Question

ln(QCOM) ⁼ ln α + β₁*(PCOM) + ϒ₁*(PELEC) + ϒ₂*ln(COM) + ϒ₃*(SALES) + ϒ₄*(DEGREE).  

QCOM = α*(PCOM)^β1*(PELEC)^ϒ1 (COM)^ϒ2 (SALES) ^ϒ3(DEGREE)^ϒ4

Where

QCOM = annual mcfs purchased by the gas utility’s commercial customers,

PCOM = average annual commercial price per mcf of gas,

PELEC = annual average commercial electric price per kwh,

COM = number of commercial gas customers,

SALES = annual area retails sales per retail establishment,

DEGREE = annual heating degree days.

Estimate equation (1). What are the estimated coefficients for β1 (PCOM) and ϒ₃ (SALES)? At what level (choose .01, .05 .10) is each coefficient significant or is it not significant (NS)? Write your answer in 3a above.

A.) β1 = _____; Significance Level = _____

B.) ϒ₃ = _____; Significance Level = _____

In words explain what R Square means in the context of this demand estimation.

C.) R Square Interpretation is =  

D.) Suppose PCOM = .66, PELEC =628, COM = 52,740, SALES = 2073 and DEGREE = 2,516. Use your estimated equation to find the price elasticity of demand.

SUMMARY OUTPUT Regression Statistics Multiple R 0.89605258 R Square 0.802910227 Adjusted R Square 0.76641212 Standard Error 9126127.394 Observations 33 ANOVA df SS MS F Significance F 9.44793E-09 5 Regression Residual Total 9.16093E+15 2.24873E+15 1.14097E+16 1.83219E+15 21.99868186 8.32862E+13 27 32 Intercept PCOM PELEC Coefficients Standard Error t Stat P-value Lower 95% -5146918.981 18318396.85 -0.280969946 0.780875383 -42733164.66 -12247743.76 6155434.881 -1.989744672 0.056835257 -24877652.89 -1818.576692 8742.36253 -0.208018906 0.83677538 -19756.42292 466.5219052 48.44917325 9.629099402 3.17433E-10 367.112413 8488.689021 6309.662931 1.345347464 0.189704024 -4457.66993 488.0357532 1125.268589 0.433706013 0.667947681 -1820.824677 Upper 95% Lower 95.0% 32439326.7 -42733164.66 382165.3756 -24877652.89 16119.26953 -19756.42292 565.9313973 367.112413 21435.04797 -4457.66993 2796.896183 -1820.824677 Upper 95.0% 32439326.7 382165.3756 16119.26953 565.9313973 21435.04797 2796.896183 COM SALES DEGREE

Answer 1

(A) From the regression equation, it can be observed that Beta1 = -12247743.76

It is significant at the level 0.10 as the p-value is > 0.05 but < 0.10

(B)From the regression equation, it can be observed tha Y3 = 8488.689021

It is not significant as the p-value is > 0.10

(C) R squres is 0.8029 whch means that roughloy 80.3% of the variation in the annual mcfs purchased by the gas utility’s commercial customers is explained within the model by variation in the independent variables chosen.

(D) Price elasticity of demand = (dQCOM/dPCOM)*(PCOM/QCOM)

Keeping all variables except PCOM constant and differentiating the equation we get

dQCOM/QCOM = Beta1*dPCOM

=> Beta1 = (dQCOM/dQCOM)*(1/QCOM)

=> Beta1*PCOM = own price elasticity

Thus, elasticty = -12247743.76*0.66 = -8083510.88