第七章 相關(guān)分析與回歸分析

1、1232 2r rs s45678910111213141516鋼材消費(fèi)量與國(guó)民收入鋼材消費(fèi)量與國(guó)民收入05001000150020002500050010001500200025003000國(guó)民收入（億元）國(guó)民收入（億元）鋼材消費(fèi)量（萬(wàn)噸）鋼材消費(fèi)量（萬(wàn)噸）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根據(jù)：根據(jù)：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汽車汽車貨運(yùn)量貨運(yùn)量（億噸（億噸/千米）千米）Y汽車汽車擁有量擁有量（萬(wàn)輛）（萬(wàn)輛）35要求：（要求：（1）根據(jù)資料作散點(diǎn)圖）根據(jù)資料作散點(diǎn)圖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根據(jù)上述資料：根據(jù)上述資料：（1）建立多元線性回歸方程；）建立多元線性回歸方程；（2）如果已知）如果已知2003年有機(jī)肥施有量為年有機(jī)肥施有量為52萬(wàn)噸萬(wàn)噸牲畜頭數(shù)為牲畜頭數(shù)為21萬(wàn)頭，預(yù)測(cè)該年糧食產(chǎn)量為多少？萬(wàn)頭，預(yù)測(cè)該年糧食產(chǎn)量為多少？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反映實(shí)際觀察值與回歸估計(jì)值離差平方和反映實(shí)際觀察值與回歸估計(jì)值離差平方和 的平方根。的平方根。 反映實(shí)際觀察值在回歸直線周圍的分散狀反映實(shí)際觀察值在回歸直線周圍的分散狀 況，說(shuō)明了回歸直線擬合況，說(shuō)明了回歸直線擬合的準(zhǔn)確的準(zhǔn)確程度。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