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Taller que incluye regresiones lineales y exponenciales con sus respectivas ecuaciones usando el metodod de minimos cuadrados.
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estudianeshoras esudio
1 13 4
10 216 320 3
PRIMERA PARTEECUACION LINEAL
Año relativo
NAÑO estud
1 1995 12 1996 33 1997 104 1998 165 1999 20
6789
101112
1314151617181920
SUMATORIA 50.0
REGRESIÒN LINEAL
horas dormirAño relativo
(año i-1995)
11.0 -1994 -643,852.210.0 -1992 -643,202.811.0 -1985 -640,930.210.0 -1979 -638,982.111.0 -1975 -637,683.5
y(Xi^2)
1 10.0
9 6.0
100 9.0
256 7.0
400 8.0
Producciòn de carbon (toneladas)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
f(x) = 0.0413533835x + 2.1864661654R² = 0.0874783112
f(x) = 0.0037593985x + 10.562406015R² = 0.0031328321
Años vs P. carbòn (Tn)
Años vs P de carbon (Tn) Linear (Años vs P de carbon (Tn) ) Regresion Lineal
Linear (Regresion Lineal)
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
766.0 0.0 40.0 0.0
(Yi^2) (Xi*Yi)
100.0 1036.0 1881.0 9049.0 11264.0 160 ∑Y
∑X∑X^2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
f(x) = 0.0413533835x + 2.1864661654R² = 0.0874783112
f(x) = 0.0037593985x + 10.562406015R² = 0.0031328321
Años vs P. carbòn (Tn)
Años vs P de carbon (Tn) Linear (Años vs P de carbon (Tn) ) Regresion Lineal
Linear (Regresion Lineal)
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
∑X*Y
N
b
330.0 390.0a
R
∑Y^2
50.0766.0
40.0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
f(x) = 0.0413533835x + 2.1864661654R² = 0.0874783112
f(x) = 0.0037593985x + 10.562406015R² = 0.0031328321
Años vs P. carbòn (Tn)
Años vs P de carbon (Tn) Linear (Años vs P de carbon (Tn) ) Regresion Lineal
Linear (Regresion Lineal)
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
330.0
390.0
20
0.45 Pendiente
0.88 Intersecciòn con el eje Y
5800.0 8006.2475604992 0.7244342566
AÑO
Año relativo
(año i-1995)
1995 01996 11997 21998 31999 42000 52001 62002 72003 82004 92005 102006 112007 122008 132009 142010 152011 162012 172013 182014 19
PRIMERA PARTEECUACION LINEAL
Año relativo
NAÑO
1 1995 02 1996 1
(año i-1995) (Xi)
3 1997 24 1998 35 1999 46 2000 57 2001 68 2002 79 2003 8
10 2004 911 2005 1012 2006 11
13 2007 1214 2008 1315 2009 1416 2010 1517 2011 1618 2012 1719 2013 1820 2014 19
SUMATORIA 190.0
REGRESIÒN LINEAL
Año relativo
(año i-1995)
4,942.0 0 3,539.84,484.0 1 3,864.56,705.0 2 4,189.12,631.0 3 4,513.82,906.0 4 4,838.53,383.0 5 5,163.24,444.0 6 5,487.84,911.0 7 5,812.54,296.0 8 6,137.27,511.0 9 6,461.88,374.0 10 6,786.59,960.0 11 7,111.28,599.0 12 7,435.86,271.0 13 7,760.56,439.0 14 8,085.29,694.0 15 8,409.99,694.0 16 8,734.510,934.0 17 9,059.27,181.0 18 9,383.99,124.0 19 9,708.5
132,483.0
(Xi^2)
0 4,942.0
1 4,484.0
Producciòn de carbon (toneladas) (Y observado)
Producciòn de carbon (toneladas) (Y* ajustado)
Producciòn de carbon (toneladas)
(Yi) observado
4 6,705.0
9 2,631.0
16 2,906.0
25 3,383.0
36 4,444.0
49 4,911.0
64 4,296.0
81 7,511.0
100 8,374.0
121 9,960.0
144 8,599.0
169 6,271.0
196 6,439.0
225 9,694.0
256 9,694.0
289 10,934.0
324 7,181.0
361 9,124.0
2,470.0 0.0 132,483.0
(Yi - Y prom)^2
∑Y1,402.20 1,966,164.84 2,829,628.62 Y prom619.53 383,817.42 4,580,242.02 ∑(Yi - Ŷi)^2
2,515.86 6,329,551.54 6,536.72 ∑(Yi - Yprom)^2-1,882.81 3,544,973.50 15,945,246.92-1,932.48 3,734,478.95 13,824,639.42 R^2-1,780.15 3,168,934.02 10,505,053.32-1,043.82 1,089,560.19 4,753,054.02-901.49 812,684.22 2,934,882.92
-1,841.16 3,389,870.15 5,420,282.421,049.17 1,100,757.69 786,502.921,587.50 2,520,156.25 3,061,975.022,848.83 8,115,832.37 11,127,895.221,163.16 1,352,941.19 3,900,032.52-1,489.51 2,218,640.04 124,714.92-1,646.18 2,709,908.59 34,280.521,284.15 1,649,041.22 9,423,979.02959.48 920,601.87 9,423,979.02
1,874.81 3,514,912.54 18,574,807.02-2,202.86 4,852,592.18 310,081.92-584.53 341,675.32 6,249,250.02
53,717,094.08 123,817,064.55
(Yi^2) (Xi*Yi)
24,423,364.0 020,106,256.0 4484
(Yi - Ŷi) (Yi - Ŷi)^2
44,957,025.0 134106,922,161.0 78938,444,836.0 1162411,444,689.0 1691519,749,136.0 2666424,117,921.0 3437718,455,616.0 3436856,415,121.0 6759970,123,876.0 8374099,201,600.0 10956073,942,801.0 10318839,325,441.0 8152341,460,721.0 9014693,973,636.0 14541093,973,636.0 155104119,552,356.0 18587851,566,761.0 12925883,247,376.0 173356
0.0 1,001,404,329.0 1,474,497.0
132,483.06,624.2
53,717,094.1123,817,064.6
0.56616
190.02,470.0
∑X∑X^2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Años vs P. carbòn (Tn)
Años vs P de carbon (Tn) Regresion Lineal
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
∑Y 132,483.0
1,001,404,329.0
∑X*Y 1,474,497.0
N 20
b 324.67 Pendiente
a 3539.79 Intersecciòn con el eje Y
R 4318170.0 5738931.8840966 0.7524344403
∑Y^2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Años vs P. carbòn (Tn)
Años vs P de carbon (Tn) Regresion Lineal
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Años vs P. carbòn (Tn)
Años vs P de carbon (Tn) Regresion Lineal
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
AÑO
Año relativo
(año i-1995)
1995 01996 11997 21998 31999 42000 52001 62002 72003 82004 92005 102006 112007 122008 132009 142010 152011 162012 172013 182014 19
PRIMERA PARTEECUACION POLINOMIAL
Año relativo
NAÑO
1 1995 02 1996 13 1997 2
(año i-1995) (Xi)
4 1998 35 1999 46 2000 57 2001 68 2002 79 2003 8
10 2004 911 2005 1012 2006 11
13 2007 1214 2008 1315 2009 1416 2010 1517 2011 1618 2012 1719 2013 1820 2014 19
SUMATORIA 190.0∑ Xi
REGRESIÒN POLINOMIAL
Año relativo
(año i-1995)
4,942.0 0 3,708.54,484.0 1 3,979.96,705.0 2 4,257.22,631.0 3 4,540.42,906.0 4 4,829.53,383.0 5 5,124.64,444.0 6 5,425.64,911.0 7 5,732.54,296.0 8 6,045.37,511.0 9 6,364.18,374.0 10 6,688.89,960.0 11 7,019.48,599.0 12 7,355.96,271.0 13 7,698.36,439.0 14 8,046.69,694.0 15 8,400.99,694.0 16 8,761.110,934.0 17 9,127.27,181.0 18 9,499.29,124.0 19 9,877.2
132,483.0
(Xi^2) (Xi^3) (Xi^4)
0 0 01 1 14 8 16
Producciòn de carbon (toneladas) (Yi observado)
Producciòn de carbon (toneladas) (Y* ajustado)
9 27 8116 64 25625 125 62536 216 129649 343 240164 512 409681 729 6561
100 1000 10000121 1331 14641144 1728 20736169 2197 28561196 2744 38416225 3375 50625256 4096 65536289 4913 83521324 5832 104976361 6859 130321
2,470.0 36,100.0 562,666.0∑ Xi^2 ∑ Xi^3 ∑ Xi^4
(Yi - Y prom)^2
∑Y1,233.54 1,521,620.93 2,829,628.62 Y prom504.15 254,167.22 4,580,242.02 ∑(Yi - Ŷi)^2
2,447.84 5,991,920.67 6,536.72 ∑(Yi - Yprom)^2-1,909.39 3,645,770.17 15,945,246.92-1,923.54 3,700,006.13 13,824,639.42 R^2-1,741.61 3,033,205.39 10,505,053.32-981.60 963,538.56 4,753,054.02-821.51 674,878.68 2,934,882.92
-1,749.34 3,060,190.44 5,420,282.421,146.91 1,315,402.55 786,502.921,685.24 2,840,033.86 3,061,975.022,940.65 8,647,422.42 11,127,895.221,243.14 1,545,397.06 3,900,032.52-1,427.29 2,037,156.74 124,714.92-1,607.64 2,584,506.37 34,280.521,293.09 1,672,081.75 9,423,979.02932.90 870,302.41 9,423,979.02
1,806.79 3,264,490.10 18,574,807.02-2,318.24 5,374,236.70 310,081.92-753.19 567,295.18 6,249,250.02
53,563,623.3 123,817,064.55
(Yi^2) (Xi*Yi) ((Xi^2)*Yi)
4,942.0 24,423,364.0 0 04,484.0 20,106,256.0 4484 44846,705.0 44,957,025.0 13410 26820
(Yi - Ŷi) (Yi - Ŷi)^2
∑ (Yi-Y*i) ^2
Producciòn de carbon (toneladas)
(Yi)
2,631.0 6,922,161.0 7893 236792,906.0 8,444,836.0 11624 464963,383.0 11,444,689.0 16915 845754,444.0 19,749,136.0 26664 1599844,911.0 24,117,921.0 34377 2406394,296.0 18,455,616.0 34368 2749447,511.0 56,415,121.0 67599 6083918,374.0 70,123,876.0 83740 8374009,960.0 99,201,600.0 109560 1205160
8,599.0 73,942,801.0 103188 12382566,271.0 39,325,441.0 81523 10597996,439.0 41,460,721.0 90146 12620449,694.0 93,973,636.0 145410 21811509,694.0 93,973,636.0 155104 248166410,934.0 119,552,356.0 185878 31599267,181.0 51,566,761.0 129258 23266449,124.0 83,247,376.0 173356 3293764
132,483.0 1,001,404,329.0 1,474,497.0 20,515,819.0∑ Yi ∑ (XiYi) ∑ ((Xi^2)Yi)
132,483.06,624.2
53,563,623.3123,817,064.6
0.56740
∑ Xi 190.0∑ Xi^2 2,470.0
36,100.0562,666.0
∑ Xi^3∑ Xi^4
132,483.01,474,497.0
20,515,819.0
N 20
b 268.43 Pendiente
a 3708.46 Determina si la curva es concava o convexa, el grado del punto donde se aleja de la recta
c 2.96 Coeficiente de posiciòn
R 0.75 R^2
∑ Yi
∑ (XiYi)
∑ ((Xi^2)Yi)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Años vs P. carbòn (Tn)
Años vs P de carbon (Tn) Polynomial (Años vs P de carbon (Tn) )
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
Determina si la curva es concava o convexa, el grado del punto donde se aleja de la recta
Coeficiente de posiciòn
0.5661575869
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Años vs P. carbòn (Tn)
Años vs P de carbon (Tn) Polynomial (Años vs P de carbon (Tn) )
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Años vs P. carbòn (Tn)
Años vs P de carbon (Tn) Polynomial (Años vs P de carbon (Tn) )
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
AÑO Año relativo
1995 1 4,942.01996 2 4,484.01997 3 6,705.0 16,131.01998 4 2,631.0 13,820.0 5377.01999 5 2,906.0 12,242.0 4606.72000 6 3,383.0 8,920.0 4080.72001 7 4,444.0 10,733.0 2973.32002 8 4,911.0 12,738.0 3577.72003 9 4,296.0 13,651.0 4246.02004 10 7,511.0 16,718.0 4550.32005 11 8,374.0 20,181.0 5572.72006 12 9,960.0 25,845.0 6727.02007 13 8,599.0 26,933.0 8615.02008 14 6,271.0 24,830.0 8977.72009 15 6,439.0 21,309.0 8276.72010 16 9,694.0 22,404.0 7103.02011 17 9,694.0 25,827.0 7468.02012 18 10,934.0 30,322.0 8609.02013 19 7,181.0 27,809.0 10107.32014 20 9,124.0 27,239.0 9269.7
110,137.7
PRIMERA PARTEECUACION LINEAL
Año relativo
N AÑO (Xi^2)
1995 01996 1
Producciòn de carbon (toneladas)
Total Movil a 3 años (Tn)
Promedio Movil a 3 años (Tn) (Yi observado)
(año i-1995) (Xi)
1997 21 1998 3 92 1999 4 163 2000 5 254 2001 6 365 2002 7 496 2003 8 647 2004 9 818 2005 10 1009 2006 11 121
10 2007 12 14411 2008 13 16912 2009 14 19613 2010 15 22514 2011 16 25615 2012 17 28916 2013 18 32417 2014 19 361
SUMATORIA 187.0 2,465.0 0.0
REGRESIÒN LINEAL
Año relativo
(año i-1998)
4 3,778.6 1,598.42 2,554,946.505 4,164.3 442.36 195,682.376 4,550.0 -469.37 220,308.207 4,935.8 -1,962.44 3,851,170.758 5,321.5 -1,743.83 3,040,943.079 5,707.2 -1,461.23 2,135,193.1110 6,093.0 -1,542.63 2,379,707.3211 6,478.7 -906.02 820,872.2412 6,864.4 -137.42 18,884.2613 7,250.2 1,364.85 1,862,815.5214 7,635.9 1,341.79 1,800,400.4015 8,021.6 255.06 65,055.6016 8,407.3 -1,304.34 1,701,302.8417 8,793.1 -1,325.07 1,755,810.5018 9,178.8 -569.80 324,672.0419 9,564.5 542.80 294,631.8420 9,950.3 -680.59 463,202.75
23,485,599.3
(Yi^2) (Xi*Yi)
Producciòn de carbon (toneladas)(Y* ajustado)
(Yi - Ŷi) (Yi - Ŷi)^2
∑ (Yi-Y*i) ^2
Producciòn de carbon (toneladas) (Yi)
observado
5,377.0 28,912,129.0 161314,606.7 21,221,408.5 18426.684,080.7 16,651,867.6 20403.352,973.3 8,840,691.3 17839.983,577.7 12,799,722.6 25043.694,246.0 18,028,516.0 339684,550.3 20,705,503.1 40952.975,572.7 31,054,650.9 55726.76,727.0 45,252,529.0 739978,615.0 74,218,225.0 1033808,977.7 80,598,558.6 116709.718,276.7 68,503,266.3 115873.387,103.0 50,452,609.0 1065457,468.0 55,771,024.0 1194888,609.0 74,114,881.0 146353
10,107.3 102,158,119.7 181931.949,269.7 85,926,781.9 176123.73
110,137.7 795,210,483.6 1,368,894.1
(Yi - Y prom)^2
∑Y 110,137.7Y prom 6,478.7∑(Yi - Ŷi)^2 23,485,599.3∑(Yi - Yprom)^2 81,662,921.5
1,213,714.383,504,447.87 R^2 0.71241
5,750,485.8112,287,528.118,415,899.984,984,891.503,718,560.95820,866.9161,659.32
4,563,832.986,244,915.743,232,742.66389,766.65978,740.10
4,538,233.2313,167,049.597,789,585.78
81,662,921.54
∑Xi 187.0∑Xi^2 2,465.0
∑Yi 110,137.7
∑Yi^2 795,210,483.6
∑X*Y 1,368,894.1
N 17
b 385.73 Pendiente
a 2235.66 Intersecciòn con el eje Y
R 2675454.1 3103069.1912
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
f(x) = 385.7344362745x + 2621.3426960784R² = 0.7433820567
Años vs P. carbòn (Tn)
Años vs P de carbon (Tn) Media Movil
AñosP
rod
ucc
iòn
de
ca
rbo
n (
To
ne
lad
as)
Intersecciòn con el eje Y
0.8621960663
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
f(x) = 385.7344362745x + 2621.3426960784R² = 0.7433820567
Años vs P. carbòn (Tn)
Años vs P de carbon (Tn) Media Movil
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Años vs P. carbòn (Tn)
Media Movil
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Años vs P. carbòn (Tn)
Media Movil
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Años vs P. carbòn (Tn)
Media Movil
Años
Pro
du
cciò
n d
e c
arb
on
(T
on
ela
da
s)
METODO
Regresion lineal 0.75Regresion Polinomial 0.75Media movil a tres periodos 0.86
Valor de R (Coef. de correlaciòn)
0.566 10,0330.567 10,2610.71 10,336
Valor e R^2 (Coef. de determinaciòn)
Exportaciòn de carbòn año 2015 en (Toneladas)