(a) Why is the coefficient of PRICE in model 1 different from the coefficient of PRICE in model 2? Which do you think is the more reliable of these two coefficients? Explain. What evidence is there to suggest that one of these two models is superior? How does the issue of the number of observations affect your answer? [40%] (b) In model 2, are the signs of the coefficients consistent with economic theory? In model 2, which of the coefficients are significantly different from zero at the 5% level? By how much are sales expected to change in response to an increase in advertising expenditure of $2 million if PRICE, INCOME and PCOMPET remain unchanged. [40%] (c) Use the correlation matrix to examine the severity of one potential violation of the Gauss-Markov conditions. Name and define this violation. In light of this potential violation, which steps would you propose to you improve this model? [20%]QUESTION 1 A company's SALES (millions of items sold) are thought to depend upon the following explanatory variables: ADS - Advertising expenditure, millions of dollars PRICE - Company's product price, dollars POOMPET - Average price charged by the company's competitors, dollars INCOME - Aggregate Income of potential customers, billions of dollars. Using 12 annual observations of each variable the following regression results have been obtained. Model 1 Ordinary Least Squares Estimation Dependent variable Is SALES 12 observations used for estimation from 1 to 12 Regressor Coerclent Standard Error T-Ratio Prob] CONSTANT 108.6054 11 0157 9.8592 PRICE -5.3997 1.0439 -5.1725 1000] -Squared .72794 R-Bar-Squared .70073 B.E. of Regression 6.9685 F-stat. F(1, 10) 26.7562[.000] Mean of Dependent Variable 52.5833 3.0. of Dependent Variable 12.7363 Residual Sum of Squares 485.6092 Equation Log-kellhood -39.2302 Akalke Info. Criterion - 41.2302 Schwarz Bayeslan Criterion -41.7152 DW-Glatloc .59216 Mirlel 2 Ordinary Least Squares Estimation Dependent variable Is SALES 12 observations used for estimation from 1 to 12 Regressor Coeliclent Standard Enor T-Ratio [Prob] CONSTANT -30.5565 9.5492 -3.1999 [.015] ADS 1.1673 16294 7.1636 [.000] PRICE -2.8425 59728 -4.7590 002 INCOME 1038978 034783 2.5581 1.0387 PCOMPET 1.9951 67292 2 9549 1.0217 R-Squared .99369 R-Bar-Squared.99009 S.E. of Regression 1.2681 F-stat. F(4, 7) 275.7299(_000] Mean of Dependent Variable 52.5633 5.D. of Dependent Variable 12.7363 Residual Sum of Squares 11.2570 Equation Log-kellhood -15.6438 Akalke Info. Criterion-21.6438 Schwarz Bayeslan Criterion -22.8561 OW-statistic 2.456! Eximated Correlation Matrix of Variables ADS PRICE INCOME PCOMPET ADS 10000 .78631 85124 -.48058 PRICE .76831 1.0000 -.65979 83554 INCOME 85124 .65979 1.00 00 -.45931 PCOMPET 48058 83554 - 4595 1 0000