You expect the demand function for natural gas is of the Cobb-Douglas form: Q = efng\": shaping\" where Q is per capita demand for natural gas, PN is the price of natural gas ($20,000 cu it), I" is state per capita income ($1,000fperson), PE is the price of electricity ($fkilowatt hour), and u is arandom error term. Taking the natural log of both sides of this equation makes it linear in its parameters: Ina!) = bi + bzln'w) + bgtnm + bn'g) +11. The data you have available for estimating this linear regression equation is cross sectional data om all y states. Your regression results, with standard errors reported in parentheses below the parameter estimates, are: {11(9) = 13.7 0.646n{PN) + 0.539!n{1') + (resuming) (5. 55) (a. 246) (o. 639) (c. 0970) R1 = 0.519 AdjR3 = 0.503 s = 24.7 F = 42.3 N=50 Note: For the questions below the lower and upper critical t values for a signicance level of 0.05 and 0.025 with 46 degrees of freedom are were, 46) = -1.6?9, T.INV(0.95, 45) = 1.5?9, T.1NV(0-025, 45) = -201, and T.]NV(0.9?5, 46) = 2.01- 2. It appears that the crossprice elasticity of the demand for natural gas with respect to the price of electricity is positive (PE). a) If this is true, what term would we use to characterize the natural gas and electricity? b} Using a 0.05 signicance level, determine if the crossprice elasticity of the demand for natural gas with respect to the price of electricity is indeed positive. Be sure to state your null and alternative hypotheses and to show your calculations