多元线性回归例题与解析

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1、作业：在农作物害虫发生趋势的预报研究中,所涉及的5个自变量及因变量的10组观测数据如下,试建立y对x1-x5的回归模型，指出那些变量对y有显著的线性贡献，贡献大小顺序。x1x2x3x4x5y9.2002.7321.4710.3321.1381.1559.1003.7321.8200.1120.8281.1468.6004.8821.8720.3832.1311.84110.2333.9681.5870.1811.3491.3565.6003.7321.8410.2971.8150.8635.3674.2361.8730.0631.352

2、0.9036.1333.1461.9870.2801.6470.1148.2004.6461.6150.3794.5650.8988.8004.3781.5430.7442.0731.9307.6003.8641.5990.3422.4231.104（！）回归性方程显著性检验：由Analysisofvariance表可知，其的值0.0170小于0.05，则、、之间具有显著性相关性；由R-square的值为0.9356可知该方程的拟合度高，（2）参数显著性检验：a.由ParameterEstimates表可知，对自变量x1。t检验值为t=

3、1.06,的值等于0.3479，大于0.05，故x1的系数为0，即x1未通过检验，去掉x1，再次运行程序。b.结果表明所有变量的系数均通过检验，得到线性模型。（3）拟合区间。故对y有显著的线性贡献大小顺序为。附件：dataex;inputx1-x5y@@;cards;9.2002.7321.4710.3321.1381.1559.1003.7321.8200.1120.8281.1468.6004.8821.8720.3832.1311.84110.2333.9681.5870.1811.3491.3565.6003.7321.8410

4、.2971.8150.8635.3674.2361.8730.0631.3520.9036.1333.1461.9870.2801.6470.1148.2004.6461.6150.3794.5650.8988.8004.3781.5430.7442.0731.9307.6003.8641.5990.3422.4231.104;procreg;modely=x1x2x3x4x5/cli;run;dataex;inputx2-x5y@@;cards;2.7321.4710.3321.1381.1553.7321.8200.1120.828

5、1.1464.8821.8720.3832.1311.8413.9681.5870.1811.3491.3563.7321.8410.2971.8150.8634.2361.8730.0631.3520.9033.1461.9870.2801.6470.1144.6461.6150.3794.5650.8984.3781.5430.7442.0731.9303.8641.5990.3422.4231.104;procreg;modely=x2x3x4x5/cli;run;