Regresion Lineal Aplicando Min Cuadrados

7/24/2019 Regresion Lineal Aplicando Min Cuadrados

1/15

Xi Yi XiYi (Xi)^2 Sr

1 0.5 0.5 1 0.16868622

2 2.5 5 4 0.5625

3 2 6 9 0.34725765

4 4 16 16 0.32653061

5 3.5 17.5 25 0.58960459

6 6 36 36 0.797193887 5.5 38.5 49 0.19929847

SUMATORIA 28 24 119.5 140 2.99107143

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

MODELO LINEAL

X

Y


2/15

St MEDIA Y MEDIA X a

8.57653061 3.42857143 4 0.07142857

0.8622449

2.04081633

0.32653061 S!"X S! r

0.00510204 0.7734 1.9457 0.9318

6.61224494.29081633

22.7142857 #$%& &i'%a& Y 007142857*0

8


3/15

ai

0.8392857143

+'$i,i'

MODE-O UE/O

83928571X


4/15

Xi Yi -' Yi Xi -'Yi (Xi)^2

1 0.5 0.69314718 0.69314718 1

2 2.5 0.91629073 1.83258146 4

3 2 0.69314718 2.07944154 9

4 4 1.38629436 5.54517744 16

5 3.5 1.25276297 6.26381484 25

6 6 1.79175947 10.7505568 367 5.5 1.70474809 11.9332366 49

SUMATORIA 28 24 7.05185562 37.7116616 140

0 1 2 3 4 5

1

0.5

0

0.5

1

1.5

2

MODELO EXPONENCIAL

X

Y


5/15

Sr St MEDIA -'Y MEDIA X

0.4654566 2.89188774 1.00740795 4

0.3454583 0.00830235

0.00063385 0.09875983 S!"X S!

0.14355492 0.14355492 0.4643 0.8470

0.00885144 0.06019909

0.01112546 0.615207310.1030225 0.48628328

1.07810306 4.30419451 ai i

0.70444819 0.33943711

#$%& %'%',ia&

6 7 8


6/15

a ai #$%& &i'%a&

0.350340494 0.33943711

r +'$i,i'

0.8657MODE-O UE/O

#$%& %'%',ia&

Y 070444819%(033943711X)


7/15

Xi Yi & Xi - Yi -Xi-Yi

1 0.5 0 0.30103 0

2 2.5 0.30103 0.39794001 0.11979188

3 2 0.47712125 0.30103 0.14362781

4 4 0.60205999 0.60205999 0.36247623

5 3.5 0.69897 0.54406804 0.38028724

6 6 0.77815125 0.77815125 0.605519377 5.5 0.84509804 0.74036269 0.62567906

SUMATORIA 28 24 3.70243054 3.06258198 2.23738159


8/15

(-Xi)^2 Sr St MEDIA -Y

0 0.01515807 0.54544385 0.43751171

0.09061906 0.05089007 0.00156592

0.22764469 0.0058084 0.01862726 S!"X

0.36247623 0.00631145 0.02707614 0.1366

0.48855907 0.00833697 0.01135425

0.60551937 0.0025649 0.11603530.7141907 0.00423017 0.09171871

2.48900912 0.09330002 0.81182143 a2

0.66387775

#$%& t%


9/15

MEDIA -X a ai #$%& &i'%a&

0.52891865 0.1779118842 1.1635505734

S! r +'$i,i'

0.3678 0.9408 #$%& %'

2 #$%& t%',ia&

1.16355057

,ia& Y 066387775X (116355057)


10/15

Xi Yi Xi^2 Xi^3 Xi^4

1 0.5 1 1 1

2 2.5 4 8 16

3 2 9 27 81

4 4 16 64 256

5 3.5 25 125 625

6 6 36 216 12967 5.5 49 343 2401

SUMATORIA 28 24 140 784 4676

MATRI I/ERSA

7 28 140 24

28 140 784 119.5

140 784 4676 665.5

2.42857143 1.28571429 0.14285714 0.28571429

1.28571429 0.79761905 0.0952381 1.07738095

0.14285714 0.0952381 0.01190476 0.0297619


11/15

XiYi (Xi^2)Yi Sr St #%$ia Y

0.5 0.5 0.068594104 8.57653061 3.42857143

5 10 0.5625 0.8622449

6 18 0.460459184 2.04081633

16 64 0.204648526 0.32653061

17.5 87.5 0.734693878 0.00510204

36 216 0.797193878 6.612244938.5 269.5 0.088577098 4.29081633

119.5 665.5 2.916666667 22.7142857

a

a1

a2


12/15

S!"X S! r +'$i,i'

0.8539 1.9457 0.9336 UE/O

M$%& &i'#ia& Y 02857*1077X002976X^2)


13/15

X1 X2 Y X1(^2) X2(^2) X1X2

0 0 5 0 0 0

2 1 10 4 1 2

2.5 2 9 6.25 4 5

1 3 0 1 9 3

4 6 3 16 36 24

7 2 27 49 4 1416.5 14 54 76.25 54 48

MATRI I/ERSA

6 16.5 14 54

16.5 76.25 48 243.5

14 48 54 100

I/ERSA0.53174021 0.06421346 0.08077994 a

0.06421346 0.03753115 0.01671309 a1

0.08077994 0.01671309 0.05431755 a2


14/15

X1Y X2Y Sr St

0 0 7.88861E029 16

20 10 0 1

22.5 18 0 0

0 0 0 81

12 18 0 36

189 54 0 324243.5 100 7.88861E029 458

5

4

3


15/15

#%$ia Y S!"X S! r +'$i,i'

9 7.03102293E15 9.5708 1.0000 UE/O

MODE-O Y 5*4X13X2

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Regresion Lineal Aplicando Min Cuadrados