Fit a single linear model

Solves the ordinary least-squares problem \(Y \approx X \beta\) for a single design matrix X and one or more response columns Y.

Usage

lm_fit(
  X,
  Y,
  intercept = FALSE,
  include_fitted = TRUE,
  include_residuals = TRUE,
  cache = TRUE,
  method = c("normal", "qr")
)

Arguments

X

Numeric matrix or adgeMatrix of predictors, shape [n, p].

Y

Numeric matrix, vector, or adgeMatrix of responses, shape [n, q].

intercept

Logical. When TRUE, a column of ones is prepended to X before fitting.

include_fitted

Logical. When TRUE, fitted values are included in the returned object.

include_residuals

Logical. When TRUE, residuals are included in the returned object.

cache

Logical. When TRUE, the \(X^T X\) or QR factorization is cached for reuse across calls sharing the same X.

method

Solver method: "normal" (normal equations, default) or "qr" (QR decomposition).

Value

An object of class "lm_fit", a named list containing:

coefficients

adgeMatrix of shape [p, q].

fitted.values

adgeMatrix of shape [n, q], or NULL when include_fitted = FALSE.

residuals

adgeMatrix of shape [n, q], or NULL when include_residuals = FALSE.

rank

Integer model rank.

df.residual

Residual degrees of freedom.

See also

many_lm, array_lm

Examples

X <- matrix(rnorm(50), nrow = 10)
y <- rnorm(10)
fit <- lm_fit(X, y)
coef(fit)
#> An amatrix dense matrix [cpu|policy=auto|precision=strict]
#> 5 x 1 Matrix of class "adgeMatrix"
#>            [,1]
#> [1,] -0.3832367
#> [2,] -0.5502750
#> [3,]  0.3492819
#> [4,]  0.5332247
#> [5,]  0.1140939