Question

Consider the following information about variable X: Mean = 4, standard deviation = 2.

Consider the following information about variable Y: Mean = 5, standard deviation = 3.

If there is a correlation of r = 0.52 between variable X and variable Y, what is the intercept for a simple linear regression equation predicting Y on the basis of X? Please provide your answer as a raw score (not a z score) with a minimum of two decimal places.

Answer 1

Solution:

Given:

variable X: Mean = 4, standard deviation = 2

, s_x = 2

variable Y: Mean =5, standard deviation = 3

, s_y = 3

a correlation of r = 0.52 between variable X and variable Y.

We have to find the intercept for a simple linear regression equation predicting Y on the basis of X.

where

Thus

Thus the intercept for a simple linear regression equation predicting Y on the basis of X is: b₀ = 1.88