from the expression involving the independent variable (x).

For this question, although the correlation coefficient, r = 0.39, is far from 1, the regression equation is

y = 0.495x - 14.914

The predicted response value will be obtained from the explanatory variable and the regression equation

x = 110

y = 0.495x - 14.914

y = (0.495×110) - 14.914 = 39.536

Note that this predicted response value will most likely be far from the actual response value because the correlation coefficient of the regression equation used (r = 0.39) is too far away from 1.

Hope this Helps!!!