Eye Associates, which runs an optical lab, experienced substantial growth over t

Question

Eye Associates, which runs an optical lab, experienced substantial growth over the last decade. It purchased additional increments of lens-grinding equipment in relatively small units. Prior analysis of its data (since its growth has been steady and constant suggests that regression analysis (as described in Chapter 4) is adequate to determine its capacity demands. Data for the past decade follow: 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 YEAR 15.0 15.5 16.25 16.75 16.9 17.24 17.5 17.3 17.75 18.1 Units Produced (in thousands) a) Determine the firm's capacity needs in units for 2006, 2008 and 2010. b) If each machine is capable of producing 2,500 lenses, how many machines should it expect to have in 2010?

Explanation / Answer

converting year 1996 to 1, and onwards

from above b1 =Sxy/Sxx =0.312

and bo=Ybar-b1*Xbar = 15.113

hence regression equation y=0.312x+15.113

a) hence for 2006 ; as x =11

hence firm's capacity =0.312*11+15.113=18.545

for 2008; as x=13

hence firm's capacity =0.312*13+15.113=19.169

for 2010. x=15

hence firm's capacity =0.312*15+15.113 =19.794

b) as per m/c capacity =2500

hence total number of m/c's required =19794/2500=7.92

hence number of m/c required =8

x y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi'=b1x+b0 (Y-Yi')^2 1.00 15.00 20.25 3.35 28.95 15.42472727 0.18039326 2.00 15.50 12.25 1.77 19.71 15.73678788 0.0560685 3.00 16.25 6.25 0.34 8.01 16.04884848 0.04046193 4.00 16.75 2.25 0.01 1.01 16.36090909 0.15139174 5.00 16.90 0.25 0.01 -0.84 16.6729697 0.05154276 6.00 17.24 0.25 0.17 -4.45 16.9850303 0.06500955 7.00 17.50 2.25 0.45 -6.60 17.29709091 0.0411721 8.00 17.30 6.25 0.22 -4.16 17.60915152 0.09557466 9.00 17.75 12.25 0.85 -7.21 17.92121212 0.02931359 10.00 18.10 20.25 1.62 -8.68 18.23327273 0.01776162 Total 55.00 168.29 82.50 8.76 25.75 0.7286897 mean 5.50 16.83 Sxx Syy Sxy

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