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“Regresión NO lineal”
Dr. Jorge Alejandro Obando Bastidas
Esta matriz determina si existe o no un
modelo de regresión; pero no nos garantiza
como es este modelo, de que tipo, si es
lineal, cuadrático, exponencial o logaritmico
El numero de
contagiados de Covid
19 y el día de
contagio son significativas
en un modelo
Hipótesis
Una hipótesis
es un
enunciado no
verificado
Al ser refutado o
confirmado dejará de
ser hipótesis y sería un
enunciado verificado
La hipótesis es una
conjetura científica
que requiere una
contrastación con la
experiencia.​
Los datos son también consistentes
con el modelo ideal elegido.
Tipos de hipótesis
Hipótesis nula verdadera Hipótesis nula falsa
No hay evidencias de
una relación entre las
variables y el modelo
concluye que
No es el modelo apropiado. Puede
existir una relación en la población,
pero la muestra elegida no la detecta.
concluye que
El modelo es apropiado.
Puede que exista una
relación lineal o no lineal.
por lo que Entonces
P-valor
Para determinar esta significancia
en el modelo es necesario obtener
el p-valor de la relación.
Ho: El numero de contagiados de Covid 19 y el día de
contagio, NO, son significativas en un modelo
Ha: El numero de contagiados de Covid 19 y el día de
contagio son significativas en un modelo
La probabilidad de que un valor
estadístico calculado sea posible
dada una hipótesis nula cierta.
Se define como
Si el modelo es ideal, siendo la hipótesis
alternativa verdadera y el R2, se acerca al
100%, entonces, la ecuación matemática que
se construye desde la correlación de los datos,
predice con certeza el comportamiento de los
mismos.
El R2
Matriz de correlación: 0,9972944 1. Como el valor de la matriz de correlación es
cercano a uno, los datos indican que pueden ser
representados por un buen modelo.
Hipótesis
Ho: El crecimiento de los contagios a covid-19 en Colombia no tienen
un comportamiento lineal
Ha: El crecimiento de los contagios a covid-19 en Colombia tienen un
comportamiento lineal
Hipótesis
Ho: El crecimiento de los contagios a covid-19 en Colombia no tienen
un comportamiento cuadrático
Ha: El crecimiento de los contagios a covid-19 en Colombia tienen un
comportamiento cuadrático
y = 154x - 84.202
R² = 0.9946
0
500
1000
1500
2000
2500
3000
3500
4000
0 5 10 15 20 25
Regresión lineal
y = 0.831x2 + 134.05x - 1.0988
R² = 0.9956
0
500
1000
1500
2000
2500
3000
3500
4000
0 5 10 15 20 25
Modelo de regresion cuadrática
y = -0.2863x3 + 11.139x2 + 32.973x + 222.25
R² = 0.9996
0
500
1000
1500
2000
2500
3000
3500
4000
0 5 10 15 20 25
Modelo de correlación cúbica
y = 361.96e0.112x
R² = 0.9352
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 5 10 15 20 25
Modelo de regresión exponencial
y = 1146.1ln(x) - 807.95
R² = 0.8181
-1500
-1000
-500
0
500
1000
1500
2000
2500
3000
3500
4000
0 5 10 15 20 25
Regresión logaritmica
Modelo R2 Modelo
Lineal 0,9946y = 154x - 84,202
Cuadratico 0,9956y = 0,831x2 + 134,05x - 1,0988
Cubico 0,9996y = -0,2863x3 + 11,139x2 + 32,973x + 222,25
Exponencial 0,9352y = 361,96e0,112x
Logaritmico 0,8181 y = 1146,1ln(x) - 807,95
Los datos se ajustan a un modelo
cuadrático de la forma:
𝒚 = 𝒂𝒙𝟐+bx +c
Los datos se ajustan a una
curva cubica de la forma:
𝒚 = 𝒂𝒙𝟑 + 𝒃𝒙𝟐 + 𝒄𝒙 + 𝒅
Los datos se exponen como una
curva normal creciente de la
forma
𝒚 = 𝒃𝒂𝒙
Modelo Expresión Matemática Coeficientes de correlación
Lineal 𝑦 = 𝛽1 + 𝛽2𝑥
𝑟𝑥𝑦 =
𝐶𝑜𝑣(𝑥, 𝑦)
𝑠𝑥𝑠𝑦
Cuadrático 𝑦 = 𝛽1 + 𝛽2𝑥 + 𝛽3𝑥2 Ecuación de predicción
𝑦 = 𝛽1 + 𝛽2𝑥 + 𝛽3𝑥2
𝑟𝑥𝑦 =
1
𝑛
= 1 𝑦1 − 𝑦 2
1
𝑛
= 1 𝑦1 − 𝑦 2
Cubico 𝑦 = 𝛽1 + 𝛽2𝑥 + 𝛽3𝑥2 + 𝛽4𝑥3
𝑦 = 𝛽1 + 𝛽2𝑥 + 𝛽3𝑥2 + 𝛽4𝑥3
𝑟𝑥𝑦 =
1
𝑛
= 1 𝑦1 − 𝑦 2
1
𝑛
= 1 𝑦1 − 𝑦 2
Potencial 𝑦 = 𝑎 ∗ 𝑥𝑏
𝑟𝑙𝑜𝑥 𝑥 𝑙𝑜𝑔𝑦 =
𝑐𝑜𝑣(log 𝑥 , log 𝑦 )
𝑠𝑙𝑜𝑔(𝑥)
𝑠𝑙𝑜𝑔(𝑦)
Exponencial 𝑦 = 𝑎 ∗ 𝑏𝑥
𝑟𝑥𝑙𝑜𝑔 𝑦
=
𝑐𝑜𝑣(x, log 𝑦 )
𝑠𝑥𝑠𝑙𝑜𝑔(𝑦)
Logarítmico 𝑦 = 𝑎 + 𝑏 ∗ log(𝑥)
𝑟𝑙𝑜𝑥 𝑥 𝑦 =
𝑐𝑜𝑣(log 𝑥 , 𝑦)
𝑠𝑙𝑜𝑔(𝑥)
𝑠𝑦
Modelos matemáticos que explican una relación en R-Kward
Dr. Jorge Alejandro Obando Bastidas
Jorge.obandob@campusucc.edu.co

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Semana13-Semana11 rlm

  • 1. “Regresión NO lineal” Dr. Jorge Alejandro Obando Bastidas
  • 2.
  • 3.
  • 4. Esta matriz determina si existe o no un modelo de regresión; pero no nos garantiza como es este modelo, de que tipo, si es lineal, cuadrático, exponencial o logaritmico
  • 5. El numero de contagiados de Covid 19 y el día de contagio son significativas en un modelo Hipótesis Una hipótesis es un enunciado no verificado Al ser refutado o confirmado dejará de ser hipótesis y sería un enunciado verificado La hipótesis es una conjetura científica que requiere una contrastación con la experiencia.​
  • 6. Los datos son también consistentes con el modelo ideal elegido. Tipos de hipótesis Hipótesis nula verdadera Hipótesis nula falsa No hay evidencias de una relación entre las variables y el modelo concluye que No es el modelo apropiado. Puede existir una relación en la población, pero la muestra elegida no la detecta. concluye que El modelo es apropiado. Puede que exista una relación lineal o no lineal. por lo que Entonces
  • 7. P-valor Para determinar esta significancia en el modelo es necesario obtener el p-valor de la relación. Ho: El numero de contagiados de Covid 19 y el día de contagio, NO, son significativas en un modelo Ha: El numero de contagiados de Covid 19 y el día de contagio son significativas en un modelo La probabilidad de que un valor estadístico calculado sea posible dada una hipótesis nula cierta. Se define como
  • 8. Si el modelo es ideal, siendo la hipótesis alternativa verdadera y el R2, se acerca al 100%, entonces, la ecuación matemática que se construye desde la correlación de los datos, predice con certeza el comportamiento de los mismos. El R2
  • 9. Matriz de correlación: 0,9972944 1. Como el valor de la matriz de correlación es cercano a uno, los datos indican que pueden ser representados por un buen modelo. Hipótesis Ho: El crecimiento de los contagios a covid-19 en Colombia no tienen un comportamiento lineal Ha: El crecimiento de los contagios a covid-19 en Colombia tienen un comportamiento lineal Hipótesis Ho: El crecimiento de los contagios a covid-19 en Colombia no tienen un comportamiento cuadrático Ha: El crecimiento de los contagios a covid-19 en Colombia tienen un comportamiento cuadrático
  • 10. y = 154x - 84.202 R² = 0.9946 0 500 1000 1500 2000 2500 3000 3500 4000 0 5 10 15 20 25 Regresión lineal y = 0.831x2 + 134.05x - 1.0988 R² = 0.9956 0 500 1000 1500 2000 2500 3000 3500 4000 0 5 10 15 20 25 Modelo de regresion cuadrática y = -0.2863x3 + 11.139x2 + 32.973x + 222.25 R² = 0.9996 0 500 1000 1500 2000 2500 3000 3500 4000 0 5 10 15 20 25 Modelo de correlación cúbica y = 361.96e0.112x R² = 0.9352 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 5 10 15 20 25 Modelo de regresión exponencial y = 1146.1ln(x) - 807.95 R² = 0.8181 -1500 -1000 -500 0 500 1000 1500 2000 2500 3000 3500 4000 0 5 10 15 20 25 Regresión logaritmica Modelo R2 Modelo Lineal 0,9946y = 154x - 84,202 Cuadratico 0,9956y = 0,831x2 + 134,05x - 1,0988 Cubico 0,9996y = -0,2863x3 + 11,139x2 + 32,973x + 222,25 Exponencial 0,9352y = 361,96e0,112x Logaritmico 0,8181 y = 1146,1ln(x) - 807,95
  • 11. Los datos se ajustan a un modelo cuadrático de la forma: 𝒚 = 𝒂𝒙𝟐+bx +c
  • 12. Los datos se ajustan a una curva cubica de la forma: 𝒚 = 𝒂𝒙𝟑 + 𝒃𝒙𝟐 + 𝒄𝒙 + 𝒅
  • 13. Los datos se exponen como una curva normal creciente de la forma 𝒚 = 𝒃𝒂𝒙
  • 14. Modelo Expresión Matemática Coeficientes de correlación Lineal 𝑦 = 𝛽1 + 𝛽2𝑥 𝑟𝑥𝑦 = 𝐶𝑜𝑣(𝑥, 𝑦) 𝑠𝑥𝑠𝑦 Cuadrático 𝑦 = 𝛽1 + 𝛽2𝑥 + 𝛽3𝑥2 Ecuación de predicción 𝑦 = 𝛽1 + 𝛽2𝑥 + 𝛽3𝑥2 𝑟𝑥𝑦 = 1 𝑛 = 1 𝑦1 − 𝑦 2 1 𝑛 = 1 𝑦1 − 𝑦 2 Cubico 𝑦 = 𝛽1 + 𝛽2𝑥 + 𝛽3𝑥2 + 𝛽4𝑥3 𝑦 = 𝛽1 + 𝛽2𝑥 + 𝛽3𝑥2 + 𝛽4𝑥3 𝑟𝑥𝑦 = 1 𝑛 = 1 𝑦1 − 𝑦 2 1 𝑛 = 1 𝑦1 − 𝑦 2 Potencial 𝑦 = 𝑎 ∗ 𝑥𝑏 𝑟𝑙𝑜𝑥 𝑥 𝑙𝑜𝑔𝑦 = 𝑐𝑜𝑣(log 𝑥 , log 𝑦 ) 𝑠𝑙𝑜𝑔(𝑥) 𝑠𝑙𝑜𝑔(𝑦) Exponencial 𝑦 = 𝑎 ∗ 𝑏𝑥 𝑟𝑥𝑙𝑜𝑔 𝑦 = 𝑐𝑜𝑣(x, log 𝑦 ) 𝑠𝑥𝑠𝑙𝑜𝑔(𝑦) Logarítmico 𝑦 = 𝑎 + 𝑏 ∗ log(𝑥) 𝑟𝑙𝑜𝑥 𝑥 𝑦 = 𝑐𝑜𝑣(log 𝑥 , 𝑦) 𝑠𝑙𝑜𝑔(𝑥) 𝑠𝑦 Modelos matemáticos que explican una relación en R-Kward
  • 15. Dr. Jorge Alejandro Obando Bastidas Jorge.obandob@campusucc.edu.co