11.76 Operations management is concerned with planning and controlling those organizational functions and systems that produce goods and services (Schroeder, Operations Management:

Decision Making in the Operations Function, McGraw-Hill, 1981). One concern of the operations manager of a production process is the level of productivity of the process. An operations manager at a large manufacturing plant is interested in predicting the level of productivity of assembly line A next year (i.e., the number of units that will be produced by the assembly line next year). To do so, she has decided to use regression analysis to model the level of productivity as a function of time . The number of units produced by assembly line A was determined for each of the past 15 years

. The model was fit to these data, using Minitab. The results shown in the printout in below were obtained.

E(Y) = b0 + b1x + b2x2

(x = 1, 2, Á , 15)

Y x E(Y ) = b0 + b2x2 + b4x2 2 SSE = 226.1

a Identify the least-squares prediction equation.
b Find and interpret its value in the context of this problem.

c Is there sufficient evidence to indicate that the model is useful for predicting the productivity of assembly line A? Test using .
d Test the null hypothesis against the alternative hypothesis by using . Interpret the results of your test in the context of this problem.
e Which (if any) of the assumptions we make about in regression analysis are likely to be violated in this problem? Explain.

Transcribed Image Text:

THE REGRESSION EQUATION IS Y = -1187 - 1333 X1 45.6 X2 ST. DEV. T-RATIO= COLUMN COEFFICIENT OF COEF. COEF./S.D. -1187 446 -2.66 X1 C2 X2 C3 1333 -45.59 128 10.38 7.80 -5.84 THE ST. DEV. OF Y ABOUT REGRESSION LINE IS S = 501 WITH (1523) = 12 DEGRESS OF FREEDOM R-SQUARED 97.3 PERCENT = R-SQUARED = 96.9 PERCENT. ADJUSTED FOR D.F. ANALYSIS OF VARIANCE DUE TO DF SS MS SS/DF REGRESSION 2 110578719 55289359 RESIDUAL 12 3013365 251114 TOTAL 14 113592083