lm                   package:base                   R Documentation

_F_i_t_t_i_n_g _L_i_n_e_a_r _M_o_d_e_l_s

_D_e_s_c_r_i_p_t_i_o_n:

     `lm' is used to fit linear models. It can be used to carry out
     regression, single stratum analysis of variance and analysis of
     covariance (although `aov' may provide a more convenient interface
     for these).

_U_s_a_g_e:

     lm(formula, data, subset, weights, na.action,
        method = "qr", model = TRUE, x = FALSE, y = FALSE, qr = TRUE,
        singular.ok = TRUE contrasts = NULL, offset = NULL, ...)

     lm.fit (x, y,    offset = NULL, method = "qr", tol = 1e-7, ...)
     lm.wfit(x, y, w, offset = NULL, method = "qr", tol = 1e-7, ...)
     lm.fit.null (x, y,    method = "qr", tol = 1e-7, ...)
     lm.wfit.null(x, y, w, method = "qr", tol = 1e-7, ...)

_A_r_g_u_m_e_n_t_s:

 formula: a symbolic description of the model to be fit. The details of
          model specification are given below.

    data: an optional data frame containing the variables in the model.
           By default the variables are taken from the environment
          which `lm' is called from.

  subset: an optional vector specifying a subset of observations to be
          used in the fitting process.

 weights: an optional vector of weights to be used in the fitting
          process. If specified, weighted least squares is used with
          weights `weights' (that is, minimizing `sum(w*e^2)');
          otherwise ordinary least squares is used.

na.action: a function which indicates what should happen when the data
          contain `NA's.  The default is set by the `na.action' setting
          of `options', and is `na.fail' if that is unset. The
          ``factory-fresh'' default is `na.omit'.

model, x, y, qr: logicals.  If `TRUE' the corresponding components of
          the fit (the model frame, the model matrix, the response, the
          QR decomposition) are returned.

singular.ok: logical, defaulting to `TRUE'. `FALSE' is not yet
          implemented.

  method: currently, only `method="qr"' is supported.

contrasts: an optional list. See the `contrasts.arg' of
          `model.matrix.default'.

  offset: this can be used to specify an a priori known component to be
          included in the linear predictor during fitting.  An `offset'
          term can be included in the formula instead or as well, and
          if both are specified their sum is used.

     tol: tolerance for the `qr' decomposition. Default is 1e-7.

     ...: currently disregarded.

_D_e_t_a_i_l_s:

     Models for `lm' are specified symbolically.  A typical model has
     the form `response ~ terms' where `response' is the (numeric)
     response vector and `terms' is a series of terms which specifies a
     linear predictor for `response'.  A terms specification of the
     form `first+second' indicates all the terms in `first' together
     with all the terms in `second' with duplicates removed.  A
     specification of the form `first:second' indicates the the set of
     terms obtained by taking the interactions of all terms in `first'
     with all terms in `second'.  The specification `first*second'
     indicates the cross of `first' and `second'.  This is the same as
     `first+second+first:second'.

_V_a_l_u_e:

     `lm' returns an object of `class' `"lm"' or for multiple responses
     of class `c("mlm", "lm")'.

     The functions `summary' and `anova' are used to obtain and print a
     summary and analysis of variance table of the results. The generic
     accessor functions `coefficients', `effects', `fitted.values' and
     `residuals' extract various useful features of the value returned
     by `lm'.

_N_o_t_e:

     Offsets specified by `offset' will not be included in predictions
     by `predict.lm', whereas those specified by an offset term in the
     formula will be.

_S_e_e _A_l_s_o:

     `summary.lm' for summaries and `anova.lm' for the ANOVA table;
     `aov' for a different interface.

     The generic functions `coefficients', `effects', `residuals',
     `fitted.values'.

     `predict.lm' (via `predict(..)') for prediction, including
     confidence and prediction intervals.

     `lm.influence' for regression diagnostics, and `glm' for
     generalized linear models.

_E_x_a_m_p_l_e_s:

     ## Annette Dobson (1990) "An Introduction to Generalized Linear Models".
     ## Page 9: Plant Weight Data.
     ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
     trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
     group <- gl(2,10,20, labels=c("Ctl","Trt"))
     weight <- c(ctl, trt)
     anova(lm.D9 <- lm(weight ~ group))
     summary(lm.D90 <- lm(weight ~ group - 1))# omitting intercept
     summary(resid(lm.D9) - resid(lm.D90)) #- residuals almost identical

     opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
     plot(lm.D9, las = 1)      # Residuals, Fitted, ...
     par(opar)

