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1、店铺租金的确定模型某商人欲在某火车站附近经营一店铺，委托本小组对相关情况进行调查。经过数月的资料收集和整理，我们的调查成果如下：进出车站的乘客为主要服务对象的10家便利店的数据。Y是日均销售额，X1为店铺面积，X2是店铺距车站的距离，X3为店员人数，X4为店铺日租金。具体数据如下表：店铺代码日均销售额（元）Y店铺面积（m2）X1离车站距离（100m）X2店员人数（人）X3店铺日租金（元）X4ABCDEFGHIJ400045008000600050002000150090003000700060100855075557095456535213461325753545644600600102075
2、07504402801425450780数据来源：为了考察店铺面积、离车站距离、店员人数和日租金对日销售额的影响，我们首先做Y关于X1、X2、X3、X4的回归，即建立如下回归模型：Y=C+1 X1+2 X2+3 X3+4 X4得回归结果如下表：Dependent Variable: YMethod: Least SquaresDate: 12/14/03 Time: 17:51Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C4815.2671536.4183.1340870.
3、0258X1128.193039.797963.2210960.0234X2-1494.966513.4078-2.9118480.0333X3-619.1674472.6664-1.3099460.2472X4-1.8772082.938471-0.6388380.5510R-squared0.970270 Mean dependent var5000.000Adjusted R-squared0.946486 S.D. dependent var2505.549S.E. of regression579.6124 Akaike info criterion15.86945Sum squar
4、ed resid1679752. Schwarz criterion16.02074Log likelihood-74.34724 F-statistic40.79489Durbin-Watson stat1.407218 Prob(F-statistic)0.000522从回归结果来看， R2接近于1，整个方程的拟合优度很高，FF0.05(4，5)5.19，变量X3、X4对应的偏回归系数之t值小于2，而且X3、X4的符号与经济意义相悖，该模型明显存在多重共线性，回归结果不显著，回归方程不能投入使用。由于变量较多，采用逐步回归法来修正模型。用Y对各个变量单独进行回归：对X1，有：Depende
5、nt Variable: YMethod: Least SquaresDate: 12/14/03 Time: 20:17Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C444.44442988.5550.1487160.8855X165.0793741.384151.5725670.1545R-squared0.236129 Mean dependent var5000.000Adjusted R-squared0.140645 S.D. dependent var2505
6、.549S.E. of regression2322.680 Akaike info criterion18.51569Sum squared resid43158730 Schwarz criterion18.57620Log likelihood-90.57844 F-statistic2.472968Durbin-Watson stat1.988381 Prob(F-statistic)0.154464对X2，有：Dependent Variable: YMethod: Least SquaresDate: 12/14/03 Time: 20:20Sample: 1 10Included
7、 observations: 10VariableCoefficientStd. Errort-StatisticProb. C8687.5001096.2327.9248710.0000X2-1229.167324.6760-3.7858260.0053R-squared0.641777 Mean dependent var5000.000Adjusted R-squared0.596999 S.D. dependent var2505.549S.E. of regression1590.581 Akaike info criterion17.75844Sum squared resid20
8、239583 Schwarz criterion17.81896Log likelihood-86.79221 F-statistic14.33248Durbin-Watson stat2.488527 Prob(F-statistic)0.005344对X3，有：Dependent Variable: YMethod: Least SquaresDate: 12/14/03 Time: 20:28Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C3344.8283791.32
9、50.8822320.4034X3344.8276770.69640.4474230.6664R-squared0.024413 Mean dependent var5000.000Adjusted R-squared-0.097536 S.D. dependent var2505.549S.E. of regression2624.897 Akaike info criterion18.76033Sum squared resid55120690 Schwarz criterion18.82084Log likelihood-91.80164 F-statistic0.200188Durbi
10、n-Watson stat2.273575 Prob(F-statistic)0.666436对X4，有：Dependent Variable: YMethod: Least SquaresDate: 12/14/03 Time: 20:30Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C-124.4556691.7552-0.1799130.8617X47.2226300.8931328.0868540.0000R-squared0.891004 Mean dependen
11、t var5000.000Adjusted R-squared0.877380 S.D. dependent var2505.549S.E. of regression877.3734 Akaike info criterion16.56860Sum squared resid6158272. Schwarz criterion16.62912Log likelihood-80.84299 F-statistic65.39721Durbin-Watson stat1.099477 Prob(F-statistic)0.000040从上面的回归结果可以看到，Y对X2的回归拟合最好，故选择该回归式
12、为基本回归表达式。现在分别加入X1、X3、X4回归结果如下：加入X1，有：Dependent Variable: YMethod: Least SquaresDate: 12/14/03 Time: 21:21Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C3641.214817.19384.4557530.0030X175.4584910.588697.1263260.0002X2-1307.769121.3087-10.780500.0000R-squared0.9566
13、05 Mean dependent var5000.000Adjusted R-squared0.944206 S.D. dependent var2505.549S.E. of regression591.8273 Akaike info criterion15.84763Sum squared resid2451817. Schwarz criterion15.93841Log likelihood-76.23816 F-statistic77.15446Durbin-Watson stat1.809788 Prob(F-statistic)0.000017可见，加入X1效果较好，这样回归
14、式中就有X1、X2两个变量了。在此基础上继续加入其他变量。加入X3，有：Dependent Variable: YMethod: Least SquaresDate: 12/14/03 Time: 21:26Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C3993.580797.84105.0054840.0024X1109.374725.406914.3049200.0051X2-1181.338142.6370-8.2821300.0002X3-647.0407446.8
15、316-1.4480640.1978R-squared0.967843 Mean dependent var5000.000Adjusted R-squared0.951765 S.D. dependent var2505.549S.E. of regression550.2815 Akaike info criterion15.74791Sum squared resid1816859. Schwarz criterion15.86895Log likelihood-74.73956 F-statistic60.19526Durbin-Watson stat1.281362 Prob(F-s
16、tatistic)0.000072可以看出，加入了X3以后引起了多重共线性，故剔除。现在加入X4，回归结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/14/03 Time: 21:29Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C4636.4821619.0772.8636580.0287X199.5763235.195072.8292690.0300X2-1674.283523.5131-3.1981670.
17、0186X4-2.2325263.095576-0.7211990.4979R-squared0.960067 Mean dependent var5000.000Adjusted R-squared0.940100 S.D. dependent var2505.549S.E. of regression613.2195 Akaike info criterion15.96450Sum squared resid2256229. Schwarz criterion16.08553Log likelihood-75.82249 F-statistic48.08356Durbin-Watson stat1.907328 Prob(F-statistic)0.000137同样，X4引起多重共线性，故剔除。故Y对X1、X2的回归拟合最好，回归表达式应为：Y=3641.214+75.45849X11307.769X2其经济意义为，在其他条件不变时，店铺面积扩大1平方米，日均销售额大约会增加75.5元；店铺如果比现在地址再远离车站100米，日均销售额大约会减少1307.8元。由于客户的资金有限，每天能负担的租金为700800元，因此我们建议在离火车站100米处租赁面积为60平方米左右的店铺，租金大约为750元。这样客户能够获得既定条件下的最大收益。以上就是我们的分析报告。
