多元线性回归练习题.doc

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1、多元线性回归1.某研究者测得29例儿童的血液中血红蛋白（Y，μg）与钙（X1）、镁（X2）、铁（X3）、锰（X4）及铜（X5）的含量值，见以下数据：X1X2X3X4X5Y54.8930.86448.70.0121.01013.5072.4942.61467.30.0081.64013.0053.8152.86425.61.0041.22013.7564.7439.18469.80.0051.22014.0058.8037.67456.55.0121.01014.2543.6726.18395.78.001.59412.7554.8930.86448.70.0

2、121.01012.5086.1243.79440.13.0171.77012.2560.3538.20394.40.0011.44012.0054.0434.23405.60.0081.30011.7561.2337.35446.00.0221.38011.5060.1733.67383.20.001.91411.2569.6940.01416.70.0121.35011.0072.2840.12430.80.0001.20010.7555.1333.02445.80.012.91810.5070.0836.80409.80.0121.99010.2563

3、.0535.07384.10.000.85310.0048.7530.53342.90.018.9249.7552.2827.14326.29.004.8179.5052.2136.18388.54.0241.0209.2549.7025.43331.10.012.8979.0061.0229.27258.94.0161.1908.7553.6828.79292.60.0481.3208.5050.2229.17292.60.0061.0408.2565.3429.99312.80.0061.0308.0056.3929.29283.00.0161.3507

4、.8066.1231.93344.20.000.6897.5073.8932.94312.50.0641.1507.2547.3128.55294.70.005.8387.00问题：（采用强迫引入法——Enter）（1）建立多元线性回归方程；（2）方程中微量元素与血红蛋白之间有无线性关系？（3）对血红蛋白的影响有统计学意义的微量元素是哪些？（4）在微量元素中，哪个对血红蛋白的作用最大？并请排出个作用大小顺序；（5）评价回归模型的拟合优度。2.为研究0～8岁儿童身高增长规律，调查了20名男童和20名女童的身高Y(cm)和年龄X1（岁），数据如下表所示，试进行二

5、元线性回归分析，并评价模型的拟合优度。20名男童和20名女童的身高和年龄数据编号性别X1年龄X2身高Y编号性别X1年龄X2身高Y110.3652100.972210.4662204.6103310.8692301.880411.0692400.872511.6752506.4118614.4982602.285714.5992704.7105814.91012802.890915.11022905.51121012.0803005.41091112.1803103.2931213.3893200.4681314.1943305.71111414.498340

6、7.11261515.41063500.7711616.71143603.3941716.91173706.91211817.11193805.71131917.51243903.6942014.81014000.872注：性别：1表示男童，0表示女童3.某学校20名一年级女大学生体重、胸围、肩宽及肺活量的实测数据如下表所示，试进行多元线性回归分析，并评价模型的拟合优度。20名一年级女大学生体重、胸围、肩宽及肺活量的实测数据编号体重X1(kg)胸围X2(cm)肩宽X3(cm)肺活量Y(L)151.373.636.42.99248.983.934.03.113

7、42.878.331.01.91455.077.131.02.63545.381.730.02.86645.374.832.01.91751.473.736.52.98853.879.437.03.28949.072.630.12.521053.979.537.13.271148.883.833.93.101252.688.438.03.281342.778.230.91.921452.588.338.13.271555.177.231.12.641645.281.630.22.851751.478.336.53.161848.772.530.02.5119

8、51.378.236.43.152045.274.7