Question

Standard scores exhibit interesting mathematical properties, such that if the regression calculations are

performed, the intercept must be 0 and the slope must be r.

For this problem, assume r = .40, and write the least-squares linear regression equation for predicting zY from zX. Then, use the regression equation to predict zY for a person whose zX is 1.60.

Answer 1

Solution:

We are given that: a standard scores exhibit interesting mathematical properties, such that if the regression calculations are

performed, the intercept must be 0 and the slope must be r.

That is: b₀ = 0   and b₁ = r

we are given that: r = 0.40 and we have to write the least-squares linear regression equation for predicting z_Y from z_X.

general least square regression equation is given by:

y = b₀ + b₁ * x

Thus new regression equation in terms of z_Y from z_X is given by:

z_Y = b₀ + b₁ * z_X

z_Y = 0 + r * z_X

z_Y =   0.40 * z_X

Now we have to use this regression equation to predict z_Y for a person whose z_X is 1.60.

Thus put z_X = 1.60 in above regression equation and solve for z_Y.

z_Y =   0.40 * z_X

z_Y =   0.40 * 1.60

z_Y = 0.64

Thus predicted z_Y for a person whose z_X is 1.60 is 0.64