龐皓計量經濟學 第二章 練習題及參考解答(第四版)

#練習題2.1表2.9中是中國歷年國內旅游總花費（Y）、國內生產總值（XI）、鐵路里程（X2）、公路里程數(shù)據(jù)（X3）的數(shù)據(jù)。表2.7中國歷年國內旅游總花費、國內生產總值、鐵路里程、公路里程數(shù)據(jù)年份國內旅游總花費（億元）國內生產總值（億元）鐵路里程（萬公里）公路里程（萬公里）19941023.548637.55.9111.7819951375.761339.96.24115.719961638.471813.66.49118.5819972112.7797156.6122.6419982391.285195.56.64127.8519992831.990564.46.74135.1720003175.5100280.16.87167.9820013522.4110863.17.01169.820023878.4121717.47.19176.5220033442.31374227.3180.9820044710.7161840.27.44187.0720055285.9187318.97.54334.5220066229.7219438.57.71345.720077770.6270232.37.8358.3720088749.3319515.57.97373.02200910183.7349081.48.55386.08201012579.8413030.39.12400.82201119305.4489300.69.32410.64201222706.2540367.49.76423.75201326276.1595244.410.31435.62201430311.964397411.18446.39201534195.1689052.112.1457.73201639390743585.512.4469.63資料來源：中國統(tǒng)計年鑒（1）分別建立線性回歸模型，分析中國國內旅游總花費與國內生產總值、鐵路里程公路里程數(shù)據(jù)的數(shù)量關系。（2）對所建立的回歸模型進行檢驗，對幾個模型估計檢驗結果進行比較【練習題2.1參考解答】1）分別建立億元線性回歸模型建立y與xl的數(shù)量關系如下:

￥；=-3228J02+0.05XliDependentVaiable:YMethod:LeastSquares□ale:03/12/18Time:22.32Sample:19942016IncludedobEervations:23VariableCoefficienlStd.Errort-Statistic尸訕.C-J22S.0213M3202-3.869043D.0039X100501310.00231?21.67931O'0000R-squaredD.957231Fvleandlependentvar11003.76AdjustedR-squaredD.9551953D.dependentvar11S66.S3S.E.cfnecression2469.540Akaikeinfocriterion18.54440Sumsquaredrssid1.28E+0SSchuvarzcriterian1864314Loglikelihood!-211.2606Hannan-Quinnenter.10.56923F-stallstlc470.0144Durbin-Watsonstat0.21577GFrC'bfF-statiBtic}0.000000建立y與x2的數(shù)量關系如下：Pf=-3943S.73+6L65.25X1lDependentVariable:YMethod:LeastSquaresDarte:03J12/18Time:2235Sample:19942D16Includledotser^alions:23VariableCoefficientStc.Errort-SlalislicProb.c-39438731950.402-20.22020o.ooodX26165.253232.68202649647O.OOODR-squaredl0.97D957Meandependent'/ar110D3.76AdjustedR-squaned0.963574S.D.dependentvar116B6.83S.E.ofregression2015.056Akaiksinfocriterion19.15739Sumsquaredresidl0697D504Schwarzcriterion10.25611LogiiKeIincod-206-8098Hannan-Quinnenter.19.18221F-statistic702.0629Durbin-Watsanstat0.699706Prob(F-s1atis1ic}o.qodooo建立y與x3的數(shù)量關系如下：=-9106.17十九丘核丘Dependl巳ndVariable:YMetnoa:Leastsquares□ate:03/8Time:22:35sample:19942016Includied□iMation￡：23VariableCoefficientStd.Errort-Stalistic^nob.C-9105.1663170.972-2.3717270.0091X371.6303810.203027.0213880.0000R-squared0.701J90Meandependent^ar■1100^76AdjjustedlR-squaredl0.667D55S.D.dependentvar11666.83S.E.afregression6526.601A<aiKeinfocritenon20.48810Sumsquaredresid8.95EJ-08Schwarzcriterion20.58684locjHKeiihood-233.6132Hannan-ddlnncrller.20.51293F-slalistic42聽gDurbin-Watsanstat0219452尸robfF-sialistic)0.000001（2）對所建立的回歸模型進行檢驗，對幾個模型估計檢驗結果進行比較。關于中國國內旅游總花費與國內生產總值模型，由上可知，，二說明所建模型整體上對樣本數(shù)據(jù)擬合較好。對于回歸系數(shù)的t檢驗-工——二二0,對斜率系數(shù)勺顯著性撿驗表明,GDP對中國國內旅游總花費有顯著影響。同理：關于中國國內旅游總花費與鐵路里程模型，由上可知，"廠】，說明所建模型整體上對樣本數(shù)據(jù)擬合較好。對于回歸系數(shù)的t檢驗：〔pl}=$切疋皐？=2.08,對斜率系數(shù)的顯著性檢驗表明，鐵路里程對中國國內旅游總花費有顯著影響。關于中國國內旅游總花費與公路里程模型，由上可知，二二「二，說明所建模型整體上對樣本數(shù)據(jù)擬合較好。對于回歸系數(shù)的t檢驗-V「二二匸二―，對斜率系數(shù)的顯著性檢驗表明，公路里程對中國國內旅游總花費有顯著影響。2.2為了研究浙江省一般預算總收入與地區(qū)生產總值的關系,由浙江省統(tǒng)計年鑒得到如表2.8所示的數(shù)據(jù)。表2.8浙江省財政預算收入與地區(qū)生產總值數(shù)據(jù)年份一般預算總收入（億元）地區(qū)生產總值（億元）年份一般預算總收入（億元）地區(qū)生產總值（億元）YXYX197827.45123.721998401.805052.62197925.87157.751999477.405443.92

198031.13179.922000658.426141.031981198219831984198519861987198819891990199119921993199419951996199734.3436.6441.7946.6758.2568.6176.3685.5598.21101.59108.94118.36166.64209.39248.50291.75340.52204.86234.01257.09323.25429.16502.47606.99770.25849.44904.691089.331375.701925.912689.283557.554188.534686.112001200220032004200520062007200820092010201120122013201420152016917.761166.581468.891805.162115.362567.663239.893730.064122.044895.415925.006408.496908.417421.708549.479225.076898.348003.679705.0211648.7013417.6815718.4718753.7321462.6922998.2427747.6532363.3834739.1337756.5840173.0342886.4947251.36198031.13179.922000658.426141.031981198219831984198519861987198819891990199119921993199419951996199734.3436.6441.7946.6758.2568.6176.3685.5598.21101.59108.94118.36166.64209.39248.50291.75340.52204.86234.01257.09323.25429.16502.47606.99770.25849.44904.691089.331375.701925.912689.283557.554188.534686.112001200220032004200520062007200820092010201120122013201420152016917.761166.581468.891805.162115.362567.663239.893730.064122.044895.415925.006408.496908.417421.708549.479225.076898.348003.679705.0211648.7013417.6815718.4718753.7321462.6922998.2427747.6532363.3834739.1337756.5840173.0342886.4947251.36(1)建立浙江省一般預算收入與全省地區(qū)生產總值的計量經濟模型,估計模型的參數(shù),檢驗模型的顯著性,用規(guī)范的形式寫出估計檢驗結果,并解釋所估計參數(shù)的經濟意義如果2017年，浙江省地區(qū)生產總值為52000億元，比上年增長10%,利用計量經濟模型對浙江省2017年的一般預算收入做出點預測和區(qū)間預測建立浙江省一般預算收入的對數(shù)與地區(qū)生產總值對數(shù)的計量經濟模型,估計模型的參數(shù),檢驗模型的顯著性,并解釋所估計參數(shù)的經濟意義?！揪毩曨}2.2參考解答】【練習題2.2參考解答】(1)建立浙江省一般預算收入與全省地區(qū)生產總值的計量經濟模型,估計模型的參數(shù),檢驗模型的顯著性,用規(guī)范的形式寫出估計檢驗結果,并解釋所估計參數(shù)的經濟意義圖形近似于線性關系,可建立線性回歸模型:y二B+Bx+ut12tt用EViews估計檢驗結果為DependentVariable:VHeihodl.LeaEtS口uavmDale:D3/I9n8Time-1S45sample:19782016included39vanstslecoenaent8tdErrort-siatjsllcProhC-227.0518dB.3d713-Jl.a989JDD.OODOX019176S0OO2S9073B00930.0000R-squ^ired0.991253-dep^ndenlvar1903.10BAdjustedR?Bquar&d0991070S.D.dependentvar2720.350SE.alregression226.4575AKBlKeinfocriterion13.73291Sumsquaredresid1B97471.senwaizcriterion13.B1822Loglikelihoadl-265.7918Hannan-Cluinncnler.137G3S2F-sta1l5tlcS-446562DurNn-W-atsDnalat0.276451ProbCF-slaGsUclQ.000DOO(1)回歸結果的規(guī)范形式：?：=-227.0518+0.191765Xl(46.34713)(0j0025^fl)t=(-4.39394)(73.S0033)R-=0,99325?^-=0,99307F=5446,562=39擬合優(yōu)度：由回歸結果可知二=二：匚「，扌：二說明整體上模型擬合較好。t檢驗：分別針對地區(qū)生產總值參數(shù)為0的原假設，給定顯著性水平上，查t分布表中自由度為--=的臨界值「：：：：「=o由回歸結果可知，參數(shù)的t值的絕對值均大于臨界值，這說明在顯著性水平：二二：下，應該拒原假設，解釋變量地區(qū)生產總值對財政收入有顯著影響。參數(shù)經濟意義:浙江全省生產總值每增長1億元,平均說來財政預算收入將增長0.1918億元.(2)如果2017年，浙江省地區(qū)生產總值為52000億元，比上年增長10%,利用計量經濟模型對浙江省2017年的一般預算收入做出點預測和區(qū)間預測

XYMean11108151903.106Median4686.11034D.5200wajilrrum47251.389225070Minimum123.72002&.970008td.D兇14137.942720360Skev/nes31..2519611.399702Kunosls3.2.339773.S47248」arquA-BAra10.2771113-41534Probability0.0056660.001222Sum433217.77+221.1JSumSqDev.7.60E+092.81E1-DBObservations1929將52000億元帶入回歸方程得到一般預算收入的點預測：Yf=-227.0518+0,191765x52000=9744.746一般預算收入的平均值預測：[Xf-打=(52000-11108.15)-=1672143396.4225當'二：_一一一時，?：：：：、—-■,代入計算可得:9711.746+2.021X226.45759711.746+2.021X226.4575X11672143396.4225\397595491202.8568=U「J二二廠二即：當?shù)貐^(qū)生產總值達到52000億元時，財政收入匚平均值置信度95%的預測區(qū)間為9517.845，9971.647)。一般預算收入的個別值預測區(qū)間為_11672143396.^22597^.746+2.021x226.4575x1+-+7￡95491202^63=9744.746+510.329即：當?shù)貐^(qū)生產總值達到52000億元時，財政收入匚個別值置信度95%的預測區(qū)間為9233.917，10255.575)。建立浙江省一般預算收入的對數(shù)與地區(qū)生產總值對數(shù)的計量經濟模型,估計模型的參數(shù),檢驗模型的顯著性,并解釋所估計參數(shù)的經濟意義。

D郎pndentvan比俺.log(y)Motnad:Squares□arte:03/19i!18Time:16：Q9Sample(adiusled):19782016Indudedobser/alions:39affteracjjustmentsVarinbls□□efficientStd.Errori-StatisiicProb.C-2.2570910236105-9.544I29SO.DODQLUGE1.0300160.02040336.19114O.DQDOR-squared0.972527Meandependentvar6.064647.AdjustedR-squaredl0.971735S.D.dlependentvar1.967081S.E.ofregressian0.330417Akaikeinfocriierion0.672999SumsquareresidlJ.039dig3-ScfftNarzcriterion0.758310LagHkeiinoodi-11.1.2347Hmnnan-Qulnnenter.0.703607F-staustc13Q9.739□urtinWatsonsta.t0.005302PnobfF-slatiatic)&.000000回歸結果的規(guī)范形式：log（r：）=-2.257051十1.03081610^）(0.2364S6)(0.C28483)(0.2364S6)(0.C28483)(-9.544293)(36.19114)ffE=0.972527^:=0,971785F=1309.799?i=39ffE=0.972527擬合優(yōu)度：由回歸結果可知m：二Cm說明整體上模型擬合較好。參數(shù)顯著性檢驗：分別針對地區(qū)生產總值參數(shù)為o的原假設，給定顯著性水平匸=-「上,查t分布表中自由度為--=的臨界值「：：：：「=-■由回歸結果可知，參數(shù)的t值的絕對值均大于臨界值，這說明在顯著性水平=■■■下，應該拒原假設，對數(shù)化的地區(qū)生產總值對對數(shù)化的財政收入有顯著影響。經濟意義：地區(qū)生產總值每增長1%，財政收入平均而言增長匚「：。2?3在線性消費函數(shù)?邛廣鎧中,C是消費支出,Y是可支配收入，收入的邊際消費傾向（MPC）是斜率0，而平均消費傾向（APC）為C/Y。由中國統(tǒng)計年鑒得到2016年2ii中國各地區(qū)居民人均消費支出和居民人均可支配收入數(shù)據(jù)：表2.92016年中國居民消費支出與可支配收入數(shù)據(jù)地區(qū)居民消費支出（元）35415.726129.314247.512682.9內蒙古18072.3居民可支配收入（元）52530.434074.519725.419048.924126.6地區(qū)居民消費支出（元）15888.715750.523448.412295.214275.4居民可支配收入(元)地區(qū)居民消費支出（元）35415.726129.314247.512682.9內蒙古18072.3居民可支配收入（元）52530.434074.519725.419048.924126.6地區(qū)居民消費支出（元）15888.715750.523448.412295.214275.4居民可支配收入(元)21786.621114.830295.818305.120653.4黑龍江19852.814772.614445.837458.322129.925526.614711.520167.513258.615926.412712.326039.719967.019838.554305.332070.138529.019998.127607.920109.624685.318443.116384.814838.511931.611768.89318.713943.012254.214774.714965.414066.522034.118808.315121.116719.913639.218873.714670.317301.818832.318354.71)在95%的置信度下，求02黑龍江19852.814772.614445.837458.322129.925526.614711.520167.513258.615926.412712.326039.719967.019838.554305.332070.138529.019998.127607.920109.624685.318443.116384.814838.511931.611768.89318.713943.012254.214774.714965.414066.522034.118808.315121.116719.913639.218873.714670.317301.818832.318354.71)在95%的置信度下，求02的置信區(qū)間。2)以可支配收入為x軸，畫出估計的MPC和APC圖。當居民人均可支配收入為60000元時，預計人均消費支出C的點預測值。在95%的置信度下，人均消費支出C平均值的預測區(qū)間。在95%的置信度下，人均消費支出C個別值的預測區(qū)間。練習題2.3參考解答】在95%的置信概率下，02的區(qū)間估計是多少？P血—遠*SE-tf3)魚民玉施十運*)]=0.95得到:-：_：一-：_<_-:0.66-taa35(29)*0.02</?=<0_66+ia0=5(29)*0.020.66一2-045*0.02</?=<0.66+taa35(29)*0.020.6191<0.7009

DependentVariable:COM3Method:LeastSquares□ale:D3/12M9Time:23:09Sample:131ncludedobe0wations:31variablecoevident5t(j.Errorr-siatisncRronC1490.50551B.32&02.0983790.0071INC0.6602710.02012832.BO3470.0000R~squared0.973757Meandlependen!var17206.92AdjustedR-squarsd0.972852S.D.dependentwar6S19.5Q1S.E.ofregression1074.189Akaikeinfocriterion16.B&896Sumsquaredresid33462662Schwarzcriterion16.95138LogHKeiinood■259.3123Hannan-aulnncrller16.B8902F-statlstlc1076.067□urbln-watsonstat1.538680^robfF-olatiEiic)0.000000當居民人均可支配收入為60000元時，預計人均消費支出C的點預測值。將點預測帶入到方程中去得到:二二w二在95%的置信概率下，人均消費支出c平均值的預測區(qū)間。平均值預測區(qū)間:匸「―-1二…八三：、；1一】=一“工_廠「：?。憾?*—(*—=(60000-23793.89)==1310885297-82259當二二；二時，「：；：：二U,代入計算可得:_11310SS5297.S225944。沁丸5+2.045XW74.189XH+2848107674.980921（5）在95%的置信概率下，人均消費支出C個別值的預測區(qū)間。41096.505+2.045X1074.1B9X1L310S35297.8225941096.505+2.045X1074.1B9X31+2S4S107674.93092141096,S05+2683.702.4假設某地區(qū)住宅建筑面積與建造單位成本的有關資料如表2.10：表2.10某地區(qū)住宅建筑面積與建造單位成本數(shù)據(jù)建筑地編號建筑面積（萬平方米）X建造單位成本（兀/平方米）Y10.6186020.95175031.45171042.1169052.56167863.54164073.89162084.37157694.821566105.661498116.111425126.231419根據(jù)上表資料：1）建立建筑面積與建造單位成本的回歸方程；2）解釋回歸系數(shù)的經濟意義；3）估計當建筑面積為4.5萬平方米時，對建造平均單位成本作區(qū)間預測?！揪毩曨}2.4參考解答】（1）建立建筑面積與建造單位成本的回歸方程

DependantVariable.YMethod.LeastSquaresDate.1O/DS/13Tme.00131Sample:112Includedobservations.12VariableCoefficientSid.Errort-StatisticProb.C184547519.2644605.796830.0000X￡4」創(chuàng)004.0Q9328-13.3443^0.0000R-squared0.940029M&a仃dependentvar101&.333AdjustedR-squared0.041512S.D.dependentvar131.22S2S.E.ofregression31.73600Akaikeinfocritenon&.903792Sumsquaredresid1007174Schwarzcriterion&984610Luglikelihood-57.42276Hannan-Quinncrite匚&.873871b-statistic178.0716Durbin-Wal5D仃stat1172407Prab(F-statistic)0.000000解釋回歸系數(shù)的經濟意義：模型的t檢驗和F檢驗均顯著,說明建筑面積每擴大1萬平方米,建造單位成本將下降64.184元/平方米.估計當建筑面積為4.5萬平方米時，預測建造的平均單位成本：￥=1845.475-64.184x4.5=1556.647(元/平方米)i平均單位成本的區(qū)間預測：t,丄+(X^22\'n工x2已經得到Y=1556.647、t00251O)=2.228、￡二31.736、n=12。X=4.5X的樣本數(shù)據(jù)得：XMean3.523333Median3.715000Maximum6.230000Minimum0.600000Std.Dev.1.989419Skewness-0.060130Kurtosis1.664917J3「qu巳-B已「日0.898454Probability0.638121Sum42.28000SumSq.Dev.43.53567Observations12工x2=2(X-X)2=q2(n-1)=1.98942x(12-1)=43.5348iiX(X-X)2=(4.5-3.5233》=0.9539f當X廣4.5時’將相關數(shù)據(jù)代入計算得到

1556.6472.228x31.736x1+0.9539=1556.64722.93761243.5348即是說，當建筑面積為4.5萬平方米時，預測建造的平均單位成本=Yf平均值置信度95%的預測區(qū)間為(1533.7094，1579.5846)元/平方米。2.5由12對觀測值估計得消費函數(shù)為：C=50+0.6X其中，C是消費支出,Y是可支ii配收入(元)，已知X二800，工(X-X)2=8000，工e2=300，t(10)=2.23。當ii0.025X=1000時，試計算：f消費支出C的點預測值；在95%的置信概率下消費支出C平均值的預測區(qū)間。在95%的置信概率下消費支出C個別值的預測區(qū)間。練習題2.5參考解答】當X=1000時，消費支出C的點預測值;C=50+0.6X=50+0.6*1000=650ii在95%的置信概率下消費支出C平均值的預測區(qū)間。入-'1(X-X)2i0.025已經得到：X=800，X=1000，工(X-X)2=8000，t(10)=2.23工e2=3000.025i￡2=^-eL=2^=30n-212-2&=齊^.30=5.47721(1000-800)2匕+8000—當X1(1000-800)2匕+8000—入'1(X-X)2+孑=6502.23x5.4772xn乙x2i=6302.23x5.4772x利5.0833=65027.5380（3）在95%的置信概率下消費支出C個別值的預測區(qū)間。Cf=6502.23Cf=6502.23x5.4772x1|1|(1000-800)2\+\2*8000=6502.23x5.4772x、+5.0833^65030.12502.6按照“弗里德曼的持久收入假說I持久消費Y正比于持久收入X，依此假說建立

的計量模型沒有截距項，設定的模型應該為：Y=卩X+u,這是一個過原點的回歸。在i2ii古典假定滿足時，（1）證明過原點的回歸中卩2的OLS估計量卩的計算公式是什么？對該模型是否仍有22工e=0和工eX=0?對比有截距項模型和無截距項模型參數(shù)的OLS估計有什么不iii同？（2）無截距項模型的二具有無偏性嗎？（3）寫出無截距項模型二的方差）的表達式?！揪毩曨}2.6參考解答】⑴沒有截距項的過原點回歸模型為：=P2Xi+U因為工e2二工(Y-PX)2ii2i求偏導二=2工)(-X.)=-2工eX求偏導i2iiii2-望=2工(Y-PX)(-X)=0'Ki2ii八而有截距項的回歸為卩八而有截距項的回歸為卩2i對于過原點的回歸，由OLS原則:工e=0已不再成立，但是工eX=0是成立的。對于過原點的回歸，由OLS原則:iii（2）無截距項模型的二具有無偏性嗎?在古典假設滿足時，無截距項的二具有無偏性。（3）無截距項模型殳的方差二「二）的表達式？

在多元回歸中n?二J二■■:二當為無截距項僅有一個變量時--=三，因此無截距且僅有一個解釋變量的情形性下：Var(B)—b22YX2iYe2還可以證明對于過原點的回歸，b2—i—n一1G2Ye2而有截距項的回歸為Var（［3)v，b2—L-2YX2in-22.7練習題2.2中如果將浙江省“一般預算總收入”和“地區(qū)生產總值”數(shù)據(jù)的計量單位分別或同時由”億元”更改為”萬元”，分別重新估計參數(shù)，對比被解釋變量與解釋變量的計量單位分別變動和同時變動的幾種情況下，參數(shù)估計及統(tǒng)計檢驗結果與計量單位與更改之前有什么區(qū)別?你能從中總結出什么規(guī)律性嗎？【練習題2.7參考解答】以億元為單位的一般預算總收入用Y1表示，以億元為單位的地區(qū)生產總值用XI表示以萬元為單位的一般預算總收入用Y2表示，以萬元為單位的地區(qū)生產總值用X2表示表2.10浙江省財政預算收入與全省生產總值數(shù)據(jù)財政預算總收入（億元）全省生產總值（億元）財政預算總收入（萬元）全省生產總值（元）Y1X1Y2X2197827.45123.722745001237200197925.87157.752587001577500198031.13179.923113001799200198134.34204.863434002048600198236.64234.013664002340100198341.79257.094179002570900198446.67323.254667003232500198558.25429.165825004291600198668.61502.476861005024700198776.36606.997636006069900198885.55770.258555007702500198998.21849.4498210084944001990101.59904.69101590090469001991108.941089.331089400108933001992118.361375.7118360013757000

1993166.641925.911666400192591001994209.392689.282093900268928001995248.53557.552485000355755001996291.754188.532917500418853001997340.524686.113405200468611001998401.85052.624018000505262001999477.45443.924774000544392002000658.426141.036584200614103002001917.766898.3491776006898340020021166.588003.67116658008003670020031468.899705.02146889009705020020041805.1611648.71805160011648700020052115.3613417.682115360013417680020062567.6615718.472567660015718470020073239.8918753.733239890018753730020083730.0621462.693730060021462690020094122.0422998.244122040022998240020104895.4127747.654895410027747650020115925.0032363.385925000032363380020126408.4934739.136408490034739130020136908.4137756.586908410037756580020147421.7040173.037421700040173030020158549.4742886.498549470042886490020169225.0747251.36922507004725136001)練習題2.2中，財政預算總收入用億元(Y1)表示,全省生產總值用億元(XI)表示的回歸:DependentVaria&le'Y1Method:Le^stSquaresDateO3/18Time:20:56Sample:19782016Includedobservations:39VanableCcefficientStd.Errort-SlatistieProb.C-22705164634713-489S94000000X101917650.00259373.800B3oooooR-squared0.993253Meandependentvar1S03106AdjustedR-squared0993070SDdependentvar2720.360S.Eofregression226.4575Akaikeinfocriterion1373291Sumsquaredresid1397471Schwarzcriterion13.8W22Loglikelihood-2657918Hannan-Quinncrrter.1176352F-statistic5446562Durbin-Watsonstal0276451Prob(F-statistic)0000000財政預算總收入用萬元(Y2)表示,全省生產總值用萬元(X2)表示的回歸:回歸結果為:

DependeniVariable:Y2Method:LeastSquaresDate03/16/18Time:20:57Sample19702016Includedobssivations:39VariableCoefficientStd.Errort-StatisticProbC-2270518463471.3-43989400.0000X20.1917650Q025S373.B00S30.0000R-squared0.993253Meandependentvar19011059AdjustedR-squared0.993070S.D.dependentvar27203599SEofregression2264575AKaiKeintocriterion3215359Sumsquaredres>d1J0EM4Sttiwarzcriterion3223090Loglikelihood-6249