Akiko Hamaguchi, the manager at a small sushi restaurant in Phoenix, Arizona, is

Question

Akiko Hamaguchi, the manager at a small sushi restaurant in Phoenix, Arizona, is concerned that the weak economic environment has hampered foot traffic in her area, thus causing a dramatic decline in sales. Her cousin in San Francisco, Hiroshi Sato, owns a similar restaurant, but he has seemed to prosper during these rough economic times. Hiroshi agrees that higher unemployment rates have likely forced some customers to dine out less frequently, but he maintains an aggressive marketing campaign to thwart this apparent trend. For instance, he advertises in local papers with valuable two-forone coupons and promotes early-bird specials over the airwaves. Despite the fact that advertising increases overall costs, he believes that this campaign has positively affected sales at his restaurant. In order to support his claim, Hiroshi provides monthly sales data and advertising costs pertaining to his restaurant, as well as the monthly unemployment rate from San Francisco County. A portion of the data is shown in the accompanying table; the entire data set, labeled Sushi_Restaurant, can be found on the text website.

Is simple regression or multiple regression more appropriate for making predictions in this case? Why?

What predictions can you make for sales based on unemployment rate and the level of advertising? What leads you to those predictions?

Month   Year   Sales    AdsCost   Unemp
January    2008   27   550   4.6
February   2008   24.2   425   4.3
March   2008   25.6   450   4.6
April   2008   28.5   625   4.3
May   2008   30.8   650   4.8
June   2008   31.5   675   5.2
July   2008   34.9   700   5.6
August   2008   32.5   650   5.8
September   2008   30.4   550   5.5
October   2008   31   525   5.8
November   2008   28.5   500   6
December   2008   29   600   6.5
January   2009   26.2   575   8
February   2009   25.4   625   8.4
March   2009   27.8   650   9.1
April   2009   26.5   600   8.9
May   2009   27.4   550   9.1

Explanation / Answer

I have worked only based on the data given here. I am using MINITAB to perform the regression.

Multiple regression is better suited here since it will take into account more variables and thus is likely to give more accurate predictions.

Regression Analysis: Sales versus Adcost, Unemp

Analysis of Variance

Source      DF Adj SS Adj MS F-Value P-Value
Regression   2   72.64 36.319     8.76    0.003
Adcost     1   64.11 64.108    15.46    0.002
Unemp      1   21.85 21.846     5.27    0.038
Error       14   58.04   4.146
Total       16 130.68

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)
2.03617 55.58%     49.24%      35.73%

Coefficients

Term         Coef SE Coef T-Value P-Value   VIF
Constant    17.51     3.98     4.40    0.001
Adcost    0.02655 0.00675     3.93    0.002 1.06
Unemp      -0.688    0.300    -2.30    0.038 1.06

Regression Equation

Sales = 17.51 + 0.02655 Adcost - 0.688 Unemp

Based on this regression equation we can state that Sales increases with increase in Advertisement costing and decreases with increase in unemployment rate.

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