11.85 An economist has proposed the following model to describe the relationship between the number of items produced per day (output) and the number of hours of labor expended per day (input) in a particular production process:

where Y number of items produced per day x number of hours of labor per day A portion of the computer printout that results from fitting this model to a sample of 25 weeks of production data is shown below. Test the hypothesis that, as the amount of input increases, the amount of output also increases, but at a decreasing rate. Do the data provide sufficient evidence to indicate that the rate of increase in output per unit increase of input decreases as the input increases? Test by using a = 0.05.

Y = b0 + b1x + b2x2 + e

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THE REGRESSION EQUATION IS Y = -6.17 +2.04 X1 -0.0323 X2 ST. DEV. T-RATIO= COLUMN COEFFICIENT COEFFICIENT OF COEF. COEF./S.D. -6.173 1.666 -3.71 C2 2.036 0.185 11.02 X2 C3 -0.03231 0.00489 -6.60 THE ST. DEV. OF Y ABOUT REGRESSION LINE IS S = 1.243 WITH (25-3) 22 = DEGREES OF FREEDOM R-SQUARED = 95.5 PERCENT R-SQUARED = 95.1 PERCENT, ADJUSTED FOR D.F. ANALYSIS OF VARIANCE DUE TO DF SS MS = SS/DF REGRESSION 2 718.168 RESIDUAL TOTAL 22 33.992 359.084 1.545 24 752.160