店鋪?zhàn)饨鸬拇_定模型
店鋪?zhàn)饨鸬拇_定模型
某商人欲在某火車站附近經(jīng)營一店鋪，委托本小組對(duì)相關(guān)情況進(jìn)行調(diào)查。經(jīng)過數(shù)月的資料收集和整理，我們的調(diào)查成果如下：
進(jìn)出車站的乘客為主要服務(wù)對(duì)象的10家便利店的數(shù)據(jù)。
Y是日均銷售額，X1為店鋪面積，X2是店鋪距車站的距離，X3為店員人數(shù)，X4為店鋪日租金。
具體數(shù)據(jù)如下表：
店鋪代碼 日均銷售額（元）Y 店鋪面積（m2）X1 離車站距離（100m）X2 店員人數(shù)（人）X3 店鋪日租金（元）X4
A
B
C
D
E
F
G
H
I
J 4000
4500
8000
6000
5000
2000
1500
9000
3000
7000 60
100
85
50
75
55
70
95
45
65 3
5
2
1
3
4
6
1
3
2 5
7
5
3
5
4
5
6
4
4 600
600
1020
750
750
440
280
1425
450
780
數(shù)據(jù)來源：
為了考察店鋪面積、離車站距離、店員人數(shù)和日租金對(duì)日銷售額的影響，我們首先做Y關(guān)于X1、X2、X3、X4的回歸，即建立如下回歸模型：
Y=C+β1 X1+β2 X2+β3 X3+β4 X4
得回歸結(jié)果如下表：
Dependent Variable: Y
Method: Least Squares
Date: 12/14/03 Time: 17:51
Sample: 1 10
Included observations: 10
Variable Coefficient Std. Error t-Statistic Prob.
C 4815.267 1536.418 3.134087 0.0258
X1 128.1930 39.79796 3.221096 0.0234
X2 -1494.966 513.4078 -2.911848 0.0333
X3 -619.1674 472.6664 -1.309946 0.2472
X4 -1.877208 2.938471 -0.638838 0.5510
R-squared 0.970270 Mean dependent var 5000.000
Adjusted R-squared 0.946486 S.D. dependent var 2505.549
S.E. of regression 579.6124 Akaike info criterion 15.86945
Sum squared resid 1679752. Schwarz criterion 16.02074
Log likelihood -74.34724 F-statistic 40.79489
Durbin-Watson stat 1.407218 Prob(F-statistic) 0.000522
從回歸結(jié)果來看， R2接近于1，整個(gè)方程的擬合優(yōu)度很高，F(xiàn)>F0.05(4，5)＝5.19，變量X3、X4對(duì)應(yīng)的偏回歸系數(shù)之t值小于2，而且X3、X4的符號(hào)與經(jīng)濟(jì)意義相悖，該模型明顯存在多重共線性，回歸結(jié)果不顯著，回歸方程不能投入使用。
由于變量較多，采用逐步回歸法來修正模型。
用Y對(duì)各個(gè)變量單獨(dú)進(jìn)行回歸：
對(duì)X1，有：
Dependent Variable: Y
Method: Least Squares
Date: 12/14/03 Time: 20:17
Sample: 1 10
Included observations: 10
Variable Coefficient Std. Error t-Statistic Prob.
C 444.4444 2988.555 0.148716 0.8855
X1 65.07937 41.38415 1.572567 0.1545
R-squared 0.236129 Mean dependent var 5000.000
Adjusted R-squared 0.140645 S.D. dependent var 2505.549
S.E. of regression 2322.680 Akaike info criterion 18.51569
Sum squared resid 43158730 Schwarz criterion 18.57620
Log likelihood -90.57844 F-statistic 2.472968
Durbin-Watson stat 1.988381 Prob(F-statistic) 0.154464
對(duì)X2，有：
Dependent Variable: Y
Method: Least Squares
Date: 12/14/03 Time: 20:20
Sample: 1 10
Included observations: 10
Variable Coefficient Std. Error t-Statistic Prob.
C 8687.500 1096.232 7.924871 0.0000
X2 -1229.167 324.6760 -3.785826 0.0053
R-squared 0.641777 Mean dependent var 5000.000
Adjusted R-squared 0.596999 S.D. dependent var 2505.549
S.E. of regression 1590.581 Akaike info criterion 17.75844
Sum squared resid 20239583 Schwarz criterion 17.81896
Log likelihood -86.79221 F-statistic 14.33248
Durbin-Watson stat 2.488527 Prob(F-statistic) 0.005344
對(duì)X3，有：
Dependent Variable: Y
Method: Least Squares
Date: 12/14/03 Time: 20:28
Sample: 1 10
Included observations: 10
Variable Coefficient Std. Error t-Statistic Prob.
C 3344.828 3791.325 0.882232 0.4034
X3 344.8276 770.6964 0.447423 0.6664
R-squared 0.024413 Mean dependent var 5000.000
Adjusted R-squared -0.097536 S.D. dependent var 2505.549
S.E. of regression 2624.897 Akaike info criterion 18.76033
Sum squared resid 55120690 Schwarz criterion 18.82084
Log likelihood -91.80164 F-statistic 0.200188
Durbin-Watson stat 2.273575 Prob(F-statistic) 0.666436
對(duì)X4，有：
Dependent Variable: Y
Method: Least Squares
Date: 12/14/03 Time: 20:30
Sample: 1 10
Included observations: 10
Variable Coefficient Std. Error t-Statistic Prob.
C -124.4556 691.7552 -0.179913 0.8617
X4 7.222630 0.893132 8.086854 0.0000
R-squared 0.891004 Mean dependent var 5000.000
Adjusted R-squared 0.877380 S.D. dependent var 2505.549
S.E. of regression 877.3734 Akaike info criterion 16.56860
Sum squared resid 6158272. Schwarz criterion 16.62912
Log likelihood -80.84299 F-statistic 65.39721
Durbin-Watson stat 1.099477 Prob(F-statistic) 0.000040
從上面的回歸結(jié)果可以看到，Y對(duì)X2的`回歸擬合最好，故選擇該回歸式為基本回歸表達(dá)式�，F(xiàn)在分別加入X1、X3、X4回歸結(jié)果如下：
加入X1，有：
Dependent Variable: Y
Method: Least Squares
Date: 12/14/03 Time: 21:21
Sample: 1 10
Included observations: 10
Variable Coefficient Std. Error t-Statistic Prob.
C 3641.214 817.1938 4.455753 0.0030
X1 75.45849 10.58869 7.126326 0.0002
X2 -1307.769 121.3087 -10.78050 0.0000
R-squared 0.956605 Mean dependent var 5000.000
Adjusted R-squared 0.944206 S.D. dependent var 2505.549
S.E. of regression 591.8273 Akaike info criterion 15.84763
Sum squared resid 2451817. Schwarz criterion 15.93841
Log likelihood -76.23816 F-statistic 77.15446
Durbin-Watson stat 1.809788 Prob(F-statistic) 0.000017
可見，加入X1效果較好，這樣回歸式中就有X1、X2兩個(gè)變量了。在此基礎(chǔ)上繼續(xù)加入其他變量。
加入X3，有：
Dependent Variable: Y
Method: Least Squares
Date: 12/14/03 Time: 21:26
Sample: 1 10
Included observations: 10
Variable Coefficient Std. Error t-Statistic Prob.
C 3993.580 797.8410 5.005484 0.0024
X1 109.3747 25.40691 4.304920 0.0051
X2 -1181.338 142.6370 -8.282130 0.0002
X3 -647.0407 446.8316 -1.448064 0.1978
R-squared 0.967843 Mean dependent var 5000.000
Adjusted R-squared 0.951765 S.D. dependent var 2505.549
S.E. of regression 550.2815 Akaike info criterion 15.74791
Sum squared resid 1816859. Schwarz criterion 15.86895
Log likelihood -74.73956 F-statistic 60.19526
Durbin-Watson stat 1.281362 Prob(F-statistic) 0.000072
可以看出，加入了X3以后引起了多重共線性，故剔除。
現(xiàn)在加入X4，回歸結(jié)果如下：
Dependent Variable: Y
Method: Least Squares
Date: 12/14/03 Time: 21:29
Sample: 1 10
Included observations: 10
Variable Coefficient Std. Error t-Statistic Prob.
C 4636.482 1619.077 2.863658 0.0287
X1 99.57632 35.19507 2.829269 0.0300
X2 -1674.283 523.5131 -3.198167 0.0186
X4 -2.232526 3.095576 -0.721199 0.4979
R-squared 0.960067 Mean dependent var 5000.000
Adjusted R-squared 0.940100 S.D. dependent var 2505.549
S.E. of regression 613.2195 Akaike info criterion 15.96450
Sum squared resid 2256229. Schwarz criterion 16.08553
Log likelihood -75.82249 F-statistic 48.08356
Durbin-Watson stat 1.907328 Prob(F-statistic) 0.000137
同樣，X4引起多重共線性，故剔除。
故Y對(duì)X1、X2的回歸擬合最好，回歸表達(dá)式應(yīng)為：
Y=3641.214+75.45849X1－1307.769X2
其經(jīng)濟(jì)意義為，在其他條件不變時(shí)，店鋪面積擴(kuò)大1平方米，日均銷售額大約會(huì)增加75.5元；店鋪如果比現(xiàn)在地址再遠(yuǎn)離車站100米，日均銷售額大約會(huì)減少1307.8元。
由于客戶的資金有限，每天能負(fù)擔(dān)的租金為700～800元，因此我們建議在離火車站100米處租賃面積為60平方米左右的店鋪，租金大約為750元。這樣客戶能夠獲得既定條件下的最大收益。
以上就是我們的分析報(bào)告。
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