X=c(15.50,23.75,8.00,17.00,5.50,19.00,24.00,2.50,7.50,11.00,13.00,3.75,25.00,9.75,22.00,18.00,6.00,12.50,2.00,21.50)
Y=c(2158.70,1678.15,2316.00,2061.30,2207.50,1708.30,1784.70,2575.00,2357.90,2256.70,2165.20,2399.55,1779.80,2336.75,1765.30,2053.50,2414.40,2200.50,2654.20,1753.70)
N=20
P=2
Model=lm(Y ~ X)
summary(Model)
##
## Call:
## lm(formula = Y ~ X)
##
## Residuals:
## Min 1Q Median 3Q Max
## -215.98 -50.68 28.74 66.61 106.76
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2627.822 44.184 59.48 < 2e-16 ***
## X -37.154 2.889 -12.86 1.64e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 96.11 on 18 degrees of freedom
## Multiple R-squared: 0.9018, Adjusted R-squared: 0.8964
## F-statistic: 165.4 on 1 and 18 DF, p-value: 1.643e-10
names(Model)
## [1] "coefficients" "residuals" "effects" "rank"
## [5] "fitted.values" "assign" "qr" "df.residual"
## [9] "xlevels" "call" "terms" "model"
Model$residuals
## 1 2 3 4 5 6
## 106.758301 -67.274574 -14.593631 65.088687 -215.977609 -213.604131
## 7 8 9 10 11 12
## 48.563824 40.061618 8.729573 37.567141 20.374323 -88.946393
## 13 14 15 16 17 18
## 80.817415 71.175153 -45.143358 94.442278 9.499187 37.097528
## 19 20
## 100.684823 -75.320154
Model$df.residual
## [1] 18
Y_Est=fitted.values(Model)
Y_Est
## 1 2 3 4 5 6 7 8
## 2051.942 1745.425 2330.594 1996.211 2423.478 1921.904 1736.136 2534.938
## 9 10 11 12 13 14 15 16
## 2349.170 2219.133 2144.826 2488.496 1698.983 2265.575 1810.443 1959.058
## 17 18 19 20
## 2404.901 2163.402 2553.515 1829.020
Residuals=residuals(Model)
Residuals
## 1 2 3 4 5 6
## 106.758301 -67.274574 -14.593631 65.088687 -215.977609 -213.604131
## 7 8 9 10 11 12
## 48.563824 40.061618 8.729573 37.567141 20.374323 -88.946393
## 13 14 15 16 17 18
## 80.817415 71.175153 -45.143358 94.442278 9.499187 37.097528
## 19 20
## 100.684823 -75.320154
SCRes=sum((Y-Y_Est)^2)
gl_SCRes = N-P
s2=SCRes/gl_SCRes
Fuente=c("regresión","Residual","Total")
Fuente
## [1] "regresión" "Residual" "Total"
SCTotal=sum((Y-mean(Y))^2)
gl_SCTotal= N-1
SCReg=sum((Y_Est-mean(Y))^2)
gl_SCReg=1
Fuente=c("regresión","Residual","Total")
suma_cuadrados=c(SCReg,SCRes,SCTotal)
suma_cuadrados
## [1] 1527482.7 166254.9 1693737.6
GL=c(gl_SCReg,gl_SCRes,gl_SCTotal)
GL
## [1] 1 18 19
cuadrados_medios=c(SCReg/gl_SCReg,SCRes/gl_SCRes,NA)
cuadrados_medios
## [1] 1527482.743 9236.381 NA
fo=c(cuadrados_medios[1]/cuadrados_medios[2],NA,NA)
fo
## [1] 165.3768 NA NA
Tabla=cbind(Fuente,suma_cuadrados,GL,cuadrados_medios,fo)
Tabla
## Fuente suma_cuadrados GL cuadrados_medios fo
## [1,] "regresión" "1527482.74330802" "1" "1527482.74330802" "165.376757703329"
## [2,] "Residual" "166254.858066981" "18" "9236.38100372114" NA
## [3,] "Total" "1693737.601375" "19" NA NA