A small specialty chain store is trying to determine how much stock to have on h

Question

A small specialty chain store is trying to determine how much stock to have on hand in each of its 30 stores for the December holiday sales season. The sales manager looked at the average sales (in thousands of dollars) for the store chains three biggest sale events. The July Blowout sales average was 12 and Black Friday sales average was14 per store, respectively. In order to determine what stock to have on hand, the sales manager then collected last year's average December sales mark, this year's July summer sales mark, and Black Friday sales mark for 30 stores. 1. What is the standard error of estimate? 2. What is the coefficient of determination? What does this statistic tell you? 3. Test the validity of the model. 4. Interpret each of the coefficients 5. Can the manager infer that the July sales average is linearly related to December sales in this model? 6. Can the manager infer that the Black Friday sales average is linearly related to December sales in this model 7. Predict the December sales with 95% confidence.

Explanation / Answer

We use Excel to solve the question,

1)
The Regression Equation is,
December = 13.01 + 0.194 July Sale + 1.112 Black Friday
2)
Coefficient of Determination R2 Square = 76.29%
R2 =76.29% indicates over all validity of model is good.

3)F =43.43 corresponding p-value =0.000 < 0.05 indicates model is vallied.

4)
The intercept 13.00908 indicates that when july sale and Black friday variables are boths 0 then December sell is 13.00908
The slope b1 = 0.193989 indicates that when Black friday variable is 0 then for one unit change in the july sale the Deceber stock is 0.193989
The slope b2 = 1.11208 indicates that when july sale is 0 then for unit change in the black friday the december sell is 1.11208
5)
Multiple R is 0.873432644 july sale average is linearly to December sales.

6)
Multiple R is 0.873432644 Black friday sale average is linearly to December sales.

SUMMARY OUTPUT Regression Statistics Multiple R 0.873433 R Square 0.762885 Adjusted R Square 0.74532 Standard Error 3.752446 Observations 30 ANOVA df SS MS F Significance F Regression 2 1223.184 611.5919 43.4343 3.65E-09 Residual 27 380.183 14.08085 Total 29 1603.367 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 13.00908 3.527786 3.687605 0.001005 5.770664 20.2475 5.770664 20.2475 X Variable 1 0.193989 0.200437 0.967832 0.341718 -0.21727 0.605251 -0.21727 0.605251 X Variable 2 1.11208 0.121944 9.119571 9.87E-10 0.861871 1.362289 0.861871 1.362289

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