predict() gives wrong matrix for bs(); how to predict linear regression?

Question

I've met a problem about function bs() .

      library(ISLR)    
      library(ggplot2)    
      library(caret)    
      data(Wage)    
      #summary(Wage)        

      set.seed(123)    
      inTrain <- createDataPartition(Wage$wage, p = 0.7, list = F)    
      training <- Wage[inTrain,]    
      testing <- Wage[-inTrain,]    

      library(splines)     
      bsBasis <- bs(training$age, df=3)      
      bsBasis[1:12,] 

      lm1 <- lm(wage ~ bsBasis, data=training)    
      lm1$coefficients    
      ## (Intercept)    bsBasis1    bsBasis2    bsBasis3     
      ##       60.22       93.39       51.05       47.28    

      plot(training$age, training$wage, pch=19, cex=0.5)    
      points(training$age, predict(lm1, newdata=training), col="red", pch=19, cex=0.5)    

      predict(bsBasis, age=testing$age)

The dimensions of predict(bsBasis, age=testing$age) is 2012x3 , while the testing$age got only 988 rows. And the results of predict(bsBasis, age=testing$age) is identical to the bsBasis .

My questions are:

1. What is predict(bsBasis, age=testing$age) actually doing?
2. How to use this bsBasis in predicting the wage in the TEST data correctly?

Answer 1

Your question 1

Use newx . Check ?predict.bs for its arguments.

x <- runif(100)
b <- bs(x, df = 3)
predict(b, newx = c(0.2, 0.5))

Different predict functions may behave differently. Here, no matter what variable you use in bs() , age , sex , height , etc, it can only be newx in predict.bs() .

Your question 2

You don't really need to form explicitly bsBasis . When using splines in regression, lm and predict.lm will hide construction and prediction of spline from you.

lm1 <- lm(wage ~ bs(age, df = 3), data=training)
predict(lm1, newdata = test)

Note the argument in predict.lm is newdata .