Error Puro y Falta de Ajuste
Ernesto Barrios
Ejemolo Error Puro y Falta de Ajuste
(Simulado)
Lectura de datos y características de los mismos:
EpFa.data <- read.csv("./EpFa.dat", sep="")
dim(EpFa.data)## [1] 39 6str(EpFa.data)## 'data.frame': 39 obs. of 6 variables:
## $ i : int 1 2 3 4 5 6 7 8 9 10 ...
## $ x : int 1 1 1 2 2 2 2 2 3 3 ...
## $ y : num -2.25 7.46 5.9 0.34 15.19 ...
## $ ymed : num 3.71 3.71 3.71 7.38 7.38 7.38 7.38 7.38 6.49 6.49 ...
## $ yhat1: num -10.96 -10.96 -10.96 1.05 1.05 ...
## $ yhat2: num 3.84 3.84 3.84 6.34 6.34 ...head(EpFa.data)## i x y ymed yhat1 yhat2
## 1 1 1 -2.25 3.71 -10.96 3.84
## 2 2 1 7.46 3.71 -10.96 3.84
## 3 3 1 5.90 3.71 -10.96 3.84
## 4 4 2 0.34 7.38 1.05 6.34
## 5 5 2 15.19 7.38 1.05 6.34
## 6 6 2 3.98 7.38 1.05 6.34summary(EpFa.data)## i x y ymed
## Min. : 1.0 Min. : 1.000 Min. : -2.25 Min. : 3.71
## 1st Qu.:10.5 1st Qu.: 3.000 1st Qu.: 10.54 1st Qu.: 7.38
## Median :20.0 Median : 5.000 Median : 33.11 Median : 31.84
## Mean :20.0 Mean : 5.487 Mean : 42.94 Mean : 42.94
## 3rd Qu.:29.5 3rd Qu.: 8.000 3rd Qu.: 67.65 3rd Qu.: 71.17
## Max. :39.0 Max. :10.000 Max. :114.44 Max. :112.79
## yhat1 yhat2
## Min. :-10.96 Min. : 3.84
## 1st Qu.: 13.06 1st Qu.: 11.24
## Median : 37.09 Median : 28.19
## Mean : 42.94 Mean : 42.94
## 3rd Qu.: 73.13 3rd Qu.: 71.52
## Max. : 97.15 Max. :112.36
Ajuste modelo lineal
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.500 -7.882 -1.406 8.416 18.425
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -22.977 3.652 -6.292 2.53e-07
## x 12.013 0.594 20.224 < 2e-16
##
## Residual standard error: 10.28 on 37 degrees of freedom
## Multiple R-squared: 0.917, Adjusted R-squared: 0.9148
## F-statistic: 409 on 1 and 37 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## x 1 43256 43256 409.03 < 2.2e-16
## Residuals 37 3913 106Ajuste modelo cuadrático
##
## Call:
## lm(formula = y ~ x + I(x^2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.6446 -2.4755 0.7354 3.2211 13.5258
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.7174 3.7326 0.996 0.326
## x -1.0761 1.5490 -0.695 0.492
## I(x^2) 1.1940 0.1378 8.665 2.47e-10
##
## Residual standard error: 5.935 on 36 degrees of freedom
## Multiple R-squared: 0.9731, Adjusted R-squared: 0.9716
## F-statistic: 651.5 on 2 and 36 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## x 1 43256 43256 1228.010 < 2.2e-16
## I(x^2) 1 2645 2645 75.084 2.467e-10
## Residuals 36 1268 35Análisis de Residuales
