1. REGRESION Y CORRELACION LINEAL
1)
AÑO POBLACION
EEUU y
millones x x^2 x^3 x^4 xy
1850 5.00 1.00 1.00 1.00 1.00 5.00
1860 3.00 2.00 4.00 8.00 16.00 6.00
1870 2.00 3.00 9.00 27.00 81.00 6.00
1880 4.00 4.00 16.00 64.00 256.00 16.00
1890 6.00 5.00 25.00 125.00 625.00 30.00
1900 10.00 6.00 36.00 216.00 1296.00 60.00
1910 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 NORMALES
48.0 =
249.0 =
1491.0 =
-1344
1743
399
-6720
10437
3717
-625632
728532
102900
c =
b =
a =
y= 9.428571429
X=

2. x^2y Yest (Yest-Ymed)^2 (Y-Ymed)^2 (Y-Yest)^2 Y^2
5.00 5.21429 2.69898 3.44898 0.045918367 1
12.00 2.78571 16.57653 14.87755 0.045918367 4
18.00 2.14286 22.22449 23.59184 0.020408163 9
64.00 3.28571 12.75510 8.16327 0.510204082 16
150.00 6.21429 0.41327 0.73469 0.045918367 25
360.00 10.92857 16.57653 9.87755 0.862244898 36
882.00 17.42857 111.75510 124.16327 0.326530612 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 -784
196.0 980
0.0 196
-980 -3920
980 5488
0 1568
-307328
307328
0
Ymed= 6.857143
0.892857143
-5.107142857
9.428571429
+ -5.107142857 X + 0.892857143 X^2
COEF. CORRELAC
COEF. DETERM

3. (Yest-Y)^2
2.69897959
16.5765306
22.2244898
12.755102
0.41326531
16.5765306
111.755102
183.00000
140.0 c -28.0 -140.0
784.0 c 7
4676.0 c 7
-3920
5488
1568 -1568
-19600
32732
13132 196
-2458624
2573872
115248
r 0.99496
r^2 0.98995

4. REGRESION LINEAL MULTIPLE
ECUACIONES NORMALES
X1 X2 Y X1^2
2 1 11 4
4 1 14 16
3 3 12 9
3 3 14 9
4 5 15 16
4 5 12 16
20 18 78 70
n= 6
ECUACIONES NORMALES 78 6 a 20
264 20 a 70
238 18 a 64
1560 120 a 400
-1584 -120 a -420
-24 0 -20
1404 108 a 360
-1428 -108 a -384
-24 0 -24
576 0 a 480
-480 0 a -480
96 0 0
c = -0.07143
b = 1.28571
a = 8.92857
y = 8.92857 +
COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X1 IGNORANDO X2.
rYX1= 0.632456
COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X2 IGNORANDO X1.

5. rYX2= 0.288675
COEFICIENTE DE CORRELACION MULTIPLE ENTRE X1, X2 IGNORANDO Y.
rX1X2= 0.547723
COEFICIENTES DE CORRELACION PARCIAL ENTRE LAS VARIABLES
Ryx1,x2= 0.592157
Ryx2,x1= -0.08909
Rx1x2,y= 0.492366
Se aprecia que la correlacion mayor es entre las variables X1 Y X2.

6. X2^2 X1X2 X1Y X2Y Yest (Yest-Ymed)^2 (Y-Ymed)^2 (Y-Yest)^2 Y^2
1 2 22 11 11.42857 2.46939 4.00000 0.183673 121
1 4 56 14 14.00000 1.00000 1.00000 3.16E-30 196
9 9 36 36 12.57143 0.18367 1.00000 0.326531 144
9 9 42 42 12.57143 0.18367 1.00000 2.040816 196
25 20 60 75 13.71429 0.51020 4.00000 1.653061 225
25 20 48 60 13.71429 0.51020 1.00000 2.938776 144
70 64 264 238 4.85714 12.00000 7.142857 1026
b 18 c 20 18
b 64 c -6
b 70 c -6
b 360 c
b -384 c
-24 c 4 -24
b 324 c
b -420 c
-96 5 20
b 576 c
b -1920 c
-1344
Sy,x= 1.33631
Spy,x= 1.091089
desv Y= 1.41421
COEF. CORRELAC r 0.636209 r 0.636209
COEF. DETERM r^2 0.4047619 r^2 0.404762
Ymed 13.00
X= 4 Y= 14.07142857
X= 12 Y= 24.35714286
1.28571 X1 + -0.07143 X2

8. (Yest-Y)^2
2.469387755
1
0.183673469
0.183673469
0.510204082
0.510204082
4.85714

9. REGRESION LINEAL MULTIPLE
ECUACIONES NORMALES
X1 X2 Y X1^2
0 1 13 0
2 3 18 4
4 3 14 16
6 7 21 36
8 5 11 64
20 19 77 120
n= 5
ECUACIONES NORMALES 77 5 a 20
306 20 a 120
311 19 a 100
1540 100 a 400
-1530 -100 a -600
10 0 -200
1463 95 a 380
-1555 -95 a -500
-92 0 -120
-1200 0 a 24000
-18400 0 a -24000
-19600 0 0
c = 3.06250
b = -1.88750
a = 11.31250
y = 11.31250 +
COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X1 IGNORANDO X2.
rYX1= -0.03916
COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X2 IGNORANDO X1.
rYX2= 0.499646

10. COEFICIENTE DE CORRELACION MULTIPLE ENTRE X1, X2 IGNORANDO Y.
rX1X2= 0.83205
COEFICIENTES DE CORRELACION PARCIAL ENTRE LAS VARIABLES
Ryx1,x2= -0.94671
Ryx2,x1= 0.960231
Rx1x2,y= 0.983887
Se aprecia que la correlacion mayor es entre las variables X1 Y X2.

11. X2^2 X1X2 X1Y X2Y Yest (Yest-Ymed)^2 (Y-Ymed)^2 (Y-Yest)^2 Y^2
1 0 0 13 14.37500 1.05063 5.76000 1.890625 169
9 6 36 54 16.72500 1.75563 6.76000 1.625625 324
9 12 56 42 12.95000 6.00250 1.96000 1.1025 196
49 42 126 147 21.42500 36.30063 31.36000 0.180625 441
25 40 88 55 11.52500 15.01563 19.36000 0.275625 121
93 100 306 311 60.12500 65.20000 5.075 1251
b 19 c 20 19
b 100 c -5
b 93 c -5
b 380 c
b -500 c
-120 c 4 -120
b 361 c
b -465 c
-104 5 200
b 14400 c
b -20800 c
-6400
Sy,x= 1.30064
Spy,x= 1.007472
desv Y= 3.61109
COEF. CORRELAC r 0.960293 r 0.960293
COEF. DETERM r^2 0.9221626 r^2 0.922163
Ymed 15.4
X= 4 Y= 3.7625
X= 12 Y= -11.3375
-1.88750 X1 + 3.06250 X2

13. (Yest-Y)^2
1.050625
1.755625
6.0025
36.300625
15.015625
60.12500

14. REGRESION LINEAL MULTIPLE
ECUACIONES NORMALES
X1 X2 Y X1^2
0 1 16 0
2 3 34 4
4 5 38 16
6 5 32 36
7 7 72 49
8 9 66 64
27 30 258 169
n= 6
ECUACIONES NORMALES 258 6 a 27
1444 27 a 169
1566 30 a 177
6966 162 a 729
-8664 -162 a -1014
-1698 0 -285
7740 180 a 810
-9396 -180 a -1062
-1656 0 -252
427896 0 a 71820
-471960 0 a -71820
-44064 0 0
c = 9.00000
b = -2.00000
a = 7.00000
y = 7.00000 +
COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X1 IGNORANDO X2.
rYX1= 0.851402
COEFICIENTE DE CORRELACION MULTIPLE ENTRE Y, X2 IGNORANDO X1.

15. rYX2= 0.904845
COEFICIENTE DE CORRELACION MULTIPLE ENTRE X1, X2 IGNORANDO Y.
rX1X2= 0.963546
COEFICIENTES DE CORRELACION PARCIAL ENTRE LAS VARIABLES
Ryx1,x2= -0.17961
Ryx2,x1= 0.60201
Rx1x2,y= 0.864994
Se aprecia que la correlacion mayor es entre las variables X1 Y X2.

16. X2^2 X1X2 X1Y X2Y Yest (Yest-Ymed)^2 (Y-Ymed)^2 (Y-Yest)^2 Y^2
1 0 0 16 16.00000 729.00000 729.00000 0 256
9 6 68 102 30.00000 169.00000 81.00000 16 1156
25 20 152 190 44.00000 1.00000 25.00000 36 1444
25 30 192 160 40.00000 9.00000 121.00000 64 1024
49 49 504 504 56.00000 169.00000 841.00000 256 5184
81 72 528 594 72.00000 841.00000 529.00000 36 4356
190 177 1444 1566 1918.00000 2326.00000 408 13420
b 30 c 27 30
b 177 c -6
b 190 c -6
b 810 c
b -1062 c
-252 c 4 -252
b 900 c
b -1140 c
-240 5 285
b 63504 c
b -68400 c
-4896
Sy,x= 10.09950
Spy,x= 8.246211
18.34572
COEF. CORRELAC r 0.9080702 r 0.893285 ERROR
COEF. DETERM r^2 0.8245916 r^2 0.797959
Ymed 43
X= 4 Y= -1
X= 12 Y= -17
-2.00000 X1 + 9.00000 X2

18. (Yest-Y)^2
729
169
1
9
169
841
1918.00000

19. REGRESION LINEAL
ECUACIONES NORMALES
X Y XY X^2 Yest
1 14 14 1 15.20000
2 33 66 4 23.60000
3 20 60 9 32.00000
4 41 164 16 40.40000
5 52 260 25 48.80000
15 160 564 55
n= 5
ECUACIONES NORMALES 160 5 a 15 b
564 15 a 55 b
2400 75 a 225 b
-2820 -75 a -275 b
-420 0 -50
b = 8.40000
a = 6.80000
y = 6.80000 + 8.40000

20. (Yest-Ymed)^2 (Y-Ymed)^2 Y^2
282.24000 324.00000 196
70.56000 1.00000 1089
0.00000 144.00000 400
70.56000 81.00000 1681
282.24000 400.00000 2704
705.60000 950.00000 6070
15
-5
COEFICIENTE DE CORRELACION
Ymed 32 r 0.861822 r 0.861822
COEFICIENTE DE DETERMINACION r^2 0.742737 r^2 0.742737
X= 4 Y= 40.4
x X= 12 Y= 107.6
X= 3.5 Y= 36.2