r2 = .81 Sy|x = 123,502 sb = .44 n = 128 — The director federal bureau trying anticipate his budget for next year that — 146 384 11X

The director of a federal bureau is trying to anticipate his budget for next year so that he can begin to plan and allocate resources. He has obtained data for this year and last year on the amount of funds budgeted to each federal agency. He regresses this year’s appropriation in dollars (Y) on last year’s appropriation in dollars (X) for the agencies and finds the following:

Ŷ= 146,384 + 1.11X

r2 = .81 Sy|x = 123,502 sb = .44 n = 128

Analyze these results for the bureau director. How strongly are these variables related? If the budget for the bureau this year is $3,280,321, what can he expect the budget to be next year?

SOLUTION

These variables are strongly related as evidenced by the r2 = .81, and a t score for the slope coefficient [t = (1.11/.44 = 2.52)] that allows rejection of the null hypothesis at the .01 level of statistical significance. (Of course, these results ignore the possible effects of third variables on the estimated relationship.) If the budget for the bureau this year is $3,280,321, then since