#UNIVERSIDAD NACIONAL DEL ALTIPLANO
#REGRESION AVANZADA
#FINESI
#TEMA: Regression Polynomial
library(readxl)
## Warning: package 'readxl' was built under R version 4.0.2
cars <- read_excel("E:/VII SEMESTRE/REGRESION AVANZADA/cars.xlsx")
cars
## # A tibble: 6 x 2
## speed dist
## <dbl> <dbl>
## 1 4 2
## 2 4 10
## 3 7 4
## 4 7 22
## 5 8 16
## 6 9 10
head(cars)
## # A tibble: 6 x 2
## speed dist
## <dbl> <dbl>
## 1 4 2
## 2 4 10
## 3 7 4
## 4 7 22
## 5 8 16
## 6 9 10
plot(cars$dist ~ cars$speed)
lines(lowess(cars$dist ~ cars$speed))
m2<- lm(dist ~ poly(speed, 2, raw = T), data = cars)
m3<- lm(dist ~ speed + I(speed^2), data = cars)
summary(m2)
##
## Call:
## lm(formula = dist ~ poly(speed, 2, raw = T), data = cars)
##
## Residuals:
## 1 2 3 4 5 6
## -3.910 4.090 -9.899 8.101 2.697 -1.079
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -27.5506 48.0265 -0.574 0.606
## poly(speed, 2, raw = T)1 11.6236 16.6044 0.700 0.534
## poly(speed, 2, raw = T)2 -0.8146 1.3269 -0.614 0.583
##
## Residual standard error: 8.248 on 3 degrees of freedom
## Multiple R-squared: 0.2642, Adjusted R-squared: -0.2264
## F-statistic: 0.5385 on 2 and 3 DF, p-value: 0.6312
summary(m3)
##
## Call:
## lm(formula = dist ~ speed + I(speed^2), data = cars)
##
## Residuals:
## 1 2 3 4 5 6
## -3.910 4.090 -9.899 8.101 2.697 -1.079
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -27.5506 48.0265 -0.574 0.606
## speed 11.6236 16.6044 0.700 0.534
## I(speed^2) -0.8146 1.3269 -0.614 0.583
##
## Residual standard error: 8.248 on 3 degrees of freedom
## Multiple R-squared: 0.2642, Adjusted R-squared: -0.2264
## F-statistic: 0.5385 on 2 and 3 DF, p-value: 0.6312