Exxon Gas stations are developing a new faster pump design. They have narrowed t

Question

Exxon Gas stations are developing a new faster pump design. They have narrowed the development to two design options and are wondering how the pump design might affect daily gas sales (Sales). In a test in 31 stations, they try out the new design A in some stations (code = 2), the new design B in other stations (code = 3) and for control they have stations that have not had a change (code = 1). From prior research, Exxon knows that three other factors are crucial in predicting gas sales for any particular station: advertising amount in the market (Ad), relative pricing (relprice), and the number of competing stations and their density (compet). For any changes, Exxon wants to be 95% confident.

Data in file “Week 4 GasStation.xls”; additional computer output: regression results tables

a) run a multiple regression analysis to assess the effect of the new pump designs

b) interpret the results

c) are the new designs better than the current design (ie leading to higher sales)

d) Assume a 1% profit margin and an investment of $1M for 100 stations for the change to a new design; will any change be profitable within the first year?

Store Sales Pump Design ad relprice compet 1 29100 2 254101 1.18 9.4 2 25620 31 26400 1.14 9.4 3 23850 1 25950 1.18 9.7 4 25200 1 27010 1.20 11.9 5 21420 2 27850 1.24 13.41 6 21300 3 25090 1.46 9.6 7 21900 1 25700 1.54 9.2 23700 1 26670 1.48 136 9 22080 2 28780 1.48 144 10 21960 3 28350 1.48 15.3 11 17580 1 28970 1.48 15.1 12 19440 11 27440 1.66 11.8 13 20940 2 25820 1.76 12.8 14 19110 3 26130 1.88 12.4 15 20310 11 25290 2.00 9.3 16 20460 11 25440 2.14 79 17 25020 26330 2.08 78 18 22380 3 28780 2.02 8.4 19 23940 11 30510 1.88 9.1 20 25860 11 32740 1.70 8.8 21 289 80 2 359 401 1.58 9.2 22 24480 31 37740 1.50 9.81 23 24600 11 38610 1.50 10.3 24 26460 1 39190 1.44 8.8 25 29880 2 40400 1.48 8.2 1 43030 1.42 7.1 27 24390 28 25980 1 43930 1.40 72 29 30450 2 45600 1.42 8.9 30 32130 3 45870 1.42 77 31 26850 11 47160 1.38 74

Explanation / Answer

Solutuion:

a)

> gasdata_model <- lm(gasdata$Sales.Pomp.Design ~.-gasdata$Pump, data=gasdata)
> summary(gasdata_model)

Call:
lm(formula = gasdata$Sales.Pomp.Design ~ . - gasdata$Pump, data = gasdata)

Residuals:
Min 1Q Median 3Q Max
-3391.7 -1280.7 -225.7 1400.6 3758.1

Coefficients: (1 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.907e+04 2.636e+04 1.482 0.151227
Store 1.565e+02 5.385e+02 0.291 0.773907
Pump 6.675e+02 4.427e+02 1.508 0.144630
ad -2.007e-02 6.615e-01 -0.030 0.976047
relprice -7.120e+03 8.697e+03 -0.819 0.421018
compet -7.336e+02 1.868e+02 -3.928 0.000633 ***
pumpfac2 2.460e+03 8.528e+02 2.884 0.008155 **
pumpfac3 NA NA NA NA
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1999 on 24 degrees of freedom
Multiple R-squared: 0.7597,   Adjusted R-squared: 0.6996
F-statistic: 12.64 on 6 and 24 DF, p-value: 2.048e-06

b) from the regression output we can say that only compet and pump desing 2 are statistically signifcant

c) As seen from the results with DesingPump 2 and compet(if increased ) then the sales will increase

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