Q1) 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.

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 np Design 2 3 compet 9.4 9.4 9.7 11.9 13.4 9.6 9.2 13.6 14.4 15.3 15.1 11.8 12.8 12.4 9.3 10 11 12 13 14 15 Sales 29100 25620 23850 25200 21420 21300 21900 23700 22080 21960 17580 19440 20940 19110 20310 20460 25020 22380 23940 25860 28980 24480 24600 26460 29880 29670 24390 25980 30450 32130 26850 ad 25410 26400 25950 27010 27850 25090 25700 26670 28780 28350 28970 27440 25820 26130 25290 25440 26330 28780 30510 32740 35940 37740 38610 39190 40400 41330 43030 43930 45600 45870 47160 relprice 1.18 1.14 1.18 1.20 1.24 1.46 1.54 1.48 1.48 1.48 1.48 1.66 1.76 1.88 2.00 2.14 2.08 2.02 1.88 1.70 1.58 1.50 1.50 1.44 1.48 1.46 1.42 1.40 1.42 1.42 1.38 7.9 16 17 2 7.8 8.4 18 9.1 19 20 21 22 23 24 25 26 27 28 8.8 9.2 9.8 10.3 8.8 8.2 7.5 7.1 7.2 8.9 7.7 7.4 29 30 31 1 Store np Design 2 3 compet 9.4 9.4 9.7 11.9 13.4 9.6 9.2 13.6 14.4 15.3 15.1 11.8 12.8 12.4 9.3 10 11 12 13 14 15 Sales 29100 25620 23850 25200 21420 21300 21900 23700 22080 21960 17580 19440 20940 19110 20310 20460 25020 22380 23940 25860 28980 24480 24600 26460 29880 29670 24390 25980 30450 32130 26850 ad 25410 26400 25950 27010 27850 25090 25700 26670 28780 28350 28970 27440 25820 26130 25290 25440 26330 28780 30510 32740 35940 37740 38610 39190 40400 41330 43030 43930 45600 45870 47160 relprice 1.18 1.14 1.18 1.20 1.24 1.46 1.54 1.48 1.48 1.48 1.48 1.66 1.76 1.88 2.00 2.14 2.08 2.02 1.88 1.70 1.58 1.50 1.50 1.44 1.48 1.46 1.42 1.40 1.42 1.42 1.38 7.9 16 17 2 7.8 8.4 18 9.1 19 20 21 22 23 24 25 26 27 28 8.8 9.2 9.8 10.3 8.8 8.2 7.5 7.1 7.2 8.9 7.7 7.4 29 30 31 1