a) Generate linear and quadratic models for this data. b) What is the marginal s
ID: 3262192 • Letter: A
Question
a) Generate linear and quadratic models for this data.
b) What is the marginal sales for this department using each model.
c) Which model do you feel best predicts future trends and explain your rational.
The data is for weekly sales in the dry goods department at a Wal*Mart store in the Northeast. Peak values, I.e. spikes, usually occur at holiday periods. Week 1 is the first week of February 2003. To show continuity, week 1 of 2004 is represented as week 53 since week 53 represents the start of the 2004 fiscal year. Dollar values are adjusted in order to disguise true sales figures, but trends in the data are retained for analysis purposes. Note that for 2002-2003 data, Wal*Mart used 53 weeks for their fiscal year data. Week Sales in $ 41 18000 42 16800 43 15200 44 15000 45 13600 46 16000 47 12600 48 14800 49 16800 50 14800 51 15200 52 16000 53 15600 54 15600 55 15000 56 15700 57 15800 58 13800 59 12800 60 14400 61 15800 62 16000 63 12400 64 16200 65 17000 66 18600 67 16000 68 18000 69 19600 70 18600 71 18450 72 18000 73 18200 74 18600 75 16000 76 15200 77 16800 78 15800 79 17600 80 15800 81 15600 82 14200 83 16600 84 16100 85 14100 86 14400 87 14500 88 16900 89 17000 90 16000 91 17800Explanation / Answer
linear model
quadratic model
linear
sales = 14322.92 + 25.217* week
quadratic
sales = 9555 +177.25 *week -1.15179*week^2
b)
marginal
linear - 25.217
quadratic - 177.253 -2*1.1517*week
c)
R^2 for linear -
for quadratic -
hence quadratic model best predicts future trends
SUMMARY OUTPUT Regression Statistics Multiple R 0.228888678 R Square 0.052390027 Adjusted R Square 0.033051048 Standard Error 1610.535748 Observations 51 ANOVA df SS MS F Significance F Regression 1 7026771.267 7026771 2.709038 0.106181 Residual 49 127097444.4 2593825 Total 50 134124215.7 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 14322.92006 1036.033985 13.82476 1.55E-18 12240.93 16404.91 12240.93 16404.91 Week 25.21719457 15.3210747 1.645916 0.106181 -5.57166 56.00605 -5.57166 56.00605Related Questions
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