Tarea 15

library("gdata")
## gdata: read.xls support for 'XLS' (Excel 97-2004) files ENABLED.
## 
## gdata: read.xls support for 'XLSX' (Excel 2007+) files ENABLED.
## 
## Attaching package: 'gdata'
## The following object is masked from 'package:stats':
## 
##     nobs
## The following object is masked from 'package:utils':
## 
##     object.size
fc = read.xls("/Users/ferarevalo1/Documents/Econometria 1 /Fotocopias .xls")
fc
##    copias estufm otrasus escolares otros  total
## 1  55.786 33.813   1.758     1.853 2.336 39.760
## 2  55.734 30.431   1.352     2.317 1.906 36.006
## 3  51.222 27.226   1.737     1.695 1.547 32.205
## 4  27.344 15.366   1.165     0.872 2.084 19.487
## 5  52.456 31.724   1.255     1.328 2.177 36.484
## 6  47.630 26.745   1.140     2.915 1.821 32.621
## 7  43.670 31.612   1.594     1.835 1.439 36.480
## 8  15.314 20.357   0.768     0.307 1.144 22.576
## 9  67.434 36.322   1.799     1.917 2.790 42.828
## 10 59.024 29.418   0.962     1.712 1.624 33.716
## 11 60.868 29.728   1.352     1.634 0.811 33.525
## 12 27.214 14.993   0.890     0.307 0.275 16.465
## 13 57.632 36.361   1.865     2.066 2.622 42.914
## 14 57.518 38.427   1.276     2.759 2.188 44.650
## 15 48.266 28.327   1.580     1.933 2.111 33.951
## 16 29.928 21.425   1.163     0.514 1.325 24.427
## 17 56.128 36.398   1.930     2.214 2.451 42.993
## 18 46.948 30.474   1.670     1.874 2.103 36.121
## 19 37.942 22.712   1.948     1.342 1.716 27.718
## 20 19.682 17.772   0.938     0.341 1.153 20.204
## 21 45.282 28.261   1.939     1.741 1.639 33.580
## 22 67.546 27.090   1.711     2.323 1.796 32.920
## 23 65.364 23.751   2.210     1.732 1.658 29.351
## 24 30.064 12.827   0.710     0.182 0.672 14.391
reg = lm(formula = fc$copias ~ fc$estufm+fc$otrasus+fc$escolares+fc$otros, data = fc)
summary(reg)
## 
## Call:
## lm(formula = fc$copias ~ fc$estufm + fc$otrasus + fc$escolares + 
##     fc$otros, data = fc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.5838  -5.9892  -0.7439   8.0433  13.2489 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept)    5.1790     8.5258   0.607   0.5507  
## fc$estufm      0.7665     0.4719   1.624   0.1208  
## fc$otrasus     9.4056     5.4859   1.715   0.1027  
## fc$escolares   9.0494     3.9891   2.269   0.0351 *
## fc$otros      -3.9982     4.5433  -0.880   0.3898  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.651 on 19 degrees of freedom
## Multiple R-squared:  0.7279, Adjusted R-squared:  0.6706 
## F-statistic: 12.71 on 4 and 19 DF,  p-value: 3.375e-05
reg1 = lm(formula = fc$copias ~ 0 +fc$estufm+fc$otrasus+fc$escolares+fc$otros, data = fc)
summary(reg1)
## 
## Call:
## lm(formula = fc$copias ~ 0 + fc$estufm + fc$otrasus + fc$escolares + 
##     fc$otros, data = fc)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -12.133  -5.803  -0.969   7.632  13.913 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## fc$estufm      0.9429     0.3659   2.577   0.0180 *
## fc$otrasus    10.8706     4.8489   2.242   0.0365 *
## fc$escolares   7.9885     3.5293   2.263   0.0349 *
## fc$otros      -4.1638     4.4630  -0.933   0.3620  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.514 on 20 degrees of freedom
## Multiple R-squared:  0.975,  Adjusted R-squared:   0.97 
## F-statistic: 195.2 on 4 and 20 DF,  p-value: 1.013e-15
reg2 = lm(formula = fc$copias ~ 0 +fc$estufm+fc$otrasus+fc$escolares, data = fc)
summary(reg2)
## 
## Call:
## lm(formula = fc$copias ~ 0 + fc$estufm + fc$otrasus + fc$escolares, 
##     data = fc)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -10.076  -6.146  -1.940   6.358  14.164 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## fc$estufm      0.7726     0.3162   2.444   0.0235 *
## fc$otrasus     9.5605     4.6268   2.066   0.0514 .
## fc$escolares   7.5549     3.4878   2.166   0.0420 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.487 on 21 degrees of freedom
## Multiple R-squared:  0.9739, Adjusted R-squared:  0.9702 
## F-statistic: 261.6 on 3 and 21 DF,  p-value: < 2.2e-16
reg3 = lm(formula = fc$estufm ~ 0 +fc$otrasus+fc$escolares, data = fc)
summary(reg3)
## 
## Call:
## lm(formula = fc$estufm ~ 0 + fc$otrasus + fc$escolares, data = fc)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -11.645  -2.913   2.210   4.466  10.077 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## fc$otrasus     10.647      2.141   4.974 5.61e-05 ***
## fc$escolares    6.850      1.844   3.716   0.0012 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.723 on 22 degrees of freedom
## Multiple R-squared:  0.9618, Adjusted R-squared:  0.9584 
## F-statistic: 277.2 on 2 and 22 DF,  p-value: 2.504e-16
reg4 = lm(formula = fc$otrasus ~ 0+fc$estufm+fc$escolares, data = fc)
summary(reg4)
## 
## Call:
## lm(formula = fc$otrasus ~ 0 + fc$estufm + fc$escolares, data = fc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.73694 -0.20174  0.03999  0.16938  0.96485 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## fc$estufm    0.049715   0.009995   4.974 5.61e-05 ***
## fc$escolares 0.037161   0.160520   0.232    0.819    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3911 on 22 degrees of freedom
## Multiple R-squared:  0.938,  Adjusted R-squared:  0.9324 
## F-statistic: 166.5 on 2 and 22 DF,  p-value: 5.176e-14
reg5 = lm(formula = fc$escolares ~ 0+fc$estufm+fc$otrasus, data = fc)
summary(reg5)
## 
## Call:
## lm(formula = fc$escolares ~ 0 + fc$estufm + fc$otrasus, data = fc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.88910 -0.31884 -0.05624  0.09587  1.33499 
## 
## Coefficients:
##            Estimate Std. Error t value Pr(>|t|)   
## fc$estufm   0.05629    0.01515   3.716   0.0012 **
## fc$otrasus  0.06540    0.28248   0.232   0.8191   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5188 on 22 degrees of freedom
## Multiple R-squared:  0.9191, Adjusted R-squared:  0.9118 
## F-statistic:   125 on 2 and 22 DF,  p-value: 9.709e-13

Se puede ver que en las regresiones encontradas ninguna supera el R^2 de la regresion original, por lo tanto no hay multicolinealidad.