In multiple regression, the standardized regression coefficient Beta () is useful, because it allows you to compare the relative strength of each independent variable's relationship with the dependent variable. In this case, the regression coefficients (b) provide you with information on how much change can be expected with a one-unit change in each independent variable, but they don't tell you the relative strength of the relationship between the dependent variable and each of the independent variables. With the standardized Beta values here, you can make that relative strength comparison.

Use the scenario below to answer a question on regression interpretation with standardized regression coefficients Beta ().

Here is the scenario: Mary wants to predict the average volunteer hours per week among managers and workers at a certain public agency. She is using multiple independent variables in a multiple regression analysis. Her regression equation or model is shown below(Note: These are the standardized regression coefficients):

Y (volunteer hours) =2.29a+.051X₁(income) +.003X₂(age) + (.39)X₃(participant_status_reference workers)

Y= volunteer hours, measured in hours

a = the constant, or intercept, the value of volunteer hours when all independent variables equal zero

X₁= income measured in income levels

X₂= age, measured in years

X₃= participant status is a dummy variable (two values are managers and workers) with workers as the reference group

Which of the choices below is the most accurate interpretation if the above are all standardized regression coefficients?

A. Participant status (.39). has the strongest relationship with volunteer hours, compared to income (.051) and age (.003).

B. Holding all other variables constant, managers put in an average of .39 hours less (per week) than workers.

C. When all independent variables equal zero, volunteer hours (per week) decrease by .39 hours for managers compared to workers.

D. Income (.051) has the strongest relationship with volunteer hours, compared to age (.003) and participant status (.39).