應(yīng)用統(tǒng)計方法(大作業(yè))

1、 例3-7在某項實驗中，測得變量y與因素x數(shù)據(jù)如表1所示。試建立適當?shù)膟與因素x的回歸方程（ ）。表3-14 例3-7實測數(shù)據(jù)x23457810111415161819y106.42108.2109.58109.5110109.93110.49110.59110.6110.9110.76111111.2解：繪制散點圖，如圖1所示：圖1從圖1中可看出，以下三種曲線方程的曲線圖都與散點圖接近，因此都可以作為曲線回歸的選擇對象。（1）.（2）.（3）.現(xiàn)對方案1和方案2方案3進行求解分析，通過對S2殘作比較，S2殘小這則回歸方程交優(yōu)1.方案1選取曲線回歸（1）進行求解。令，應(yīng)用EXCEL進行相應(yīng)處理

2、算得數(shù)據(jù)，列入表1。表1 方案1數(shù)據(jù)處理計算xx=xyx'-x'yi-y(x'-x')(yi-y)21.414213562106.42-1.628216714-3.5161538465.72506046131.732050808108.2-1.310379469-1.7361538462.27502035542109.58-1.042430277-0.3561538460.37126555252.236067977109.5-0.806362299-0.4361538460.35169801872.645751311110-0.3966789660.063846

3、154-0.02532642682.828427125109.93-0.214003152-0.0061538460.001316942103.16227766110.490.1198473830.5538461540.066377012113.31662479110.590.2741945140.6538461540.179281028143.741657387110.60.699227110.6638461540.464179228153.872983346110.90.8305530690.9638461540.800525381164110.760.9575697230.8238461

4、540.788890133184.2426406871111.200210411.0638461541.276839229194.358898944111.21.3164686671.2638461541.66381386239.55159361429.1713.93894078平均3.042430277109.9362平方和132157138.711.6670341421.2105076944.12800113由表2得： 由此得： 故所求的回歸方程為： 進行變量還原得回歸方程： 檢驗假設(shè)H01：. 對給定的，查F(1,11)表（附表5）得臨界值。由于F>，檢驗效果顯著，所以拒絕H01，

5、即回歸方程有意義。2.方案2表2 方案2數(shù)據(jù)處理計算xx=lgxYx'-x'yi-y(x'-x')(yi-y)20.301030106.420000-0.616595-3.5162002.16807130.477121108.200000-0.440504-1.7362000.76480340.602060109.580000-0.315565-0.3562000.11240450.698970109.500000-0.218655-0.4362000.09537770.845098110.000000-0.0725270.063800-0.00462780.9

6、03090109.930000-0.014535-0.0062000.000090101.000000110.4900000.0823750.5538000.045619111.041393110.5900000.1237680.6538000.080919141.146128110.6000000.2285030.6638000.151680151.176091110.9000000.2584660.9638000.249110161.204120110.7600000.2864950.8238000.236015181.255273111.0000000.3376481.0638000.3

7、59189191.278754111.2000000.3611291.2638000.456394總和11.9291271429.170000平均0.917625109.936154平方和1.19471721.21.5104.715045由此得：故所求回歸方程：進行變量還原得回歸方程：檢驗假設(shè)： 對給定的=0.01，查F(1，11)表得到臨界值=9.65.由于F>,檢驗效果顯著，所以拒絕,即回歸方程有意義。3.方案3選取曲線回歸（3）求解。令，應(yīng)用EXCEL可算的數(shù)據(jù)，列入表3。表3 方案3數(shù)據(jù)處理計算xx=xyx'-x'yi-y(x'-x')(yi-y)

8、20.5106.420.342239851-3.516153846-1.20336796830.333333333108.20.175573184-1.736153846-0.30482205940.25109.580.092239851-0.356153846-0.03285157850.2109.50.042239851-0.436153846-0.01842307370.142857143110-0.0149030060.063846154-0.000951580.125109.93-0.032760149-0.0061538460.000201601100.1110.49-0.0577

9、601490.553846154-0.031990236110.090909091110.59-0.0668510580.653846154-0.043710307140.071428571110.6-0.0863315780.663846154-0.057310886150.066666667110.9-0.0910934820.963846154-0.087800103160.0625110.76-0.0952601490.823846154-0.078479707180.055555556111-0.1022045931.063846154-0.108729964190.05263157

10、9111.2-0.105128571.263846154-0.1328663392.050881941429.170.21367053421.21050769-2.101102119平均0.157760149109.93615平方和0.537217975157138.66由表3得由此得：故所求的回歸方程為：進行變量還原得回歸方程：檢驗假設(shè)H01：.對給定的，查F(1,11)表（附表5）得臨界值。由于F>，檢驗效果顯著，所以拒絕H01，即回歸方程有意義。表4方案回歸方程F14.557740.191522.602278.660530.5525411.2905由表4，方案3的殘差平方和是最小的

11、，因而其回歸方程是最優(yōu)的，擬合效果是最好的，方案2次之，方案1最差。第三章課后題5、研究平爐煉鋼的效率y與出鋼量（）和FeO（）的關(guān)系，測得數(shù)據(jù)如下：x1115.396.556.9101.0102.987.9101.4109.8103.4x214.214.614.914.918.213.213.520.013.0y83.578.073.091.483.482.084.080.088.0x1110.680.393.088.088.0108.989.5104.4101.9x215.312.914.718.118.115.418.313.812.2y86.581.088.685.785.781.97

12、9.189.980.6（1）建立y關(guān)于，的線性回歸方程（2）檢驗所建方程是否有意義（=0.10）（3）檢驗，是否對y有顯著影響（=0.10）（4）如果有對y影響不顯著的變量，將其去掉再建立一元回歸方程 表 1數(shù)據(jù)預(yù)處理計算1115.314.283.513294.09201.641637.269627.551185.76972.25296.514.6789312.25213.161408.975271138.86084356.914.9733237.61222.01847.814153.71087.75329410114.991.410201222.011504.99231.41361.8683

13、53.965102.918.283.410588.41331.241872.788581.861517.886955.56687.913.2827726.41174.241160.287207.81082.467247101.413.58410281.96182.251368.98517.6113470568109.8208012056.0440021968784160064009103.4138810691.561691344.29099.21144774410110.615.386.512232.36234.091692.189566.91323.457482.251180.312.981

14、6448.09166.411035.876504.31044.96561129314.788.68649216.091367.18239.81302.427849.96138816.481.57744268.961443.271721336.66642.25148818.185.77744327.611592.87541.61551.177344.4915108.915.481.911859.21237.161677.068918.911261.266707.611689.518.379.18010.25334.891637.857079.451447.536256.8117104.413.889.910899.36190.441440.729385.561240.628082.0118101.912.280.610383.61148.841243.188213.14983.326496.36和1739.7273.61498.1171359.214240.0426470.99145351.