1. Al querer probar la hipotesis que el buen estado de los locales escolares depende del porcentaje de la poblacion que contribuye a la SUNAT; y del porcentaje de la PEA que está laborando; se llega a comprobar que (con una significancia del 0.05):
library(rio)
data=import("dataPeru.xlsx")
str(data)
## 'data.frame':    25 obs. of  8 variables:
##  $ DEPARTAMENTO       : chr  "AMAZONAS" "ÁNCASH" "APURÍMAC" "AREQUIPA" ...
##  $ UBIGEO             : chr  "010000" "020000" "030000" "040000" ...
##  $ buenEstado         : num  18.6 13.9 8.7 27.4 17 18 33.8 11.9 10.1 15.6 ...
##  $ contribuyentesSunat: num  75035 302906 103981 585628 151191 ...
##  $ peaOcupada         : num  130019 387976 140341 645001 235857 ...
##  $ pobUrbana          : num  205976 806065 243354 1383694 444473 ...
##  $ PobRural           : num  211389 333050 180905 76739 206467 ...
##  $ pobTotal           : num  417365 1139115 424259 1460433 650940 ...
 modelo1=formula(buenEstado~contribuyentesSunat+peaOcupada)
 reg1=lm(modelo1,data=data)
 summary(reg1)
## 
## Call:
## lm(formula = modelo1, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -10.589  -3.966  -1.347   1.907  21.518 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          1.865e+01  2.694e+00   6.922 5.98e-07 ***
## contribuyentesSunat  1.786e-05  2.060e-05   0.867    0.395    
## peaOcupada          -1.596e-05  2.241e-05  -0.712    0.484    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.925 on 22 degrees of freedom
## Multiple R-squared:  0.1561, Adjusted R-squared:  0.07939 
## F-statistic: 2.035 on 2 and 22 DF,  p-value: 0.1546
modelo1_st = formula(scale(buenEstado)~scale(contribuyentesSunat)+scale(peaOcupada))
 modelo1_st = lm(modelo1_st, data = data)
 summary(modelo1_st)
## 
## Call:
## lm(formula = modelo1_st, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.2821 -0.4802 -0.1631  0.2309  2.6052 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)
## (Intercept)                 3.313e-16  1.919e-01   0.000    1.000
## scale(contribuyentesSunat)  2.034e+00  2.346e+00   0.867    0.395
## scale(peaOcupada)          -1.670e+00  2.346e+00  -0.712    0.484
## 
## Residual standard error: 0.9595 on 22 degrees of freedom
## Multiple R-squared:  0.1561, Adjusted R-squared:  0.07939 
## F-statistic: 2.035 on 2 and 22 DF,  p-value: 0.1546
  1. Al querer probar la hipotesis que la cantidad de PEA ocupada dependen de la cantidad de contribuyentes a la SUNAT ; y del porcentaje de locales escolares en buen estado; se llega a comprobar que (con una significancia del 0.05)
modelo2=formula(peaOcupada~contribuyentesSunat+buenEstado)
 reg2=lm(modelo2,data=data)
 summary(reg2)
## 
## Call:
## lm(formula = modelo2, data = data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -91867 -58573 -11166  46174 155851 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          1.155e+05  3.787e+04   3.049  0.00588 ** 
## contribuyentesSunat  9.206e-01  1.741e-02  52.872  < 2e-16 ***
## buenEstado          -1.412e+03  1.983e+03  -0.712  0.48395    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 74540 on 22 degrees of freedom
## Multiple R-squared:  0.9932, Adjusted R-squared:  0.9926 
## F-statistic:  1603 on 2 and 22 DF,  p-value: < 2.2e-16
library(modelsummary)
## `modelsummary` 2.0.0 now uses `tinytable` as its default table-drawing
##   backend. Learn more at: https://vincentarelbundock.github.io/tinytable/
## 
## Revert to `kableExtra` for one session:
## 
##   options(modelsummary_factory_default = 'kableExtra')
##   options(modelsummary_factory_latex = 'kableExtra')
##   options(modelsummary_factory_html = 'kableExtra')
## 
## Silence this message forever:
## 
##   config_modelsummary(startup_message = FALSE)
 modelo2_st = formula(scale(peaOcupada)~scale(contribuyentesSunat)+scale(buenEstado))
 modelo2_st = lm(modelo2_st, data = data)
 summary(modelo2_st)
## 
## Call:
## lm(formula = modelo2_st, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.10626 -0.06775 -0.01292  0.05341  0.18027 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 8.043e-17  1.724e-02   0.000    1.000    
## scale(contribuyentesSunat)  1.001e+00  1.894e-02  52.872   <2e-16 ***
## scale(buenEstado)          -1.349e-02  1.894e-02  -0.712    0.484    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08622 on 22 degrees of freedom
## Multiple R-squared:  0.9932, Adjusted R-squared:  0.9926 
## F-statistic:  1603 on 2 and 22 DF,  p-value: < 2.2e-16