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Econometrics-I-12

# 46197918-1.770.0946.62272267t.01251291.01263559.990.33

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Unformatted text preview: 46197918-1.770 .0946 -.62272267T -.01251291 .01263559 -.990 .3359 13.0000000&#152;&#152;&#152;&#152;™™ 27/38Part 12: Asymptotics for the Regression ModelCovariance Matrix&#152;&#152;&#152;&#152;™™ 28/38Part 12: Asymptotics for the Regression ModelLinear HypothesisH0: Aggregate price variables are not significant determinants of gasoline consumptionH0: β7 = β8 = β9 = 0H1: At least one is nonzero&#152;&#152;&#152;&#152;™™ 29/380 0 0 0 0 0 1 0 0 0= 0 0 0 0 0 0 0 1 0 0 , = 00 0 0 0 0 0 0 0 1 0 R- q = 0βRqPart 12: Asymptotics for the Regression ModelWald TestMatrix ; R = [0,0,0,0,0,0,1,0,0,0/ 0,0,0,0,0,0,0,1,0,0/ 0,0,0,0,0,0,0,0,1,0] ; q = [0 / 0 / 0 ] \$Matrix ; m = R*b - q ; Vm = R*Varb*R' ; List ; Wald = m'<Vm>m \$Matrix WALD has 1 rows and 1 columns. 1 +-------------- 1| 66.91506&#152;&#152;&#152;&#152;™™ 30/38Part 12: Asymptotics for the Regression ModelRestricted RegressionCompare Sums of SquaresRegress; lhs=g;rhs=X;cls:b(7)=0,b(8)=0,b(9)=0\$+----------------------------------------------------+| Linearly restricted regression || Ordinary least squares regression || LHS=G Mean = 5.308616 || Standard deviation = .2313508 || Residuals Sum of squares = .01864365 | .00377694| Standard error of e = .3053166E-01 | | Fit R-squared = .9866028 | .9972859 without restrictions| Adjusted R-squared = .9825836 || Model test F[ 6, 20] (prob) = 245.47 (.0000) || Restrictns. F[ 3, 17] (prob) = 22.31 (.0000) | Note: J(=3)*F = Chi-Squared = 66.915 from before| Not using OLS or no constant. Rsqd & F may be < 0. || Note, with restrictions imposed, Rsqd may be < 0. |+----------------------------------------------------++---------+--------------+----------------+--------+---------+----------+|Variable | Coefficient | Standard Error |t-ratio |P[|T|>t] | Mean of X|+---------+--------------+----------------+--------+---------+----------+Constant -4.46504223 4.77789711 -.935 .3631Y 1.05851456 .55196204 1.918 .0721 9.03448264PG -.15852276 .05008100 -3.165 .0057 .47679491PNC .21765564 .18336687 1.187 .2516 .28100132PUC -.24298315 .10328032 -2.353 .0309 .40523616PPT -.12617610 .10436708 -1.209 .2432 .47071442PD .000000 ......(Fixed Parameter)....... -.44279509PN .222045D-15 ......(Fixed Parameter)....... -.58532943PS -.444089D-15 ......(Fixed Parameter)....... -.62272267T .02944666 .02126600 1.385 .1841 13.0000000&#152;&#152;&#152;&#152;™™ 31/38Part 12: Asymptotics for the Regression ModelNonlinear RestrictionsI am interested in testing the hypothesis that certain ratios of elasticities are equal. In particular,1 = 4/5 - 7/8 = 02 = 4/5 - 9/8 = 0 &#152;&#152;&#152;&#152;™™ 32/38Part 12: Asymptotics for the Regression Model...
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