PLC Inc. is a manufacturer in food industry. Its marketing department is seeking to develop an econometric model for forecasting the future sales of one of its products. An analyst feels that the most important factors affecting the sales (measured in Kgs) are the selling price X1 (measured in dollars), advertisement spending X2 (measured in thousand dollars), the purchasing power of its potential buyers X3 (represented by GDP per person which is measured in thousand dollars), and time T measure in quarter (valued 1, 30). Thirty (30) consecutive quarters of quarterly data for these variables were obtained. The following three regression equations were tried.
1. Y = ß0 + ß1X1 + ß2X2 + ß3X3 + ß4T + µ
2. Y = ß0 + ß1lnX1 + ß2lnX2 + ß3lnX + µ
3. lnY = ß0 + ß1X1 + ß2X2 + ß3X3 + ß4T + µ
The regression results of these three models are as follows (figures in the parentheses are the standard errors of the corresponding estimated regression coefficients):
Model 1: Y = -15.00 - 0.20X1+ 0.06X2 + 2.00X3 + 1.00T
(5.293) (0.20) (0.02) (1.00) (2.00)
R2=0.67 adj R2=0.55
Model 2: Y= -50.453 - 3.168lnX1+ 2.308lnX2+14.687lnX3
(13.728) (2.917) (0.110) (3.10)
R2=0.65 adj R2=0.58
Model 3: lnY= -3.131 - 0.45lnX1+ 8.04lnX2+ 0.250X3+ 0.02T
(1.216) (0. 015) (1.865) (0.121) (0.100)
R2=0.725 adj R2=0.68
In Model 3, test if the regression coefficient of T (i.e. 0.02) is statistically greater than 0.01 at 5% level of significance. Show your test step by step. (3 points)
In Model 3, what would be the advertisement elasticity of sales, (2 points), and the quantitative impact of advertisement spending on the sales, i.e. ? (2 points). Show your work step by step. ( total 4 points for Question 8)