Q3. [23 points] You are the manager of a restaurant chain in charge of setting its pricing and advertising strategies. You have tried different prices/advertising expenditure in outlets located in 68 cities and the data are given in Assignment 3 data.xls where REV = monthly sales revenue of the outlet in city i (in $1,000) PRICE;= price set for the outlet in city i (in dollar) ADV; monthly advertising spending of the outlet in city i (in $1,000) Estimate the model: REV = Bo + B1 PRICE + B2 ADV + u and answer parts (i) and (ii) (i) (4 points) Please find the 90% confidence interval for B1. What does this interval suggest about the effect of a 10 cents price reduction on the revenue of an outlet? (ii) (6 points) Your marketing manager claims that cutting price by 20 cents is more effective in raising revenue than raising monthly advertising spending by $600. Please express the manager's claim in terms of the parameters of the model. Then test the validity of her claim with at test at 5% level of significance using the substitution method to reparametrize a model introduced in slide 24 of Lecture 7. Estimate the model: REV = Bo + B1 PRICE + B2 ADV + B3 ADV2 + u and answer parts (iii) and (iv) (iii) (5 points) Do you recommend adding the regressor ADV2? (iv) (8 points) Suppose the current company policy sets the monthly advertising spending at $2,000 per month. You would like to review if this is optimal or not. The marginal cost (MC) of each dollar of monthly advertising spending is equal to this one dollar plus 20 cents of the cost of producing additional output to meet the increase in demand as a result of the advertising. up the null hypothesis under which $2,000 of monthly advertising spending is optimal against a two-sided alternative. Then conduct an F test (not t test) to see if you can reject the null at 5% level of significance. (Note: F test also works for null hypotheses with one restriction. You estimate a restricted and an unrestricted models as usual to conduct the F test.) Hint: At the optimal level of advertising, MC of advertising spending is equal to the marginal revenue (MR) brought about by advertising spending. Set A B C D ADV OUTLET 1 REV 86.1 2.4 Anmt in 2 81 0.7 3 3 4 5 6 7 2.8 2.7 2.8 2.8 2.3 1.7 1.5 0.8 0 8 9 WN 10 11 12 2.9 0.5 13 2.1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 14 15 PRICE 5.41 6.24 6.2 5.48 6.14 5.37 6.45 5.35 5.22 5.89 5.21 6 6.37 5.33 5.23 5.88 6.24 5.59 6.22 6.41 4.96 4.83 6.35 6.47 5.69 5.56 6.41 5.54 6.47 4.94 0.8 16 1.1 76.4 76.6 82.2 82.1 68.6 76.5 80.3 70.7 75 73.7 71.2 84.7 73.6 73.7 78.1 75.7 74.4 68.7 83.9 86.1 73.7 75.7 78.8 73.7 80.2 69.9 69.1 83.8 17 1.9 18 2.1 1.3 19 20 1.1 21 1.1 2.9 22 23 1.4 24 2.5 3 25 26 1 27 3.1 28 0.5 29 2.7 0.9 31 30 32 33 34 35 36 37 31 32 33 34 38 35 36 37 38 39 40 84.3 66 84.3 79.5 80.2 67.6 86.5 87.6 84.2 75.2 84.7 73.7 81.2 69 69.7 78.1 6.16 5.93 5.2 5.62 5.28 5.46 5.11 5.04 5.08 5.86 4.89 5.68 5.83 6.33 39 40 41 42 43 44 45 1.5 2.8 2.3 1.2 3.1 1 2.5 2.1 2.8 3.1 3.1 0.9 1.8 3.1 1.9 0.7 41 42 43 44 46 45 6.47 5.7 46 47 88 1.6 48 80.4 2.9 79.7 2.3 49 50 51 73.2 1.7 85.9 47 48 49 50 51 52 53 54 55 56 57 58 59 5.22 5.05 5.76 6.25 5.34 4.98 6.39 6.22 5.1 1.8 52 83.3 53 73.6 79.2 0.6 3.1 1.2 54 55 88.1 2.1 64.5 6.49 0.5 2.9 56 57 58 59 1.6 1.5 60 4.86 5.1 5.98 5.02 5.08 60 84.1 91.2 71.8 80.6 73.1 81 73.7 61 62 63 2 61 1.3 62 1.1 5.23 6.02 64 63 2.2 64 1.7 65 66 67 | 82.2 74.2 75.4 5.73 5.11 65 0.7 66 0.7 68 67 81.3 5.71 5.45 6.05 2 69 68 75 2.2 Q3. [23 points] You are the manager of a restaurant chain in charge of setting its pricing and advertising strategies. You have tried different prices/advertising expenditure in outlets located in 68 cities and the data are given in Assignment 3 data.xls where REV = monthly sales revenue of the outlet in city i (in $1,000) PRICE;= price set for the outlet in city i (in dollar) ADV; monthly advertising spending of the outlet in city i (in $1,000) Estimate the model: REV = Bo + B1 PRICE + B2 ADV + u and answer parts (i) and (ii) (i) (4 points) Please find the 90% confidence interval for B1. What does this interval suggest about the effect of a 10 cents price reduction on the revenue of an outlet? (ii) (6 points) Your marketing manager claims that cutting price by 20 cents is more effective in raising revenue than raising monthly advertising spending by $600. Please express the manager's claim in terms of the parameters of the model. Then test the validity of her claim with at test at 5% level of significance using the substitution method to reparametrize a model introduced in slide 24 of Lecture 7. Estimate the model: REV = Bo + B1 PRICE + B2 ADV + B3 ADV2 + u and answer parts (iii) and (iv) (iii) (5 points) Do you recommend adding the regressor ADV2? (iv) (8 points) Suppose the current company policy sets the monthly advertising spending at $2,000 per month. You would like to review if this is optimal or not. The marginal cost (MC) of each dollar of monthly advertising spending is equal to this one dollar plus 20 cents of the cost of producing additional output to meet the increase in demand as a result of the advertising. up the null hypothesis under which $2,000 of monthly advertising spending is optimal against a two-sided alternative. Then conduct an F test (not t test) to see if you can reject the null at 5% level of significance. (Note: F test also works for null hypotheses with one restriction. You estimate a restricted and an unrestricted models as usual to conduct the F test.) Hint: At the optimal level of advertising, MC of advertising spending is equal to the marginal revenue (MR) brought about by advertising spending. Set A B C D ADV OUTLET 1 REV 86.1 2.4 Anmt in 2 81 0.7 3 3 4 5 6 7 2.8 2.7 2.8 2.8 2.3 1.7 1.5 0.8 0 8 9 WN 10 11 12 2.9 0.5 13 2.1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 14 15 PRICE 5.41 6.24 6.2 5.48 6.14 5.37 6.45 5.35 5.22 5.89 5.21 6 6.37 5.33 5.23 5.88 6.24 5.59 6.22 6.41 4.96 4.83 6.35 6.47 5.69 5.56 6.41 5.54 6.47 4.94 0.8 16 1.1 76.4 76.6 82.2 82.1 68.6 76.5 80.3 70.7 75 73.7 71.2 84.7 73.6 73.7 78.1 75.7 74.4 68.7 83.9 86.1 73.7 75.7 78.8 73.7 80.2 69.9 69.1 83.8 17 1.9 18 2.1 1.3 19 20 1.1 21 1.1 2.9 22 23 1.4 24 2.5 3 25 26 1 27 3.1 28 0.5 29 2.7 0.9 31 30 32 33 34 35 36 37 31 32 33 34 38 35 36 37 38 39 40 84.3 66 84.3 79.5 80.2 67.6 86.5 87.6 84.2 75.2 84.7 73.7 81.2 69 69.7 78.1 6.16 5.93 5.2 5.62 5.28 5.46 5.11 5.04 5.08 5.86 4.89 5.68 5.83 6.33 39 40 41 42 43 44 45 1.5 2.8 2.3 1.2 3.1 1 2.5 2.1 2.8 3.1 3.1 0.9 1.8 3.1 1.9 0.7 41 42 43 44 46 45 6.47 5.7 46 47 88 1.6 48 80.4 2.9 79.7 2.3 49 50 51 73.2 1.7 85.9 47 48 49 50 51 52 53 54 55 56 57 58 59 5.22 5.05 5.76 6.25 5.34 4.98 6.39 6.22 5.1 1.8 52 83.3 53 73.6 79.2 0.6 3.1 1.2 54 55 88.1 2.1 64.5 6.49 0.5 2.9 56 57 58 59 1.6 1.5 60 4.86 5.1 5.98 5.02 5.08 60 84.1 91.2 71.8 80.6 73.1 81 73.7 61 62 63 2 61 1.3 62 1.1 5.23 6.02 64 63 2.2 64 1.7 65 66 67 | 82.2 74.2 75.4 5.73 5.11 65 0.7 66 0.7 68 67 81.3 5.71 5.45 6.05 2 69 68 75 2.2