（精選）應(yīng)用統(tǒng)計(jì)方法(大作業(yè))

1、應(yīng)用統(tǒng)計(jì)方法作業(yè)一、在某項(xiàng)實(shí)驗(yàn)中，測(cè)得變量y與因素x數(shù)據(jù)如表1所示。試建立適當(dāng)?shù)膟與因素x的回歸方程（ ）。表1 實(shí)測(cè)數(shù)據(jù)x23457810111415161819y106.42108.20109.58109.50110.00109.93110.49110.59110.60110.90110.76110.00111.20解：繪制散點(diǎn)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(diǎn)圖接近，因此都可以作為曲線回歸的選擇對(duì)象。（1）.（2）.（3）.為了更好的擬合給定數(shù)據(jù)，確定最優(yōu)的回歸方程，需對(duì)以上3式分別進(jìn)行檢驗(yàn)，求取 并比較其大小，將最小者作為因素y與x的最優(yōu)回歸方程。1.

2、方案1選取曲線回歸（1）進(jìn)行求解。令，應(yīng)用EXCEL進(jìn)行相應(yīng)處理算得數(shù)據(jù)，列入表2。表2 方案1數(shù)據(jù)處理計(jì)算xy21.414213562106.4200-1.628216714-3.5161538465.72506046331.732050808108.2000-1.310379469-1.7361538462.27502035542.000000000109.5800-1.042430277-0.3561538460.37126555252.236067977109.5000-0.806362299-0.4361538460.35169801872.645751311110.0000-0.3

3、966789660.063846154-0.02532642682.828427125109.9300-0.214003152-0.0061538460.001316942103.16227766110.49000.1198473830.5538461540.066377012113.31662479110.59000.2741945140.6538461540.179281028143.741657387110.60000.699227110.6638461540.464179228153.872983346110.90000.8305530690.9638461540.8005253821

4、64.000000000110.76000.9575697230.8238461540.788890134184.242640687111.00001.200210411.0638461541.276839229194.358898944111.20001.3164686671.2638461541.66381386139.551593601429.1700均值3.042430277109.9362平方和1.414213562106.420011.6670341521.2105076913.93894078由表2得： 由此得： 故所求的回歸方程為： 進(jìn)行變量還原得回歸方程： 檢驗(yàn)假設(shè)H01：.

5、 對(duì)給定的，查F(1,11)表（附表5）得臨界值。由于F>，檢驗(yàn)效果顯著，所以拒絕H01，即回歸方程有意義。2.方案2曲線回歸（2）的求取過(guò)程，如課本例3-7示。最終求得的回歸方程為：。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(jì)算xy20.500000000106.42000.342239851-3.516153846-1.20336796830.333333333108.20000.175573184-1.736153846-0.30482205940.250000000109.58000.092239851-0.356153846

6、-0.03285157850.200000000109.50000.042239851-0.436153846-0.01842307370.142857143110.0000-0.0149030060.063846154-0.000951580.125000000109.9300-0.032760149-0.0061538460.000201601100.100000000110.4900-0.0577601490.553846154-0.031990236110.090909091110.5900-0.0668510580.653846154-0.043710307140.071428571

7、110.6000-0.0863315780.663846154-0.057310886150.066666667110.900-0.0910934830.963846154-0.087800103160.062500000110.7600-0.0952601490.823846154-0.078479708180.055555556111.0000-0.1022045941.063846154-0.108729964190.052631579111.2000-0.105128571.263846154-0.1328663392.0508819401429.170均值0.157760149109.9362平方和0.500000000106.42000.21367053421.21050769-2.101102119由表3得由此得：故所求的回歸方程為：進(jìn)行變量還原得回歸方程：檢驗(yàn)假設(shè)H01：.對(duì)給定的，查F(1,11)表（附表5）得臨界值。由于F>，檢驗(yàn)效果顯著，所以拒絕H01，即回歸方程有意義。4.三種方案的綜合對(duì)比通過(guò)以上求解分析，可知式（1）、（2）和（3）作為回歸方程表征y與因素x的關(guān)系均是有意義的。三者統(tǒng)計(jì)的計(jì)算結(jié)果如表4示：表4 三種方案綜合對(duì)比方案回歸方程F