REGRESION Y CORRELACION LINEAL1)

AÑO POBLACION

millones x x^2 x^3 x^4 xy1850 5.00 1.00 1.00 1.00 1.00 5.001860 3.00 2.00 4.00 8.00 16.00 6.001870 2.00 3.00 9.00 27.00 81.00 6.001880 4.00 4.00 16.00 64.00 256.00 16.001890 6.00 5.00 25.00 125.00 625.00 30.001900 10.00 6.00 36.00 216.00 1296.00 60.001910 18.00 7.00 49.00 343.00 2401.00 126.00

48.0 28.0 140.0 784.0 4676.0 249.0

ECUACIONES NORMALES48.0 =

249.0 =1491.0 =

-13441743

399

-672010437

3717

-625632728532102900

c =b =a =

y= 9.428571428571

X=

EEUU y

x^2y Yest (Yest-Ymed)^2 (Y-Ymed)^2 (Y-Yest)^2 Y^25.00 5.21429 2.69898 3.44898 0.04591836735 1

12.00 2.78571 16.57653 14.87755 0.04591836735 418.00 2.14286 22.22449 23.59184 0.02040816327 964.00 3.28571 12.75510 8.16327 0.51020408163 16

150.00 6.21429 0.41327 0.73469 0.04591836735 25360.00 10.92857 16.57653 9.87755 0.86224489796 36882.00 17.42857 111.75510 124.16327 0.32653061224 49

1491.0 183.00000 184.85714 1.85714 140.00000

7 a + 28.0 b +28.0 a + 140.0 b +

140.0 a + 784.0 b +

-196 -784196.0 980

0.0 196

-980 -3920980 5488

0 1568

-307328307328

0Ymed= 6.857143

0.89285714286-5.107142857149.42857142857

+ -5.1071428571 X + 0.89285714286 X^2

COEF. CORRELACCOEF. DETERM

(Yest-Y)^22.69897959216.57653061

22.224489812.755102040.41326530616.57653061

111.755102183.00000

140.0 c -28.0 -140.0784.0 c 7

4676.0 c 7

-392054881568 -1568

-196003273213132 196

-24586242573872

115248

r 0.99496r^2 0.98995

REGRESION LINEAL MULTIPLE

ECUACIONES NORMALES

X1 X2 Y X1^2 X2^22 1 11 4 14 1 14 16 13 3 12 9 93 3 14 9 94 5 15 16 254 5 12 16 2520 18 78 70 70

n= 6

ECUACIONES NORMALES 78 6 a 20 b264 20 a 70 b238 18 a 64 b

1560 120 a 400 b-1584 -120 a -420 b

-24 0 -20

1404 108 a 360 b-1428 -108 a -384 b

-24 0 -24

576 0 a 480 b-480 0 a -480 b

96 0 0

c = -0.07143b = 1.28571a = 8.92857

y = 8.92857 + 1.28571

COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X1 IGNORANDO X2.rYX1= 0.632456

COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X2 IGNORANDO X1.rYX2= 0.288675

COEFICIENTE DE CORRELACION MULTIPLE ENTRE X1, X2 IGNORANDO Y.rX1X2= 0.547723

COEFICIENTES DE CORRELACION PARCIAL ENTRE LAS VARIABLESRyx1,x2= 0.592157Ryx2,x1= -0.089087Rx1x2,y= 0.492366

Se aprecia que la correlacion mayor es entre las variables X1 Y X2.

X1X2 X1Y X2Y Yest (Yest-Ymed)^2 (Y-Ymed)^2 (Y-Yest)^2 Y^22 22 11 11.42857 2.46939 4.00000 0.1836735 1214 56 14 14.00000 1.00000 1.00000 0 1969 36 36 12.57143 0.18367 1.00000 0.3265306 1449 42 42 12.57143 0.18367 1.00000 2.0408163 196

20 60 75 13.71429 0.51020 4.00000 1.6530612 22520 48 60 13.71429 0.51020 1.00000 2.9387755 144

64 264 238 4.85714 12.00000 7.1428571 1026

18 c 20 1864 c -670 c -6

360 c-384 c

-24 c 4 -24

324 c-420 c

-96 5 20

576 c-1920 c-1344

Sy,x= 1.33631Spy,x= 1.0910895

desv Y= 1.41421COEF. CORR r 0.63620901 r 0.636209COEF. DETE r^2 0.4047619 r^2 0.4047619

Ymed 13.00X= 4 Y= 14.0714285714X= 12 Y= 24.3571428571

X1 + -0.07143 X2

(Yest-Y)^22.4693877551

10.183673469390.183673469390.510204081630.51020408163

4.85714

REGRESION LINEAL MULTIPLE

ECUACIONES NORMALES

X1 X2 Y X1^2 X2^20 1 13 0 12 3 18 4 94 3 14 16 96 7 21 36 498 5 11 64 2520 19 77 120 93

n= 5

ECUACIONES NORMALES 77 5 a 20 b306 20 a 120 b311 19 a 100 b

1540 100 a 400 b-1530 -100 a -600 b

10 0 -200

1463 95 a 380 b-1555 -95 a -500 b

-92 0 -120

-1200 0 a 24000 b-18400 0 a -24000 b-19600 0 0

c = 3.06250b = -1.88750a = 11.31250

y = 11.31250 + -1.88750

COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X1 IGNORANDO X2.rYX1= -0.039163

COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X2 IGNORANDO X1.

rYX2= 0.499646COEFICIENTE DE CORRELACION MULTIPLE ENTRE X1, X2 IGNORANDO Y.

rX1X2= 0.83205

COEFICIENTES DE CORRELACION PARCIAL ENTRE LAS VARIABLESRyx1,x2= -0.946713Ryx2,x1= 0.960231Rx1x2,y= 0.983887

Se aprecia que la correlacion mayor es entre las variables X1 Y X2.

X1X2 X1Y X2Y Yest (Yest-Ymed)^2 (Y-Ymed)^2 (Y-Yest)^2 Y^20 0 13 14.37500 1.05063 5.76000 1.890625 1696 36 54 16.72500 1.75563 6.76000 1.625625 324

12 56 42 12.95000 6.00250 1.96000 1.1025 19642 126 147 21.42500 36.30063 31.36000 0.180625 44140 88 55 11.52500 15.01563 19.36000 0.275625 121

100 306 311 60.12500 65.20000 5.075 1251

19 c 20 19100 c -5

93 c -5

380 c-500 c-120 c 4 -120

361 c-465 c-104 5 200

14400 c-20800 c

-6400Sy,x= 1.30064

Spy,x= 1.0074721desv Y= 3.61109

COEF. CORR r 0.96029296 r 0.960293COEF. DETE r^2 0.92216258 r^2 0.9221626

Ymed 15.4X= 4 Y= 3.7625X= 12 Y= -11.3375

X1 + 3.06250 X2

(Yest-Y)^21.0506251.755625

6.002536.30062515.015625

60.12500

REGRESION LINEAL MULTIPLE

ECUACIONES NORMALES

X1 X2 Y X1^2 X2^20 1 16 0 12 3 34 4 94 5 38 16 256 5 32 36 257 7 72 49 498 9 66 64 8127 30 258 169 190

n= 6

ECUACIONES NORMALES 258 6 a 27 b1444 27 a 169 b1566 30 a 177 b

6966 162 a 729 b-8664 -162 a -1014 b-1698 0 -285

7740 180 a 810 b-9396 -180 a -1062 b-1656 0 -252

427896 0 a 71820 b-471960 0 a -71820 b

-44064 0 0

c = 9.00000b = -2.00000a = 7.00000

y = 7.00000 + -2.00000

COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X1 IGNORANDO X2.rYX1= 0.851402

COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X2 IGNORANDO X1.rYX2= 0.904845

COEFICIENTE DE CORRELACION MULTIPLE ENTRE X1, X2 IGNORANDO Y.rX1X2= 0.963546

COEFICIENTES DE CORRELACION PARCIAL ENTRE LAS VARIABLESRyx1,x2= -0.179605Ryx2,x1= 0.60201Rx1x2,y= 0.864994

Se aprecia que la correlacion mayor es entre las variables X1 Y X2.

X1X2 X1Y X2Y Yest (Yest-Ymed)^2 (Y-Ymed)^2 (Y-Yest)^2 Y^20 0 16 16.00000 729.00000 729.00000 0 2566 68 102 30.00000 169.00000 81.00000 16 1156

20 152 190 44.00000 1.00000 25.00000 36 144430 192 160 40.00000 9.00000 121.00000 64 102449 504 504 56.00000 169.00000 841.00000 256 518472 528 594 72.00000 841.00000 529.00000 36 4356

177 1444 1566 1918.00000 2326.00000 408 13420

30 c 27 30177 c -6190 c -6

810 c-1062 c

-252 c 4 -252

900 c-1140 c

-240 5 285

63504 c-68400 c

-4896Sy,x= 10.09950

Spy,x= 8.246211318.34572

COEF. CORR r 0.90807025 r 0.8932855 ERRORCOEF. DETE r^2 0.82459157 r^2 0.797959

Ymed 43X= 4 Y= -1X= 12 Y= -17

X1 + 9.00000 X2

(Yest-Y)^2729169

19

169841

1918.00000

REGRESION LINEAL

ECUACIONES NORMALES

X Y XY X^2 Yest (Yest-Ymed)^21 14 14 1 15.20000 282.240002 33 66 4 23.60000 70.560003 20 60 9 32.00000 0.000004 41 164 16 40.40000 70.560005 52 260 25 48.80000 282.2400015 160 564 55 705.60000

n= 5

ECUACIONES NORMALES 160 5 a 15 b564 15 a 55 b

2400 75 a 225 b-2820 -75 a -275 b

-420 0 -50

b = 8.40000 Ymeda = 6.80000 COEFICIENTE DE DETERMINACION

y = 6.80000 + 8.40000 x

(Y-Ymed)^2 Y^2324.00000 196

1.00000 1089144.00000 400

81.00000 1681400.00000 2704950.00000 6070

15-5

COEFICIENTE DE CORRELACION32 r 0.861822 r 0.861822

COEFICIENTE DE DETERMINACION r^2 0.742737 r^2 0.742737X= 4 Y= 40.4X= 12 Y= 107.6X= 3.5 Y= 36.2