Fiabilidad
library(readr)
## Warning: package 'readr' was built under R version 3.5.3
library(dplyr)
## Warning: package 'dplyr' was built under R version 3.5.3
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 3.5.3
PARTE I
1. Descargue el dataset de admis1.csv del GES.
admis1 <- read_csv("admis1.csv")
## Parsed with column specification:
## cols(
## `Serial No.` = col_double(),
## `GRE Score` = col_double(),
## `TOEFL Score` = col_double(),
## `University Rating` = col_double(),
## SOP = col_double(),
## LOR = col_double(),
## CGPA = col_double(),
## Research = col_double(),
## `Chance of Admit` = col_double()
## )
2. Separe su dataset en 70% para train y 30% para test
train<-admis1[1:(0.7*(nrow(admis1))), ]
test<-admis1[(0.7*nrow(admis1)):nrow(admis1),]
3. Diga cuales son las variables que tiene este dataset y que significa cada una
colnames(admis1)
## [1] "Serial No." "GRE Score" "TOEFL Score"
## [4] "University Rating" "SOP" "LOR"
## [7] "CGPA" "Research" "Chance of Admit"
GRE Score = Razonamiento verbal, razonamiento cuantitativo y escritura analĆtica.
TOEFL Score = Prueba estandarizada de dominio del idioma inglƩs.
University Rating = ClasificaciĆ³n de la universidad.
SOP = Ensayo de vida.
LOR = Documento que proporciona una visiĆ³n completa de la candidatura adecuada para la admisiĆ³n en la Universidad.
CGPA = Promedio acumulado de puntos de calificaciĆ³n.
Research = SecciĆ³n verbal sin puntuaciĆ³n.
Chance of Admit = La probabilidad de ser admitido.
4. Realice una grƔfica de (separada) para las variables GRE.Score, TOEFEL.Score, SOP, LOR, CGPA, University.Rating contra Chance.of.Admit.
train %>%
ggplot(aes(x=`GRE Score`, y=`Chance of Admit`)) +
geom_point() + geom_abline(data = lm.fit)
train %>%
ggplot(aes(x=`TOEFL Score`, y=`Chance of Admit`)) +
geom_point()
train %>%
ggplot(aes(x=`University Rating`, y=`Chance of Admit`)) +
geom_point()
train %>%
ggplot(aes(x=SOP, y=`Chance of Admit`)) +
geom_point()
train %>%
ggplot(aes(x=LOR, y=`Chance of Admit`)) +
geom_point()
train %>%
ggplot(aes(x=CGPA, y=`Chance of Admit`)) +
geom_point()
5. Diga quĆ© tipo de regresiĆ³n utilizarĆa para construir un modelo de regresiĆ³n que permita predecir el Chance.of.Admit, esto debe realizarlo con cada variable independiente es decir construir un modelo de dos variables, una explicada y una explicatoria.
lm.fit=lm(`Chance of Admit`~`GRE Score`,data=train)
summary(lm.fit)
##
## Call:
## lm(formula = `Chance of Admit` ~ `GRE Score`, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.33492 -0.04646 0.00554 0.06125 0.18135
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.384815 0.128764 -18.52 <2e-16 ***
## `GRE Score` 0.009813 0.000406 24.17 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08583 on 348 degrees of freedom
## Multiple R-squared: 0.6267, Adjusted R-squared: 0.6256
## F-statistic: 584.1 on 1 and 348 DF, p-value: < 2.2e-16
lm.fit2=lm(`Chance of Admit`~`TOEFL Score`,data=train)
summary(lm.fit2)
##
## Call:
## lm(formula = `Chance of Admit` ~ `TOEFL Score`, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.30856 -0.05342 0.01292 0.05792 0.21201
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.2533359 0.0828279 -15.13 <2e-16 ***
## `TOEFL Score` 0.0183809 0.0007683 23.93 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08637 on 348 degrees of freedom
## Multiple R-squared: 0.6219, Adjusted R-squared: 0.6208
## F-statistic: 572.4 on 1 and 348 DF, p-value: < 2.2e-16
lm.fit3=lm(`Chance of Admit`~`University Rating`,data=train)
summary(lm.fit3)
##
## Call:
## lm(formula = `Chance of Admit` ~ `University Rating`, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.38016 -0.04310 0.01690 0.05617 0.27397
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.451909 0.015355 29.43 <2e-16 ***
## `University Rating` 0.087063 0.004594 18.95 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09854 on 348 degrees of freedom
## Multiple R-squared: 0.5079, Adjusted R-squared: 0.5065
## F-statistic: 359.2 on 1 and 348 DF, p-value: < 2.2e-16
lm.fit4=lm(`Chance of Admit`~`SOP`,data=train)
summary(lm.fit4)
##
## Call:
## lm(formula = `Chance of Admit` ~ SOP, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.48995 -0.05072 0.01646 0.07159 0.22569
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.405850 0.020297 20.00 <2e-16 ***
## SOP 0.092821 0.005666 16.38 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1055 on 348 degrees of freedom
## Multiple R-squared: 0.4354, Adjusted R-squared: 0.4338
## F-statistic: 268.4 on 1 and 348 DF, p-value: < 2.2e-16
lm.fit5=lm(`Chance of Admit`~`LOR`,data=train)
summary(lm.fit5)
##
## Call:
## lm(formula = `Chance of Admit` ~ LOR, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.34858 -0.05980 -0.00102 0.07325 0.24142
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.361519 0.022009 16.43 <2e-16 ***
## LOR 0.104875 0.006141 17.08 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1036 on 348 degrees of freedom
## Multiple R-squared: 0.4559, Adjusted R-squared: 0.4544
## F-statistic: 291.6 on 1 and 348 DF, p-value: < 2.2e-16
lm.fit6=lm(`Chance of Admit`~`CGPA`,data=train)
summary(lm.fit6)
##
## Call:
## lm(formula = `Chance of Admit` ~ CGPA, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.27321 -0.02959 0.01006 0.04333 0.18134
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.062047 0.054768 -19.39 <2e-16 ***
## CGPA 0.207588 0.006346 32.71 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06959 on 348 degrees of freedom
## Multiple R-squared: 0.7546, Adjusted R-squared: 0.7539
## F-statistic: 1070 on 1 and 348 DF, p-value: < 2.2e-16
6. Utilice el mƩtodo smooth para mostrar en cada grƔfica el modelo que mejor se ajusta a los datos, esto debe hacerlo para cada grƔfica por separado
train %>%
ggplot(aes(x=`GRE Score`, y=`Chance of Admit`)) +
geom_point() +
geom_smooth()
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
train %>%
ggplot(aes(x=`TOEFL Score`, y=`Chance of Admit`)) +
geom_point() +
geom_smooth()
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
train %>%
ggplot(aes(x=`University Rating`, y=`Chance of Admit`)) +
geom_point() +
geom_smooth()
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : pseudoinverse used at 3
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : neighborhood radius 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : reciprocal condition number 0
## Warning in predLoess(object$y, object$x, newx = if
## (is.null(newdata)) object$x else if (is.data.frame(newdata))
## as.matrix(model.frame(delete.response(terms(object)), : pseudoinverse used
## at 3
## Warning in predLoess(object$y, object$x, newx = if
## (is.null(newdata)) object$x else if (is.data.frame(newdata))
## as.matrix(model.frame(delete.response(terms(object)), : neighborhood radius
## 1
## Warning in predLoess(object$y, object$x, newx = if
## (is.null(newdata)) object$x else if (is.data.frame(newdata))
## as.matrix(model.frame(delete.response(terms(object)), : reciprocal
## condition number 0
train %>%
ggplot(aes(x=SOP, y=`Chance of Admit`)) +
geom_point() +
geom_smooth()
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
train %>%
ggplot(aes(x=LOR, y=`Chance of Admit`)) +
geom_point() +
geom_smooth()
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
train %>%
ggplot(aes(x=CGPA, y=`Chance of Admit`)) +
geom_point() +
geom_smooth()
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
PARTE II
1. Realice un modelo de regresiĆ³n (lineal/no lineal) con todas las variables anteriores, y diga la significancia de cada una de las variables.
fit_modelo <- lm(data = train, train$`Chance of Admit` ~ poly(train$`GRE Score`,2)+ poly(train$`TOEFL Score`,2) + train$CGPA + train$SOP + train$LOR + train$`University Rating`)
summary(fit_modelo)
##
## Call:
## lm(formula = train$`Chance of Admit` ~ poly(train$`GRE Score`,
## 2) + poly(train$`TOEFL Score`, 2) + train$CGPA + train$SOP +
## train$LOR + train$`University Rating`, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.27463 -0.02366 0.01092 0.03667 0.16192
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.353193 0.105829 -3.337 0.000939 ***
## poly(train$`GRE Score`, 2)1 0.424508 0.133796 3.173 0.001647 **
## poly(train$`GRE Score`, 2)2 -0.021811 0.089546 -0.244 0.807710
## poly(train$`TOEFL Score`, 2)1 0.357443 0.131190 2.725 0.006770 **
## poly(train$`TOEFL Score`, 2)2 0.006077 0.088303 0.069 0.945172
## train$CGPA 0.112982 0.013236 8.536 4.66e-16 ***
## train$SOP -0.003592 0.005804 -0.619 0.536364
## train$LOR 0.024859 0.005917 4.201 3.40e-05 ***
## train$`University Rating` 0.010140 0.005016 2.022 0.043993 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06402 on 341 degrees of freedom
## Multiple R-squared: 0.7965, Adjusted R-squared: 0.7917
## F-statistic: 166.8 on 8 and 341 DF, p-value: < 2.2e-16
2. Produzca el modelo que usted considere mejor para predecir el Chance.of.Admit.
fit_modelo2 <- lm(data = train, train$`Chance of Admit` ~ poly(train$`GRE Score`,2) + train$CGPA + train$`TOEFL Score`)
y_hat_train <- predict(fit_modelo2, train)
MSE6_train <- sum((train$`Chance of Admit` - y_hat_train)^2)
MSE6_train
## [1] 1.527538
summary(fit_modelo2)
##
## Call:
## lm(formula = train$`Chance of Admit` ~ poly(train$`GRE Score`,
## 2) + train$CGPA + train$`TOEFL Score`, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.28772 -0.02609 0.01026 0.03970 0.14303
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.907401 0.124169 -7.308 1.9e-12 ***
## poly(train$`GRE Score`, 2)1 0.428082 0.133874 3.198 0.00151 **
## poly(train$`GRE Score`, 2)2 -0.010563 0.067359 -0.157 0.87548
## train$CGPA 0.145619 0.012068 12.067 < 2e-16 ***
## train$`TOEFL Score` 0.003520 0.001184 2.973 0.00316 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06654 on 345 degrees of freedom
## Multiple R-squared: 0.7775, Adjusted R-squared: 0.775
## F-statistic: 301.5 on 4 and 345 DF, p-value: < 2.2e-16