第4讲 相关分析

1、y = pxS= R2y = x1 x2 x3相关关系的例子相关关系的例子父亲身高父亲身高(y)与子女身高与子女身高(x)之间的关系之间的关系收入水平收入水平(y)与受教育程度与受教育程度(x)之间的关系之间的关系粮食亩产量粮食亩产量(y)与施肥量与施肥量(x1) 、降雨量、降雨量(x2) 、温度、温度(x3)之间的关系之间的关系商品的消费量商品的消费量(y)与居民收入与居民收入(x)之间的关系之间的关系商品销售额商品销售额(y)与广告费支出与广告费支出(x)之间的关系之间的关系不相关不相关负线性相关负线性相关正线性相关正线性相关非线性相关非线性相关完全负线性相关完全负线性相关完全正线性相关完

2、全正线性相关三种相关分析对应着相应的相关系数三种相关分析对应着相应的相关系数22()()()()xyxxyyLxxyyrLLxxyy8 . 01 r5 . 08 . 0 r3 . 05 . 0 rr3 . 0高度高度线性相关线性相关显著显著线性相关线性相关低度低度线性相关线性相关非线性非线性相关相关212rnrt2ttSPSSANALYZECorrelateBivariateCorrelations1.467*.992*.667*.021.000.00024242424.467*1.481*.859*.021.017.00024242424.992*.481*1.673*.000.017.00

3、024242424.667*.859*.673*1.000.000.000.24242424Pearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)N研究成果工作时间资助额年工资额研究成果工作时间资助额年工资额Correlation is significant at the 0.05 level (2-tailed).*. Correlation is significan

4、t at the 0.01 level (2-tailed).*. 21261(1)niisDrn n 2211()nniiiiiDUV2id2id22266 4241110.8857(1)6 (61)210iSPdrn n SPSSANALYZECorrelateSpearmanCorrelations1.000.886*.01966.886*1.000.019.66Correlation CoefficientSig. (2-tailed)NCorrelation CoefficientSig. (2-tailed)N口试成绩操作成绩Spearmans rho口试成绩操作成绩Correla

5、tion is significant at the 0.05 level (2-tailed).*. 41(1)VTn n 44 222110.733(1)6 530VTn n SPSSANALYZECorrelateKendalls tau-bCorrelations1.000.733*.03966.733*1.000.039.66Correlation CoefficientSig. (2-tailed)NCorrelation CoefficientSig. (2-tailed)N口 试 成 绩操 作 成 绩Kendalls tau_b口 试 成 绩操 作 成 绩Correlation

6、 is significant at the 0.05 level (2-tailed).*. Correlations1.467*.992*.667*.021.000.00024242424.467*1.481*.859*.021.017.00024242424.992*.481*1.673*.000.017.00024242424.667*.859*.673*1.000.000.000.24242424Pearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (

7、2-tailed)NPearson CorrelationSig. (2-tailed)N研究成果工作时间资助额年工资额研究成果工作时间资助额年工资额Correlation is significant at the 0.05 level (2-tailed).*. Correlation is significant at the 0.01 level (2-tailed).*. 1213 2312,3221323(1)(1)rr rrrr13,214,2 24 212,342214 224 2(1)(1),rrrrrrSPSSANALYZECorrelatePartialSPSSANALY

8、ZECorrelateDistanceProximity Matrix.00037.00113.60328.64211.3234.12831.4119.43437.001.00024.33116.28430.08536.2237.83332.98513.60324.331.00015.2696.41014.42720.13414.42428.64216.28415.269.00018.44029.69117.72629.00611.32330.0856.41018.440.00013.90826.42716.2854.12836.22314.42729.69113.908.00030.0305

9、.66031.4117.83320.13417.72626.42730.030.00026.1859.43432.98514.42429.00616.2855.66026.185.0001234567812345678 Euclidean DistanceThis is a dissimilarity matrixSPSSANALYZECorrelateDistanceProximity Matrix1.0001.000.999.996.9981.0001.000.9991.0001.0001.000.998.999.9991.000.997.9991.0001.000.9991.000.998.999.996.996.998.9991.0001.000.993.995.990.998.9991.0001.0001.000.996.998.9941.000.999.998.993.9961.0001.0001.0001.0