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Q1 1. The estimated equation is: However, from table 1 we note that the t-statistic values are greater than the 5% critical value of 1.96 for the variables price, radio and the squared value of radio. The variable TV as well as the squared value of the variable price is significant only at the 10% level…
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Download file to see previous pages Thus, while the beta coefficients measure the first order impacts, i.e., the slope of the partial functions, the theta coefficients measure the second order impacts or the curvature. The expected signs on these coefficients will depend upon the nature of the relationship that the variable has with sales revenue. If the true relationship that is being estimated is truly nonlinear, then the beta coefficients themselves would be functions of the corresponding independent variables. The signs would depend upon the value of the independent variable itself. For instance, a rise in price of mobile phones would lead to a certain rise in revenue if other things, in particular the number of units sold remained unaltered. However, as price rises, the demand for the product would go down thereby implying a potential fall in the overall sales. The final impact would depend upon the price elasticity of demand of the product. For lower level of sales the demand would be highly inelastic implying that rising price would still generate increased revenue. But if the demand became elastic, then there would be a definite decline in revenue. Since demand for average mobile phones tend to be relatively inelastic, we should expect to see a positive beta coefficient and a negative theta coefficient. In case of advertising, again the beta coefficient measures the impact of a rise in advertising on total sales while the theta coefficient measures the marginal impact. We should expect that increase in advertising should stimulate additional sales. However, the incremental benefits of more advertising typically are found to be declining. In simpler terms, as there is more and more advertising, the incremental impact on sales declines. Thus, we should expect a positive beta but a negative theta coefficient for all the advertising variables. Table 1: Results of OLS regression, problem 1 Dependent Variable: REVENUE Method: Least Squares Date: 09/29/11 Time: 13:10 Sample: 1 60 Included observations: 60 Coefficient Std. Error t-Statistic Prob.   C 359.1101 76.04848 4.722120 0.0000 PRICE 2.880176 1.411429 2.040609 0.0465 PRICE^2 -0.011268 0.006384 -1.765162 0.0835 TV 6.383748 3.514018 1.816652 0.0751 TV^2 -0.418966 0.359010 -1.167003 0.2486 NEWSPAPER 3.480550 2.251321 1.546003 0.1283 NEWSPAPER^2 -0.107221 0.160149 -0.669510 0.5062 RADIO 11.10707 1.184501 9.377007 0.0000 RADIO^2 -0.336564 0.053449 -6.296872 0.0000 R-squared 0.876161     Mean dependent var 646.5073 Adjusted R-squared 0.856736     S.D. dependent var 30.92782 S.E. of regression 11.70626     Akaike info criterion 7.895606 Sum squared resid 6988.868     Schwarz criterion 8.209758 Log likelihood -227.8682     Hannan-Quinn criter. 8.018488 F-statistic 45.10326     Durbin-Watson stat 2.333861 Prob(F-statistic) 0.000000 2. We test the joint significances of the variables first in levels (table 2) and then in squares (table 3). Table 2: Testing Joint significance of the variables in their levels Wald Test: Equation: Untitled Test Statistic Value   df     Probability F-statistic 8.295663 (3, 51)   0.0001 Chi-square 24.88699 3   0.0000 Null Hypothesis Summary: Normalized Restriction (= 0) Value   Std. Err. C(2) - C(8) -8.226895 1.877380 C(4) - C(8) -4.723323 3.679021 C(6) - C(8) -7.626522 2.427360 Restrictions are linear in coefficients. The ...Download file to see next pagesRead More
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