function 从 r 中的 X 和 y 生成值 beta 的向量

Question

I would like to write a function that generates a vector of values of beta from X and y, we get

beta = [(X^T)*X]^-1 * (X^T) * y

I Wrote a code as this, but it turns error as Error in t(X) * X: non-conformable arrays

please help me with this.

code:

set.seed(143)
X <- cbind(rep(1,50), rnorm(50,0,1), rnorm(50,0,1))
y <- 3 + -4*X[,2] + 2*X[,3] + rnorm(50,0,1)

BetaEstimator <- function(X, y){
Beta <- solve(t(X)*X) * t(X) * y
  return(Beta)}
BetaEstimator(X,y)

Answer 1

You should use the notation for matrix multiplication, that is, use %*% instead of * .

Try:

BetaEstimator <- function(X, y) {
  solve(t(X) %*% X) %*% t(X) * y
}

Answer 2

You should use matrix product %*% , rather than element-wise product * . Also, crossprod can be used to simplify your expression, like below

BetaEstimator <- function(X, y) {
  solve(crossprod(X)) %*% crossprod(X, y)
}

Answer 3

Here is a way using the QR decomposition.

BetaEstimator <- function(X, y) solve.qr(qr(X), y)

set.seed(143)
X <- cbind(rep(1,50), rnorm(50,0,1), rnorm(50,0,1))
y <- 3 + -4*X[,2] + 2*X[,3] + rnorm(50,0,1)

# compare with R's linear model    
fit <- lm.fit(X, y)

coef(fit)
#       x1        x2        x3 
# 3.101107 -3.976275  1.966437 

BetaEstimator(X, y)
#[1]  3.101107 -3.976275  1.966437

The coefficients are equal to R's.