Linear Prog COP4355_Part_30

# Linear Prog COP4355_Part_30 - Chapter 11 Forecasting 124...

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124 Chapter 11 Forecasting 11.20 (continued) (d) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 10 3650 - 65 525 R = 10 505 65 10 29625 525 5,640,625 = = 0.331 825 20,625 R = 0.331 = 0.576     (e) ( ) ˆ Y = 33.788 + 2.879 14 = 74.091 (f) No, the independent variable (X) accounts for only 33.1% of the variation in Y, therefore the forecast is not accurate. 11.21 (a) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 10 20 30 40 50 60 Age Monthly Income

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Solutions Manual and Workbook 125 11.21 (continued) (b) X Y XY X 2 Y 2 29 1200 34800 841 1440000 44 2600 114400 1936 6760000 27 1000 27000 729 1000000 29 1400 40600 841 1960000 37 2700 99900 1369 7290000 31 2200 68200 961 4840000 41 3500 143500 1681 1225000 54 4000 216000 2916 1600000 36 3100 111600 1296 9610000 27 1600 43200 729 2560000 30 1900 57000 900 3610000 43 3700 159100 1849 1369000 428 28900 1115300 16048 81010000 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 428 28900 X = = 35.67 Y = = 2408.33 12 12 1115300 - 12 35.67 2408.33 b = = 108.28 16048 - 12 35.67 a = 2408.33 - 108.28 35.67 = -1454 (c) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 8 12 1115300 - 428 28900 R = 12 16048 428 12 81010000 28900 1014400 = = 0.8 9392 1.3691 x 10 R = 0.8 = 0.894     80% of the variation in monthly income is explained by the variation in age.
126 Chapter 11 Forecasting 11.21 (continued)

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