Polynomial Regression with for loop - r

Question

for Boston dataset perform polynomial regression with degree 5,4,3 and 2 I want to use loop but get error :
Error in [.data.frame(data, 0, cols, drop = FALSE) :
undefined columns selected
library(caret)
train_control <- trainControl(method = "cv", number=10)
#set.seed(5)
cv <-rep(NA,4)
n=c(5,4,3,2)
for (i in n) {
cv[i]=train(nox ~ poly(dis,degree=i ), data = Boston, trncontrol = train_control, method = "lm")
}
outside the loop train(nox ~ poly(dis,degree=i ), data = Boston, trncontrol = train_control, method = "lm")
works well

Answer 1

Since you are using poly(..., raw = FALSE) that means you are getting orthogonal contrasts. Hence no need of for-loop, use the maximum degree since the coefficients and standard errors will not change for each coefficient.
Check quick example below using lm and iris dataset:
summary(lm(Sepal.Length~poly(Sepal.Width, 2), iris))
Call:
lm(formula = Sepal.Length ~ poly(Sepal.Width, 2), data = iris)
Residuals:
Min 1Q Median 3Q Max
-1.63153 -0.62177 -0.08282 0.50531 2.33336
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.84333 0.06692 87.316 <2e-16 ***
poly(Sepal.Width, 2)1 -1.18838 0.81962 -1.450 0.1492
poly(Sepal.Width, 2)2 -1.41578 0.81962 -1.727 0.0862 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.8196 on 147 degrees of freedom
Multiple R-squared: 0.03344, Adjusted R-squared: 0.02029
F-statistic: 2.543 on 2 and 147 DF, p-value: 0.08209
> summary(lm(Sepal.Length~poly(Sepal.Width, 3), iris))
Call:
lm(formula = Sepal.Length ~ poly(Sepal.Width, 3), data = iris)
Residuals:
Min 1Q Median 3Q Max
-1.6876 -0.5001 -0.0876 0.5493 2.4600
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.84333 0.06588 88.696 <2e-16 ***
poly(Sepal.Width, 3)1 -1.18838 0.80687 -1.473 0.1430
poly(Sepal.Width, 3)2 -1.41578 0.80687 -1.755 0.0814 .
poly(Sepal.Width, 3)3 1.92349 0.80687 2.384 0.0184 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.8069 on 146 degrees of freedom
Multiple R-squared: 0.06965, Adjusted R-squared: 0.05054
F-statistic: 3.644 on 3 and 146 DF, p-value: 0.01425
Take a look at the summary table. Everything is the same. Only the poly(Sepal.Width,3)3 was added when a degree of 3 was used. Meaning if we used a degree of 3, we could easily tell what degree 2 will look like. Hence no need of for loop.
Note that you could use different variables in poly: eg poly(cbind(Sepal.Width, Petal.Length, Petal.Width), 4) and still be able to easily recover poly(Sepal.Width, 2).