多元線性回歸進行及spss服裝銷售量預測

1、決策支持系統(tǒng)課程實驗報告實驗名稱：根據(jù)已知數(shù)據(jù)運用多元線性回歸的方法的預測服裝銷售量實驗目的：通過掌握軟件的應用并熟練運用加深對預測方法的了解，根據(jù)已知數(shù)據(jù)預測未來服裝銷售量，分析結果誤差，完善預測過程。實驗步驟：1、熟悉軟件使用方法2、加深預測方法了解并建立相關建模（多元線性回歸）3、分析數(shù)據(jù)4、數(shù)據(jù)運行并得到預測結果（多元線性回歸的預測方法）5、預測結果與已知數(shù)據(jù)比對，進行誤差分析，檢驗并評價6、綜合整理得到最終預測結果7、過程整合梳理并完善實驗報告8、運用時間序列建模方法在spss上再次進行數(shù)據(jù)預測，數(shù)據(jù)分析實驗內容：1、實驗數(shù)據(jù)實驗中已知數(shù)據(jù)年月居民月可服裝商品零居民消費市場占有季節(jié)性

2、指周期指數(shù)銷售量支配收入售價格指數(shù)價格指數(shù)率（）數(shù)2002.01143798.3101.013.421.2271.0151257582002.02121998.2102.912.191.3991.0041126062002.03105897.9101.112.080.8820.959789952002.04102598.199.613.760.8771.000810862002.05107498.3100.412.971.1341.0151060732002.06103598.1100.911.800.9021.027865072002.07104697.9100.213.270.8961.0

3、34879882002.08104097.8100.712.130.9491.039923912002.09110697.6101.713.460.9311.030926042002.10108597.599.813.521.0821.0311059712002.11109197.698.512.830.8451.041842982002.12109897.899.212.910.8761.001915322003.01117296.598.914.351.2270.9961084052003.02163596.698.614.601.3990.9671406972003.03111997.0

4、99.610.580.8820.989862742003.04118897.4100.311.370.8770.925850952003.05116097.4100.211.421.1340.914942632003.06113997.4100.110.960.9020.921871972003.07117997.799.512.010.8960.971906972003.08125997.8100.112.390.9490.992953382003.09124697.9100.212.680.9310.982975472003.10127498.2100.913.231.0821.00610

5、84862003.11124598.2101.313.120.8451.016931272003.12124998.1101.412.480.8761.072963142004.01186098.5101.913.281.2271.0051475412004.02148398.7100.112.991.3990.9761270842004.03126998.7101.612.170.8820.943904232004.04133098.4102.313.850.8771.004980432004.05133898.3102.414.201.1341.0071276082004.06123498

6、.2102.912.690.9020.991952512004.07132597.9103.611.890.8960.984974292004.08137597.9103.212.870.9490.9781067382004.09136398.0102.412.330.9310.985981762004.10139097.7102.013.631.0820.9761224992004.11135097.8101.912.180.8450.986940522004.12136897.8101.611.880.8760.980972352005.01166297.899.913.571.2270.

7、9941388942005.02222197.3102.913.281.3991.0081654372005.03141896.8101.612.490.8821.0241039592005.04144897.0101.213.200.8771.0231058742005.05149197.3100.514.951.1341.0471362832005.06141897.5100.013.440.9021.0411157752005.07145297.8100.213.540.8961.0301083612005.08151598.0101.313.580.9491.0041120912005

8、.09151298.6101.414.620.9311.0311131052005.10153599.0101.115.071.0821.0231434722005.11147999.2100.813.890.8451.001991342005.12149599.3100.513.380.8760.986101156實驗中應預測數(shù)據(jù)2006.01205098.4102.115.131.2271.0021586912006.02226198.8100.815.261.3991.0331652722006.03155799.7100.614.190.8821.0041139382006.04158

9、999.9100.814.550.8771.0061055032006.051671100.0101.514.681.1341.0061455872006.061574100.0101.814.030.9021.0191085322006.071626100.0101.813.870.8961.0131039372006.081648100.0101.215.660.9490.9961218322006.09166299.9101.015.190.9311.0201182732006.101692100.2100.915.381.0820.9981498612006.111649100.310

10、0.914.770.8450.9721028682006.121686100.3101.313.980.8760.9231041622、多元線性回歸建模變量：應變量一個，自變量M個，共M+1個樣本含量：N數(shù)據(jù)格式見表回歸模型的一般形式：Y=mO+m1X1+m2X2+.+mnXn+b上式表示數(shù)據(jù)中應變量可以近似的表示為自變量XI,X2,Xn的線性函數(shù)。m0為常數(shù)項，ml,m2,.,mn為偏回歸系數(shù)，表示在其他自變量保持不變時，Xj增加或減少一個單位時Y的平均變化量，b是去除n個自變量對Y影響后的隨機誤差（殘差）。某服裝幾年的月度銷售數(shù)據(jù)及相關資料（1）Y與Xl，X2，.Xn之間具有線性關系（2）

11、各例觀測值Yi（i=1,2,.n湘互獨立（3）殘差b服從均值0方差為r2的正態(tài)分布，它等價于與對任意的一組自變量X1,X2,.Xn值，應變量Y具有相同方差，并且服從正態(tài)分布。實施步驟為：（1）求偏回歸系數(shù)m0,m1,m2,.m（2）建立回歸方程Y=m0+m1X1+m2X2+.+mXn3、數(shù)據(jù)分析運行（excel軟件）數(shù)據(jù)分析分析工具迢宀-1H星君位sm平排HI平憂百囹平曹HSUMMARYOUTPUT回歸統(tǒng)計Multiple0.968766RSquare0.938508Adjusted0.929509標準誤差5141.691觀測值48方笨分析dfSSMSFnificance,F回歸分析61.65

12、E+102.76E+09104.29253.18E-23殘差411.08E+0926436988總471.76E+10Coefficien-標淮誤爭tStatP-valueLower95%Upper95%F限95.上限95.OWIntercept-66605.7131979.9-0.504670.616496-333144199933.1-333144199933.1XVariabl45.410284.27524910.621672.43E-1336.7762454.0443236.7762454.04432XVariabl-881.4431381.78-0.63790.527083-3672

13、1909.117-36721909.117XVariabl415.4671721.54920.5757990.567898-1041.731872.665-1041.731872.665XVariabl3500.0611047.933.3399740.0017931383.7225616.3991383.7225616.399XVariabl52737.295387.6849.7884892.74E-1241856.6463617.9441856.6463617.94XVariabl58506.5627317.312.1417390.0382053338.1291136753338.12911

14、3675多元線性回歸系數(shù)57958.3602727354.101130.945853157119.366699952545.647363518.69848419.823525518.3676161039.73813721.693495140.4445541189249959451083390977-908.01371394.223245.47285623-64041.2924.120710412133187.029/A/A/ANNN#/A/A/ANNN#y=inl+m辟x戈+id3*x3+id4*x4+id5*x5+id6*x6+b2005.12149599.3100.513.380.8760

15、.986101156預測值（多元線性回歸）誤差%2006.01205098.4102.115.131.2271.002158691158458.71790.1463732006.02226198.8100.815.261.3991.033165272178487.127779959872006.03155799.7100.614.190.8821.004113938112934.96290.8803372006.04158999.9100.814.550.8771.006105503115408.24529.3885912006.051671100.0101.514.681.1341.0061

16、45587133343.062384100492006.061574100.0101.814.030.9021.019108532115313.39966.2482952006.071626100.0101.813.870.8961.013103937116447.261412.0363882006.081648100.0101.215.660.9490.996121832125262.5812.8158292006.09166299.9101.015.190.9311.020118273124713.23355.4452272006.101692100.2100.915.381.0820.9

17、98149861133110.7603111771842006.111649100.3100.914.770.8450.972102868114915.028511.7111492006.121686100.3101.313.980.8760.923104162112764.38248.258657x1x2x3x4x5x6y平均誤差7.04283883觀測值預測Y殘差標準殘差百分比排位Y1125028.8729.17270.1518381.041667789952120129.1-7523.08-1.566563.12581086382051.64-3056.64-0.63655.208333

18、84298487768.8-6682.8-1.391587.2916678509551018164256.980.8864479.375862746848011706.0030.35524711.4583386507790424.18-2436.18-0.507313.5416787197889545.142845.860.59260415.62587988996313.22-3709.22-0.7723917.708339042310102890.23080.7940.64152519.79167906971188205.7-3907.7-0.8137221.875915321288212.

19、713319.2890.69118823.958339239113115852.7-7447.65-1.5508526.041679260414144914-4216.97-0.8781128.125931271581496.874777.1280.99475930.20833940521683325.371769.6270.36849632.29167942631795097.25-834.253-0.1737234.375952511880666.566530.4431.35985836.45833953381988253.222443.7770.50887738.541679631420

20、97400.92-2062.92-0.4295740.625972352196244.671302.3320.27118942.708339742922108835.1-349.071-0.0726944.79167975472395385.68-2258.68-0.4703346.875980432498368.2-2054.2-0.4277548.958339817625143359.94181.0660.87063951.041679913426131675.2-4591.23-0.9560553.1251011562790514.69-91.6896-0.0190955.2083310

21、395928103025.3-4982.29-1.0374857.2916710587429118472.39135.711.90236359.3751059713095589.25-338.251-0.0704461.458331060733196750.83678.17170.14121863.5416710673832104729.32008.7480.41828965.62510836133101334.1-3158.05-0.6576167.7083310840534114645.27853.7731.6354269.791671084863595710.36-1658.36-0.3

22、453371.8751120913696636.91598.09210.12454373.9583311260637134526.24367.780.90951976.0416711310538170472.6-5035.58-1.0485878.12511577539104814.6-855.615-0.1781780.2083312249940107997.3-2123.3-0.4421482.2916712575841130477.45805.5731.20891684.37512708442108907.36867.7281.43009286.4583312760843109659.9

23、-1298.89-0.2704788.5416713628344114215.4-2124.37-0.4423790.62513889445117862.3-4757.29-0.9906392.7083314069746127499.815972.183.32594794.7916714347247106740-7605.96-1.5838296.87514754148106226-5069.97-1.0557498.958331654374、預測數(shù)據(jù)誤差分析多元回歸分析預測法，是指通過對兩個或兩個以上的自變量與一個因變量的相關分析，建立預測模型進行預測的方法。當自變量與因變量之間存在線性關系

24、時，稱為多元線性回歸分析。回歸處理后得到的是一種平均化的數(shù)學模型。盡管平均值并不能完全消除隨機誤差,但可以作為依據(jù)。多元線性回歸最難的是選擇自變量，如果自變量選的太少，則自變量對Y的決定系數(shù)太小，導致過大的偏差，因此，包含所有作用顯著的自變量，引入的自變量個數(shù)盡可能小，殘差平方和盡可能小。多元線性回歸的預測方法是根據(jù)已知的數(shù)據(jù)作為存在的散點，用最小二乘法擬合出一條曲線即函數(shù)關系，根據(jù)曲線的延伸來預測未來的發(fā)展趨勢。顯而易見的是，由于所給的已知點數(shù)量多，事實上并不存在一條這樣的平滑曲線即函數(shù)關系能夠滿足所有的點都在這條曲線上。但是正是由于已知點的數(shù)量即已知數(shù)據(jù)的充足，雖然不存在完全符合的曲線，但

25、是預測的準確率卻能夠有所增高。同時在用多元線性回歸預測時，自變量的數(shù)量充足也更好地提升了預測的準確度。在本實驗中自變量為六個，分別是居民月可支配收入，服裝商品零售價格指數(shù),居民消費價格指數(shù)，市場占有率，季節(jié)性指數(shù)，周期指數(shù)，它們都作為X來影響銷售量Y，因素越多就能更好地約束函數(shù)變化，即更好的進行擬合預測。而我們用線性回歸的方法求得的是函數(shù)的系數(shù)，最終得到相應的因變量即Y值也就是銷售量。但是我們的系數(shù)是根據(jù)已知數(shù)據(jù)的變化趨勢求得的，當然不是真的存在這樣準確的函數(shù)關系的，那么所得值也就當然會與真實值存在差異。綜上，運用多元線性回歸的方法進行預測是一定會出現(xiàn)誤差的，這是這種方法本身所帶的缺陷。但是在

26、所有的預測方法中我們不可能找到一種，能夠完全預測未來發(fā)展，我們能做的就是盡量考慮各種因素來減小誤差，使其無限接近真實值。5、實驗結果分析總結在這次預測分析中，正確應用回歸分析預測時應注意：用定性分析判斷現(xiàn)象之間的依存關系；避免回歸預測的任意外推；應用合適的數(shù)據(jù)資料；應用回歸預測法時應首先確定變量之間是否存在相關關系。如果變量之間不存在相關關系,對這些變量應用回歸預測法就會得出錯誤的結果。多元線性回歸應用的注意事項1、指標的數(shù)量化（1）自變量為連續(xù)性變量：必要時做變換（2）自變量為有序變量：依此賦值，如優(yōu)良中差，可以分別賦值3、2、1、0（3）自變量為二分類：如令男=1,女=0（4）自變量為名義

27、分類：需要采用啞變量進行編碼2、樣本含量觀察個體數(shù)n與變量個數(shù)m的比例一般至少應為：n：m=5103、統(tǒng)計“最優(yōu)”與專業(yè)的“最優(yōu)”不同準則、方法得出的“最優(yōu)”方程不同；不同的引入、剔除標準獲得的“最優(yōu)”方程不同；方程還受數(shù)據(jù)的正確性、共線性影響4、交互作用當某一自變量對應變量的作用大小與另一個自變量的取值有關時，則表示兩個變量有交互作用檢驗兩個變量之間有無交互作用，普通的做法是在方程中加入他們的乘積項再做檢驗。如考察X1、X2間的交互作用，可在模型中加入X1X2項。總結：通過這次實驗，我們認識到利用excel進行數(shù)據(jù)的分析預測是相當簡便的。當然在這期間需要一步步的探索，一旦掌握了用excel驚

28、醒數(shù)據(jù)分析的方法，做如上預測的時候就會得心應手！最后我們得出的結論如上表。預測數(shù)據(jù)的分析結果難免會有誤差的存在，但這并不影響整體！首先我們了解了實驗目的和實驗的要求，明確要用相關軟件進行銷售數(shù)據(jù)的預測，預測方法有指數(shù)平滑法、多元線性回歸和移動平均法。我們選擇了較為熟悉的軟件excel和多元線性回歸方法進行實驗。為了能夠更好地完成實驗我們先系統(tǒng)的回顧了多元線性回歸預測方法并建立了相關模型，并在excel上選擇該方法進行預測。輸入為20022005年的要素即BG列，輸出為對應的H列，得到了相關的函數(shù)系數(shù)：m1、m2、m3、m4、m5、m6和截距b，因此預測的Y即銷售量就可以根據(jù)函數(shù)求得。在得到預測

29、數(shù)據(jù)后我們進行了數(shù)據(jù)分析比對和誤差分析，了解了誤差產生的原因，進一步完善了我們的預測和實驗過程。在完成預測后我們又進行了實驗的總結，希望能夠彌補疏漏，梳理流程。最后為了能夠更好地完成實驗,了解預測方法及過程，我們熟悉軟件spss,并在該軟件上運用時間序列建模方法再一次進行了預測分析。綜上所述，我們運用兩個預測軟件（excel，spss）并采用了兩種預測方法（多元線性回歸和時間序列建模）進行預測分析，以便于更好的了解數(shù)據(jù)預測和完成預測實驗。6、為了能夠更好的掌握預測方法，我們嘗試用第二種方法來進行數(shù)據(jù)的預測（spss時間序列建模法）年份月份居民月可支配收入服裝商品零售價格指數(shù)居民消費價格指數(shù)市場

30、占有率季節(jié)性指數(shù)周期指數(shù)銷售量PRE_1RES_1LMCI_1UMCI_120042148398.7100.112.99001.399.976127084.00117086.688149997.31186113356.98198120816.3942920043126998.7101.612.1700.882.94390423.00101880.47305-11457.4730598743.47562105017.4704920044133098.4102.313.8600.8771.00498043.00106214.95492-8171.95492103161.69468109268.21

31、51720045133898.3102.414.20001.1341.007127608.00106783.4115620824.58844103725.03112109841.79201200461234&8.2102.912.6900.902.99195251.0099393.47526-4142.4752696115.90837102671.0421620047132597.9103.611.8900-896一98497429.00105859.66952-8430.66952102807.69804108911.6410120048137597.9103.212.8700-949.97

32、8106738.00109412.52352-2674.52352106282.37014112542.6768920049136398.0102.412.3300.931.98598176.00108559.83856-10383.83856105461.47574111658.20137200410139097.7102.013.63001.082.976122499.00110478.3797112020.62029107297.46681113659.29262200411135097.8101.912.1800.845.98694052.00107636.09652-13584.09

33、652104563.02108110709.17196200413136897.8101.611.8800876.98097235.00108915.12396-11680.12396106804.48721112025.7607020051166297.899.913.57001.227.994138894.00129805.905429088.09458124331.73993135280.0709220062222197.3102.913.28001.3991.008165437.00169526.81304-4089.81304157105.04651181948.5795820063

34、141896.8101.612.4900.8821.024103959.00112467.97795-8508.97795109161.51163115774.4442620054144897.0101.213.2000.8771.023105874.00114599.69034-8725.69034111118.54976118080.8309220055149197.3100.514.95001.1341.047136283.00117655.1447718627.85523113862.74996121447.5395920056141897.5100.013.4400.9021.041

35、115775.00112467.977953307.02205109161.51163115774.4442620057145297.8100.213.5400.8961.030108361.00114883.91866-6522.91866111376.65745118391.17987200581515&8.0101.313.5800.9491.004112091.00119360.51469-7269.51469116368.64423123352.3851520059151298.6101.414.6200.9311.031113105.00119147.34345-6042.3434

36、5115181.28707123113.39983200510153599-0101.115.07001.0821.023143472.00120781.6562922690.34371116611.85192124951.46065200511147999.2100.813.8900.8451.00199134.00116802.45982-17668.45982113103.3294-8120501.59016建立散點圖居民月可支配收入根據(jù)上述的散點圖觀察，居民的月可支配收入與銷售量具有一定的相關關系，此時我們對上述的二者變量進行相關性作出擬合成度的預測得出以下的表格,根據(jù)R2的檢驗楔型擬

37、合擬合統(tǒng)計量SE百分位嘆擊以5102550759095平穩(wěn)的R方激活丁打.701.701.701.701.701.701701.701.701E方.701.701.701.701.701.701.701.701.701.701RMSE1058370110583.70110503.70110503.70110583.70110583.70110503.70110583.70110583.70110583.701MAFE8.1358.1358.135S.1358.1358.1358.1358.1358.1358.135Ma.FE19.35119.35119.35119.35119.35119.35

38、119.35119.35119.35119.351MAE8746.4908746.4908746.4908746.4900746.4908746.4908746.4908746.4900746.4908746.490MajiAE21205.65221205.65221205.65221205.65221205.65221205.65221205.65221205.65221205.65221205.652正態(tài)化的EHC18.61518.61518.61510.61518.61518.61518.61518.61518.61518.615根據(jù)以上的相關關系，我們對以上的數(shù)據(jù)作出模型統(tǒng)計量的擬合，得出以