You expect the demand function for natural gas is of the Cobb-Douglas form: Q = ebipb2yb3p, b4eu where Q is per capita demand for natural gas, Py is the price of natural gas ($/1,000 cu ft.), Y is state per capita income ($1,000/person), Pe is the price of electricity ($/kilowatt hour), and u is a random error term. Taking the natural log of both sides of this equation makes it linear in its parameters: In(Q) = b; + b2ln(Pn) + b2ln(Y) + beIn(Pe) + u. The data you have available for estimating this linear regression equation is cross sectional data from all fifty states. Your regression results, with standard errors reported in parentheses below the parameter estimates, are: In(Q) = -13.7 -0.646ln(PN) + 0.539 (Y) +0.231ln(Pe) (5.55) (0.246) (0.639) (0.0970) R2 = 0.619 S= 24.7 N=50 Adj-R2 = 0.603 F=42.3 Note: For the questions below the lower and upper critical t values for a significance level of 0.05 and 0.025 with 46 degrees of freedom are T.INV(0.05, 46)=-1.679, T.INV(0.95, 46) = 1.679, T.INV(0.025, 46) = -2.01, and T.INV(0.975, 46)=2.01. 1. As expected, the regression results point to an inverse relationship between the quantity demanded (Q) and price of natural gas (PN). Test if this inverse relationship is significant at the 0.05 level. Be sure to state your null and alternative hypotheses and to show your calculations. (25 Points) 2. It appears that the cross-price 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? (12.5 Points) b) Using a 0.05 significance level, determine if the cross-price 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. (25 Points) 3. It appears that the per capita income elasticity of demand for natural gas is less than 1.0. a) If this is true, what term would we use to characterize the demand for natural gas? (12.5 points) b) Using a 0.05 significance level, determine if the per capita income elasticity of demand for natural gas is indeed less than 1.0. Be sure to state your null and alternative hypotheses and to show your calculations. (25 Points) You expect the demand function for natural gas is of the Cobb-Douglas form: Q = ebipb2yb3p, b4eu where Q is per capita demand for natural gas, Py is the price of natural gas ($/1,000 cu ft.), Y is state per capita income ($1,000/person), Pe is the price of electricity ($/kilowatt hour), and u is a random error term. Taking the natural log of both sides of this equation makes it linear in its parameters: In(Q) = b; + b2ln(Pn) + b2ln(Y) + beIn(Pe) + u. The data you have available for estimating this linear regression equation is cross sectional data from all fifty states. Your regression results, with standard errors reported in parentheses below the parameter estimates, are: In(Q) = -13.7 -0.646ln(PN) + 0.539 (Y) +0.231ln(Pe) (5.55) (0.246) (0.639) (0.0970) R2 = 0.619 S= 24.7 N=50 Adj-R2 = 0.603 F=42.3 Note: For the questions below the lower and upper critical t values for a significance level of 0.05 and 0.025 with 46 degrees of freedom are T.INV(0.05, 46)=-1.679, T.INV(0.95, 46) = 1.679, T.INV(0.025, 46) = -2.01, and T.INV(0.975, 46)=2.01. 1. As expected, the regression results point to an inverse relationship between the quantity demanded (Q) and price of natural gas (PN). Test if this inverse relationship is significant at the 0.05 level. Be sure to state your null and alternative hypotheses and to show your calculations. (25 Points) 2. It appears that the cross-price 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? (12.5 Points) b) Using a 0.05 significance level, determine if the cross-price 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. (25 Points) 3. It appears that the per capita income elasticity of demand for natural gas is less than 1.0. a) If this is true, what term would we use to characterize the demand for natural gas? (12.5 points) b) Using a 0.05 significance level, determine if the per capita income elasticity of demand for natural gas is indeed less than 1.0. Be sure to state your null and alternative hypotheses and to show your calculations. (25 Points)
