Question

We wish to estimate a demand function for commercial gas utility customers using a multiplicative form as follows:

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

Estimate equation. 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)?  

β1 = _____; Significance Level = _____

ϒ₃ = _____; Significance Level = _____

You now have estimations of both the linear (1) and a multiplicative (2) specifications of commercial gas demand. As a manager and a decision maker, choose one specification that you prefer and support your choice.

Specification = choose linear (1) or multiplicative (2)

Justification = support your choice

QCOM PCOM PELEC COM SALES DEGREE 37033016 0.655072 627.6365 52739.5 2073.445 2515.956 16870863 1.613603 837.5992 30476.35 2303.738 6084.5 10482414 1.575179 964.3883 29848.09 2073.445 5578.008 7487700 0.766416 603.7899 14595.48 2682.32 5988.596 9683834 1.107066 239.0958 12661.59 2461.336 6039.545 1797314 1.338402 964.3883 3101.413 2073.445 5578.008 12578659 0.703501 603.7899 14376.72 2682.32 5988.596 22316808 0.841567 587.5043 34720.34 2512.511 5675.91 5291498 1.511017 552.025 8598.918 2579.388 4144.419 9647897 0.81687 587.5043 19811.66 2512.511 5675.91 2496184 1.088698 742.7968 4284.283 2492.739 4421.15 10282770 0.601996 613.6775 15635.33 1986.212 6948.623 12417948 0.592025 480.4839 16979.84 1914.099 5014.568 10582236 0.771211 589.8309 7380.181 2024.594 7478.08 8690589 0.677852 371.7159 10619.79 1829.773 8836.67 5291498 0.598468 406.6151 11768.56 2253.725 1605.77 8785422 0.925767 964.3883 14376.72 2073.445 5578.008 20909421 1.132867 964.3883 29454.55 2073.445 5578.008 7587525 0.758094 603.7899 4379.191 2682.32 5988.596 24856071 0.829995 496.1881 33799.43 2440.982 5609.976 10781880 1.307632 302.4983 22830.23 2372.36 5431.155 3694203 0.655096 513.0556 6062.522 1683.801 7930.613 4293196 1.065185 964.3883 5890.695 2073.445 5578.008 87034849 0.784676 507.8208 153814.4 2510.185 2999.509 56595139 0.77856 603.7899 42102.49 2682.32 5988.596 52802547 0.589576 462.453 59794.76 2217.669 7518.039 5491156 1.000635 492.1166 12518.75 1930.964 3180.339 44718239 1.333737 870.7506 149437.3 2371.197 5205.379 7787176 1.014371 964.3883 11330.03 2073.445 5578.008 3458596 0.561774 496.1881 4434.137 2440.982 5609.976 21063137 0.935322 239.0958 23270.72 2461.336 6039.545 7288048 0.743321 589.8309 8717.794 2024.594 7478.08 3394702 0.855831 589.8309 9545.925 2024.594 7478.08

Answer 1

First we take the log values to make the regression equation as additive one

$QCOM = \alpha * (PCOM)\beta_1*(PELEC)\gamma_1*(COM)\gamma_2*(SALES)\gamma_3*(Degree)\gamma_4$

$log (QCOM) = \alpha + \beta_1log(PCOM) + \gamma_1log(PELEC) + \gamma_2log(COM)+\gamma_3log(SALES)+ \gamma_4log(Degree)$

Changed dataset

LOG VALUES
QCOM	PCOM	PELEC	COM	SALES	DEGREE
7.5685891	-0.18371	2.797708	4.722136	3.316693	3.400703
7.2271373	0.207797	2.923036	4.483963	3.362433	3.784225
7.0204613	0.19733	2.984252	4.474917	3.316693	3.746479
6.8743484	-0.11554	2.780886	4.164218	3.428511	3.777325
6.9860473	0.044174	2.378572	4.102488	3.391171	3.781004
6.254624	0.126587	2.984252	3.49156	3.316693	3.746479
7.0996343	-0.15274	2.780886	4.15766	3.428511	3.777325
7.3486321	-0.07491	2.769011	4.540584	3.400108	3.754036
6.7235786	0.179269	2.741959	3.934444	3.411517	3.617464
6.9844327	-0.08785	2.769011	4.296921	3.400108	3.754036
6.3972766	0.036907	2.87087	3.631878	3.396677	3.645535
7.0121101	-0.22041	2.78794	4.194107	3.298026	3.841899
7.0940498	-0.22766	2.681679	4.229934	3.281964	3.700234
7.0245774	-0.11283	2.770728	3.868067	3.306338	3.87379
6.9390492	-0.16887	2.570211	4.026116	3.262397	3.946289
6.7235786	-0.22296	2.609184	4.070723	3.352901	3.205683
6.9437626	-0.0335	2.984252	4.15766	3.316693	3.746479
7.320342	0.054179	2.984252	4.289021	3.316693	3.746479
6.8801001	-0.12028	2.780886	3.641394	3.428511	3.777325
7.3954325	-0.08092	2.695646	4.528909	3.387565	3.748961
7.0326945	0.116486	2.480723	4.35851	3.375181	3.734892
6.5675208	-0.1837	2.710164	3.782653	3.226291	3.899307
6.6327807	0.027425	2.984252	3.770167	3.316693	3.746479
7.9395934	-0.10531	2.70571	5.186997	3.399706	3.47705
7.7527791	-0.10871	2.780886	4.624308	3.428511	3.777325
7.7226549	-0.22946	2.665068	4.776663	3.345897	3.876105
6.7396638	0.000276	2.692068	4.097561	3.285774	3.502473
7.6504847	0.12507	2.939894	5.174459	3.374968	3.716452
6.89138	0.006197	2.984252	4.054231	3.316693	3.746479
6.5388998	-0.25044	2.695646	3.646809	3.387565	3.748961
7.3235231	-0.02904	2.378572	4.36681	3.391171	3.781004
6.8626112	-0.12882	2.770728	3.940407	3.306338	3.87379
6.5308017	-0.06761	2.770728	3.979818	3.306338	3.87379

Regression Analysis (Done in Excel > Data > Data Analysis)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.939922488
R Square	0.883454284
Adjusted R Square	0.861871744
Standard Error	0.149930624
Observations	33
ANOVA
	df	SS	MS	F	Significance F
Regression	5	4.60078802	0.920157604	40.93374928	8.9595E-12
Residual	27	0.60693818	0.022479192
Total	32	5.2077262
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-1.254435598	2.101449663	-0.596938209	0.555521706	-5.566254145	3.057382948
PCOM	-0.51542486	0.216156372	-2.384499961	0.024389697	-0.9589411	-0.07190862
PELEC	0.020838886	0.177504672	0.117399085	0.907412784	-0.343370618	0.38504839
COM	0.909254931	0.067624696	13.44560463	1.76154E-13	0.770500515	1.048009347
SALES	0.922844079	0.521483821	1.769650451	0.088079934	-0.147152339	1.992840497
DEGREE	0.344010464	0.183221284	1.877568243	0.071283044	-0.031928557	0.719949485

B1 = -0.5154

$\gamma_3 = 0.9228$

The P-value for $\beta_1 = 0.024$ , is the significant level

The P-value for $\gamma_3 = 0.088$ , is the significant level

Note: Linear Model is not part of the question. Question states only multiplicative model