Question

Case 15.4: Sapphire Coffee - Part 2 This case is an extension of the Sapphire Coffee case from Chapter 14. Case the issue would be: Is the $5.00 increase in sales for each one square foot increase in store size adequate and if not would knowing the location of the store and whether it had a drive through window help explain sales. A stand alone analysis would start with the output from the case in Chapter 14 with a discussion that the low R-square value and relatively high confidence interval would justify looking for additional independent variables. This would lead to dummy variables: dl No 0 Yes 1 Near a college Drive through window No0 Yes 1 The Excel output with the dummy variables is: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square0.71011358 0.852547827 0.726837797 Standard Error Observations 252.0293585 53 df Ss MS Regressiorn Residual Total 3 8281618.949 2760540 43.4602 7.58205E-14 49 3112421.08 63518.8 52 11394040.03 Coefficients Standard Error titat P-value Lower 95% Upper 95% 1481.063116 273.490089 5.342289 2.37E-06 911.4645391 2010.662 Store Size (Sq. Ft.) 3.256333342 0.289857069 11.23427 3.68E-15 2.673844106 3.838823 -109.3628452 84.63282732 1.2922 0.202348 -279.4387761 60.71309 314 3532146 105.6491529 2.975445 0.004533 102.0434219 526.663 Intercept College Nearby Drive Thru Adding the dummy variables increased the R-square value of the model, but knowing if there is a college near-by is not significant. Having a drive through window seems to significantly increase sales but how much is somewhat questionable given the wide confidence interval.

Answer 1

15.4) As per the excel results given above having the dummy variable drive through window,

Increase in one drive through window increases the sales by $314.

Problem 2:-

given equation y = 22,167 - 412x₁ + 818x₂ - 93x₃ - 71x₄

this equation can be related to

y = b₀ +b₁x₁+b₂x₂+b₃x₃+b₄x₄

a) as per the given data above the coefficients of variables can be explained as below

b₁ = With increase in 1 unit of local unemployment rate (x₁) weekly sales (y) decreases by 412 units.

b₂ = With increase in 1 unit of weekly average high temperature (x₂) weekly sales (y) increases by 818 units.

b₃ = With increase in 1 unit of number of activities in the local community (x₃) weekly sales (y) decreases by 93 units.

b₄ = With increase in 1 unit of Average gasoline price (x₄) weekly sales (y) decreases by 71 units.

b) given x₁ =5.7% x₂ = 61^o x₃ =14 x₄ = $1.39

y = 22,167 - 412(5.7) + 818 (61) - 93 (14) - 71(1.39) = 68315.91 units