MODELO DE REGRESION MULTIPLE

Introducimos los valores del desgaste de un cojinete y su relacion con \(x_1=\)viscosidad del aceite y \(x_2=\)carga.

y<-c(193,230,172,91,113,125)
x1<-c(1.6,15.5,22,43,33,40)
x2<-c(851,816,1058,1201,1357,1115)
cojinetes<-data.frame(y,x1,x2)

Calcularemos los coeficientes del vector\(\beta\) utilizando la formula \(\beta=(H^t\times{H})^{-1}\times{H^t\times{Y}}\)

H<-data.frame(rep(1,6),x1,x2)
H_matriz<-as.matrix(H)
p1<-solve(t(H_matriz) %*% H_matriz)
p2<-t(H_matriz)%*%y
Betas<-p1%*%p2
Betas

                 [,1]
rep.1..6. 350.9942706
x1         -1.2719944
x2         -0.1539042

cor_cojinetes<-cor(cojinetes)
cor_cojinetes

            y         x1         x2
y   1.0000000 -0.8518508 -0.8984749
x1 -0.8518508  1.0000000  0.7881313
x2 -0.8984749  0.7881313  1.0000000

Calculando el modelo de regresion multiple.

Regr_cojinetes<-lm(cojinetes)
summary(Regr_cojinetes)

Call:
lm(formula = cojinetes)

Residuals:
      1       2       3       4       5       6 
-24.987  24.307  11.820 -20.460  12.830  -3.511 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)  
(Intercept) 350.99427   74.75307   4.695   0.0183 *
x1           -1.27199    1.16914  -1.088   0.3562  
x2           -0.15390    0.08953  -1.719   0.1841  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 25.5 on 3 degrees of freedom
Multiple R-squared:  0.8618,    Adjusted R-squared:  0.7696 
F-statistic: 9.353 on 2 and 3 DF,  p-value: 0.05138

pairs(cojinetes)

residuos<-residuals(Regr_cojinetes)
qqnorm(residuos)
qqline(residuos)

library(GGally)

Cargando paquete requerido: ggplot2

Registered S3 method overwritten by 'GGally':
  method from   
  +.gg   ggplot2

ggpairs(cojinetes)

library(readxl)
library(GGally)
practica<-read_excel('C:/Users/MINEDUCYT/Desktop/REGRESION LINEAL PRACTICA.xlsx')
regr_practica<-lm(practica$Y~practica$x1+practica$x2+practica$x3,data=practica)
summary(regr_practica)

Call:
lm(formula = practica$Y ~ practica$x1 + practica$x2 + practica$x3, 
    data = practica)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.47459 -0.08119 -0.01986  0.14153  0.39018 

Coefficients:
             Estimate Std. Error  t value Pr(>|t|)    
(Intercept)  0.661975   0.405306    1.633    0.131    
practica$x1  1.992761   0.011729  169.901  < 2e-16 ***
practica$x2 -2.993595   0.008090 -370.021  < 2e-16 ***
practica$x3  0.497545   0.008371   59.435 3.78e-15 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2518 on 11 degrees of freedom
Multiple R-squared:  0.9999,    Adjusted R-squared:  0.9999 
F-statistic: 5.01e+04 on 3 and 11 DF,  p-value: < 2.2e-16

ggpairs(practica)

qqnorm(residuals(regr_practica))
qqline(residuals(regr_practica))