Consider a model explaining the weekly sales for a major brand of canned tuna by a supermarket chain in a large city. In sales; =B2 +B2 pricel, +B; price2; +B.price3; +B;disp; +Bqdispad; +e (3.1) where sales1 = unit sales of brand no.1 canned tuna pricel = price per can of brand no.1 canned tuna. price2 = price per can of brand no.2 canned tuna. price] =price per can of brand no.3 canned tuna, disp = 1 if there is a store display for brand no.1 during the week but no advertising in the newspapers; = 0 otherwise. dispad = 1 if there is a store display and a newspaper advertisement for brand no.1 during the week; = 0 otherwise. (a) The results from estimation of equation (3.1) are in Table 3.1 below. Discuss and interpret the estimates for B, and B; . Are the signs according to what you expected? (4 marks) (6) Perform an appropriate test using a 5% significance level to test whether Bo>B5. Discuss the result. What is the interpretation for this hypothesis test? (6 marks) (c) Obtain a 95% interval estimate for (63-B4). Discuss the result. What is the interpretation for this interval estimate? 6 marks) Table 3.1 Dependent Variable: LOG(SALES1) Method: Least Squares Sample: 152 Included observations: 52 Variable Coefficient Std Error t-Statistic Prob. PRICE1 PRICE2 PRICE DISP DISPAD 8.9848 -3.7463 1.1495 1.2880 0.4237 1.4313 0.6463 0.5765 0.4486 0.6053 0.1052 0.1561 13.901 -6.4982 2.5622 2.1279 4.0276 9.1652 0.0000 0.0000 0.0137 0.0387 0.0002 0.0000 R-squared Adjusted R-squared S.E. of regression Sum squared resid F-statistic Prob(F-statistic) 0.8428 Mean dependent var 0.8257 S.D. dependent var 0.3397 Akaike info criterion 5.3073 Schwarz criterion 49.329 Durbin-Watson stat 0.0000 8.4372 0.8137 0.7865 1.0116 1.6759 DISPAD PRICE1 PRICE2 PRICE3 DISP DISPAD The variance and covariance matrix for the coefficients PRICE1 PRICE2 PRICE3 DISP 0.4177 -0.1914 -0.0801 -0.2442 -0.0066 -0.1914 0.3323 -0.0738 -0.0255 0.0087 -0.0801 -0.0738 0.2012 -0.0275 -0.0037 -0.2442 -0.0255 -0.0275 0.3664 -0.0040 -0.0066 0.0087 -0.0037 -0.0040 0.0110 -0.0250 0.0422 -0.0044 -0.0146 0.0069 -0.0250 0.0422 -0.0044 -0.0146 0.0069 0.0243 Consider a model explaining the weekly sales for a major brand of canned tuna by a supermarket chain in a large city. In sales; =B2 +B2 pricel, +B; price2; +B.price3; +B;disp; +Bqdispad; +e (3.1) where sales1 = unit sales of brand no.1 canned tuna pricel = price per can of brand no.1 canned tuna. price2 = price per can of brand no.2 canned tuna. price] =price per can of brand no.3 canned tuna, disp = 1 if there is a store display for brand no.1 during the week but no advertising in the newspapers; = 0 otherwise. dispad = 1 if there is a store display and a newspaper advertisement for brand no.1 during the week; = 0 otherwise. (a) The results from estimation of equation (3.1) are in Table 3.1 below. Discuss and interpret the estimates for B, and B; . Are the signs according to what you expected? (4 marks) (6) Perform an appropriate test using a 5% significance level to test whether Bo>B5. Discuss the result. What is the interpretation for this hypothesis test? (6 marks) (c) Obtain a 95% interval estimate for (63-B4). Discuss the result. What is the interpretation for this interval estimate? 6 marks) Table 3.1 Dependent Variable: LOG(SALES1) Method: Least Squares Sample: 152 Included observations: 52 Variable Coefficient Std Error t-Statistic Prob. PRICE1 PRICE2 PRICE DISP DISPAD 8.9848 -3.7463 1.1495 1.2880 0.4237 1.4313 0.6463 0.5765 0.4486 0.6053 0.1052 0.1561 13.901 -6.4982 2.5622 2.1279 4.0276 9.1652 0.0000 0.0000 0.0137 0.0387 0.0002 0.0000 R-squared Adjusted R-squared S.E. of regression Sum squared resid F-statistic Prob(F-statistic) 0.8428 Mean dependent var 0.8257 S.D. dependent var 0.3397 Akaike info criterion 5.3073 Schwarz criterion 49.329 Durbin-Watson stat 0.0000 8.4372 0.8137 0.7865 1.0116 1.6759 DISPAD PRICE1 PRICE2 PRICE3 DISP DISPAD The variance and covariance matrix for the coefficients PRICE1 PRICE2 PRICE3 DISP 0.4177 -0.1914 -0.0801 -0.2442 -0.0066 -0.1914 0.3323 -0.0738 -0.0255 0.0087 -0.0801 -0.0738 0.2012 -0.0275 -0.0037 -0.2442 -0.0255 -0.0275 0.3664 -0.0040 -0.0066 0.0087 -0.0037 -0.0040 0.0110 -0.0250 0.0422 -0.0044 -0.0146 0.0069 -0.0250 0.0422 -0.0044 -0.0146 0.0069 0.0243