第七章 相关分析与回归分析

1、1232 2r rs s45678910111213141516钢材消费量与国民收入钢材消费量与国民收入05001000150020002500050010001500200025003000国民收入（亿元）国民收入（亿元）钢材消费量（万吨）钢材消费量（万吨）17y yx x2 2xyxyr r 18) )y y)(y)(yx x(x(xn n1 1n n) )y y)(y)(yx x(x(x2 2xyxy2 22 2x x) )x x(x(xn n1 1n n) )x x(x(x2 22 2y y) )y y(y(yn n1 1n n) )y y(y(y192 22 2y yx x2 2xy

2、xy) )y y(y(y) )x x(x(x) )y y)(y)(yx x(x(xr r) )y yy y2y2y(y(y) )x xx x2x2x(x(x) )y yx xy yx xy yx x(xy(xyr r2 22 22 22 2202 22 22 22 2y yn ny yy y2 2y yx xn nx xx x2 2x xy yx xn nx xy yy yx xxyxyr ry yn ny y, , x xn nx x得：得：, ,n ny yy y, ,n nx xx x根据：根据：2 22 22 22 2y yn ny yx xn nx xy yx xn nxyxyr r

3、212 22 22 22 22 22 2n n) )y y( (n ny yn n) )x x( (n nx xn ny yn nx xn nxyxyr r 2 22 22 22 2) )y y( (y yn n) )x x( (x xn ny yx xxyxyn nr r22即：即：X=24，Y=300， XY=1182， n=6，X2 = 106， Y2 = 15048 23 2 22 22 22 2) )y y( (y yn n) )x x( (x xn ny yx xxyxyn nr r2 22 230030015048150486 624241061066 6300300242411

4、8211826 6r r0.82160.821616.970616.97067.74607.74601081082882886060108108r r242526272829303132最最小小值值) )y y( (y y2 2c c2 2x xb bx xa ax xy yx xb bn na ay yx xb by ya ax)x)( (x xn ny yx xxyxyn nb b2 22 2 33y yd dx xc cy)y)( (y yn nx xy yyxyxn nd d2 22 2 最最小小值值) )x x( (x x2 2c c2 2y yd dy yc cyxyxy yd d

5、ncncx x34X汽车汽车货运量货运量（亿吨（亿吨/千米）千米）Y汽车汽车拥有量拥有量（万辆）（万辆）35要求：（要求：（1）根据资料作散点图）根据资料作散点图3637 2 22 22 22 2) )y y( (y yn n) )x x( (x xn ny yx xxyxyn nr r2 22 24.964.962.67622.6762101070.270.2537.16537.1610104.964.9670.270.237.7837.781010r r0.9560.95630.95630.95629.60829.6082.16042.1604443.56443.5629.60829.60

6、8r r38x xb by ya ax)x)( (x xn ny yx xxyxyn nb b2 22 2 0.06680.0668443.56443.5629.60829.60870.270.2537.16537.1610104.964.9670.270.237.7837.781010b b2 20.0270.027101070.270.20.06680.066810104.964.96n nx xb bn ny ya a3940最最小小值值) )y y( (y y2 2c c412 21 11 1x xb bx xb bn na ay y22 21 12 22 21 11 11 11 1x

7、 xx xb bx xb bx xa ay yx x2 22 22 22 21 11 12 22 2x xb bx xx xb bx xa ay yx x4243根据上述资料：根据上述资料：（1）建立多元线性回归方程；）建立多元线性回归方程；（2）如果已知）如果已知2003年有机肥施有量为年有机肥施有量为52万吨万吨牲畜头数为牲畜头数为21万头，预测该年粮食产量为多少？万头，预测该年粮食产量为多少？442 21 1x x2 22 2x x452 21 1x x2 22 2x x2 21 12 21 11 1b b5 59 91 1b b1 13 3a a3 33 37 72 21 19 96

8、62 20 0b b2 26 69 91 15 5b b5 59 91 1a a1 15 53 36 69 92 21 13 34 46 63 3b b9 96 62 20 0b b2 21 11 1a a5 55 51 15 546n n3 32 21 1x x , , , , x x , , x x , , x x47yc = a + b1x1 + b2x2 +b3x3 + bnxnn nn n2 21 11 1x xb bx xb bx xb bn na ay y2n n1 1n n2 21 12 22 21 11 11 11 1x xx xb bx xx xb bx xb bx xa

9、ay yx xn n2 2n n2 22 22 22 21 11 12 22 2x xx xb bx xb bx xx xb bx xa ay yx x2 2n nn nn n2 22 2n n1 11 1n nn nx xb bx xx xb bx xx xb bx xa ay yx x4849502)(2nyyScyx512)()(2nxybyaySyx反映实际观察值与回归估计值离差平方和反映实际观察值与回归估计值离差平方和 的平方根。的平方根。 反映实际观察值在回归直线周围的分散状反映实际观察值在回归直线周围的分散状 况，说明了回归直线拟合况，说明了回归直线拟合的准确的准确程度。程度。5

10、2nxx2)(2)(2nyyScyx53222221yyxyyxySSr)1 (222rSyyx)1 (2rSyyx545556x xb by ya ax)x)( (x xn ny yx xxyxyn nb b2 22 2 1.80771.807715615628228234341641648 85575573434233223328 8b b2 2- -77.307777.30778 834341.80771.8077- -8 8557557n nx xb bn ny ya a57 2 22 22 22 2) )y y( (y yn n) )x x( (x xn ny yx xxyxyn nr r2 22 255755738849388498 834341681688 85575573434233223328 8r r580.96890