1d:T7b5,# Linear regression models Linear regression models (uses function `lm`). latin1 ```r lmr(X, Y, weights = NULL) ## S3 method for class 'Lmr' coef(object, ...) ## S3 method for class 'Lmr' predict(object, X, ...) ``` ## Arguments - `X`: For the main function: Training X-data ($n, p$). --- For the auxiliary functions: New X-data ($m, p$) to consider. - `Y`: Training Y-data ($n, q$). - `weights`: Weights ($n, 1$) to apply to the training observations. Internally, weights are "normalized" to sum to 1. Default to `NULL` (weights are set to $1 / n$). - `object`: For the auxiliary functions:A fitted model, output of a call to the main functions. - `...`: For the auxiliary functions: Optional arguments. Not used. ## Returns For `lmr`: - **coefficients**: coefficient matrix. - **residuals**: residual matrix. - **effects**: component relating to the linear fit, for use by extractor functions. - **rank**: the numeric rank of the fitted linear model. - **fitted.values**: the fitted mean values. - **assign**: component relating to the linear fit, for use by extractor functions. - **qr**: component relating to the linear fit, for use by extractor functions. - **df.residual**: the residual degrees of freedom. - **xlevels**: (only where relevant) a record of the levels of the factors used in fitting. - **call**: the matched call. - **terms**: the terms object used. - **model**: the model frame used. For `coef.Lmr`: - **int**: matrix (1,nlv) with the intercepts - **B**: matrix (n,nlv) with the coefficients For `predict.Lmr`: - **pred**: A list of matrices ($m, q$) with the Y predicted values for the new X-data ## Examples ```r n <- 8 ; p <- 3 X <- matrix(rnorm(n * p, mean = 10), ncol = p, byrow = TRUE) y <- rnorm(n) Y <- cbind(y, rnorm(n)) Xtrain <- X[1:6, ] ; Ytrain <- Y[1:6, ] Xtest <- X[7:8, ] ; Ytest <- Y[7:8, ] fm <- lmr(Xtrain, Ytrain) coef(fm) predict(fm, Xtest) pred <- predict(fm, Xtest)$pred msep(pred, Ytest) ```

lmr function