Question 1.1. (TCO E) Holding goods in inventory is costly because inventoried goods are susceptible to breakage and other forms of physical damage. Typically, the amount of damage increases with the level of inventory, but some of the damage is unrelated to the amount of inventory. In addition, the seasonality may make a difference. A random sample of 10 observations is selected with the variables INVTRY (X1, inventory in $1,000,000s), SEASON (X2, with spring and summer being 0 and fall and winter being 1), and DAMAGE (Y, in $10,000s). The results are found below.
INVTRY

SEASON

DAMAGE

11

1

80

15

1

100

13

0

70

10

1

60

7

0

50

9

0

70

13

1

100

10

0

65

14

1

95

8

0

54

15

0

96

9

1

91

13

1

85

Correlations: INVTRY, SEASON, DAMAGE INVTRY SEASON SEASON 0.349 0.242 DAMAGE 0.798 0.578 0.001 0.038 Cell Contents: Pearson correlation PValue Regression Analysis: DAMAGE versus INVTRY, SEASON The regression equation is DAMAGE = 21.2 + 4.49 INVTRY + 11.7 SEASON. Predictor Coef SE Coef T P Constant 21.16 12.44 1.70 0.120 INVTRY 4.485 1.138 3.94 0.003 SEASON 11.670 5.896 1.98 0.076 S = 9.93147 RSq = 73.9% RSq(adj) = 68.7% Analysis of Variance Source DF SS MS F P Regression 2 2797.4 1398.7 14.18 0.001 Residual Error 10 986.3 98.6 Total 12 3783.7 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 86.65 3.76 (78.27, 95.02) (62.99, 110.30) Values of Predictors for New Observations New Obs INVTRY SEASON 1 12.0 1.00 a. Analyze the above output to determine the multiple regression equation. b. Find and interpret the multiple index of determination (RSq). c. Perform the multiple regression ttests on βË–1, βË–2 (use two tailed test with (a = .10). Interpret your results. d. Predict the damage for a single case in the spring or summer with an inventory of $12,000,000. Use both a point estimate and the appropriate interval estimate. (Points : 31)
