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页数:5页
时间:2020-07-06
《应用统计方法(大作业).doc》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、应用统计方法作业一、在某项实验中,测得变量y与因素x数据如表1所示。试建立适当的y与因素x的回归方程()。表1实测数据x23457810111415161819y106.42108.20109.58109.50110.00109.93110.49110.59110.60110.90110.76110.00111.20解:绘制散点图,如图1所示:图1从图1中可看出,以下三种曲线方程的曲线图都与散点图接近,因此都可以作为曲线回归的选择对象。(1).(2).(3).为了更好的拟合给定数据,确定最优的回归方程,需对以上3式分别进行检验,求取并比较其
2、大小,将最小者作为因素y与x的最优回归方程。1.方案1选取曲线回归(1)进行求解。令,应用EXCEL进行相应处理算得数据,列入表2。表2方案1数据处理计算xy21.414213562106.4200-1.628216714-3.5161538465.72506046331.732050808108.2000-1.310379469-1.7361538462.27502035542.000000000109.5800-1.042430277-0.3561538460.37126555252.236067977109.5000-0.806362
3、299-0.4361538460.35169801872.645751311110.0000-0.3966789660.063846154-0.02532642682.828427125109.9300-0.214003152-0.0061538460.001316942103.16227766110.49000.1198473830.5538461540.066377012113.31662479110.59000.2741945140.6538461540.179281028143.741657387110.60000.69922711
4、0.6638461540.464179228153.872983346110.90000.8305530690.9638461540.800525382164.000000000110.76000.9575697230.8238461540.788890134184.242640687111.00001.200210411.0638461541.276839229194.358898944111.20001.3164686671.2638461541.66381386139.551593601429.1700———均值3.042430277
5、109.9362———平方和1.414213562106.420011.6670341521.2105076913.93894078由表2得:由此得:故所求的回归方程为:进行变量还原得回归方程:检验假设H01:.对给定的,查F(1,11)表(附表5)得临界值。由于F>,检验效果显著,所以拒绝H01,即回归方程有意义。2.方案2曲线回归(2)的求取过程,如课本例3-7示。最终求得的回归方程为:。3.方案3选取曲线回归(3)求解。令,应用EXCEL可算的数据,列入表3。表3方案3数据处理计算xy20.500000000106.42000.342
6、239851-3.516153846-1.20336796830.333333333108.20000.175573184-1.736153846-0.30482205940.250000000109.58000.092239851-0.356153846-0.03285157850.200000000109.50000.042239851-0.436153846-0.01842307370.142857143110.0000-0.0149030060.063846154-0.000951580.125000000109.9300-0.03
7、2760149-0.0061538460.000201601100.100000000110.4900-0.0577601490.553846154-0.031990236110.090909091110.5900-0.0668510580.653846154-0.043710307140.071428571110.6000-0.0863315780.663846154-0.057310886150.066666667110.900-0.0910934830.963846154-0.087800103160.062500000110.760
8、0-0.0952601490.823846154-0.078479708180.055555556111.0000-0.1022045941.063846154-0.108729
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