

lm {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 vari-
     ance and analysis of covariance.

_U_s_a_g_e_:

     lm(formula, data, subset, weights, na.action=na.omit,
        method="qr", model=TRUE, singular.ok = TRUE)

     lm.fit (x, y,    method = "qr", tol = 1e-7, ...)
     lm.wfit(x, y, w, 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 observa-
          tions 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 action
          (`na.omit') is to omit any incomplete observa-
          tions.  The alternative action `na.fail' causes
          `lm' to print an error message and terminate if
          there are any incomplete observations.

   model: logical.  If `TRUE' (default), the model.frame is
          also returned.

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

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

     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"'.

     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 `coeffi-
     cients', `effects', `fitted.values' and `residuals'
     extract various useful features of the value returned
     by `lm'.

_S_e_e _A_l_s_o_:

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

     The generic functions `coefficients', `effects',
     `residuals', `fitted.values'; `lm.influence' for
     regression diagnostics, and `glm' for generalized lin-
     ear models.

_E_x_a_m_p_l_e_s_:

     ## Annette Dobson (1990) "An Introduction to Statistical Modelling".
     ## 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

     plot(lm.D9)# Residuals, Fitted,..

