In a regression equation applied to data in which the X and Y scores are standardized (i.e., transformed into z scores), what value of zY would you predict for a zX value of 0?

Question

BlackTom AI · Accepted Answer

In a regression context where both X and Y scores have been standardized to z scores, the regression line is typically expressed as zY = r * zX, where r is the correlation coefficient between X and Y. 
When zX equals 0, the term r * zX becomes 0 no matter what r is, because any number times zero is zero. Therefore, the predicted standardized Y value (zY) is 0. 
This relies on the standard property of linear regression with standardized variables: the regression line passes through the origin in z-score space, so predictions at zX = 0 are zY = 0. 
Note: the provided answer_options field appears empty in this item, so there are no alternative choice statements to evaluate here. If options were present, you would compare each to the derived prediction (0) and identify which option matches 0, while explaining why the others would be inconsistent.

PSYCH 3321 SP2025 (28481) Homework 9

In a regression equation applied to data in which the X and Y scores are standardized (i.e., transformed into z scores), what value of zY would you predict for a zX value of 0?

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