bptest            package:lmtest            R Documentation(latin1)

_B_r_e_u_s_c_h-_P_a_g_a_n _T_e_s_t

_D_e_s_c_r_i_p_t_i_o_n:

     Performs the Breusch-Pagan test against heteroskedasticity.

_U_s_a_g_e:

     bptest(formula, varformula = NULL, studentize = TRUE, data = list())

_A_r_g_u_m_e_n_t_s:

 formula: a symbolic description for the model to be tested (or a
          fitted '"lm"' object).

varformula: a formula describing only the potential explanatory
          variables for the variance (no dependent variable needed). By
          default the same explanatory variables are taken as in the
          main regression model.

studentize: logical. If set to 'TRUE' Koenker's studentized version of
          the test statistic will be used.

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

_D_e_t_a_i_l_s:

     The Breusch-Pagan test fits a linear regression model to the
     residuals of a linear regression model (by default the same
     explanatory variables are taken as in the main regression model)
     and rejects if too much of the variance is explained by the
     additional explanatory variables.

     Under H_0 the test statistic of the Breusch-Pagan test follows a
     chi-squared distribution with 'parameter' (the number of
     regressors without the constant in the model) degrees of freedom.

     Examples can not only be found on this page, but also on the help
     pages of the data sets 'bondyield', 'currencysubstitution',
     'growthofmoney', 'moneydemand', 'unemployment', 'wages'.

_V_a_l_u_e:

     A list with class '"htest"' containing the following components: 

statistic: the value of the test statistic.

 p.value: the p-value of the test.

parameter: degrees of freedom.

  method: a character string indicating what type of test was
          performed.

data.name: a character string giving the name(s) of the data.

_R_e_f_e_r_e_n_c_e_s:

     T.S. Breusch & A.R. Pagan (1979), A Simple Test for
     Heteroscedasticity and Random Coefficient Variation.
     _Econometrica_ *47*, 1287-1294

     R. Koenker (1981), A Note on Studentizing a Test for
     Heteroscedasticity. _Journal of Econometrics_ *17*, 107-112.

     W. Krmer & H. Sonnberger (1986), _The Linear Regression Model
     under Test_. Heidelberg: Physica

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

     'lm', 'ncv.test'

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

     ## generate a regressor
     x <- rep(c(-1,1), 50)
     ## generate heteroskedastic and homoskedastic disturbances
     err1 <- rnorm(100, sd=rep(c(1,2), 50))
     err2 <- rnorm(100)
     ## generate a linear relationship
     y1 <- 1 + x + err1
     y2 <- 1 + x + err2
     ## perform Breusch-Pagan test
     bptest(y1 ~ x)
     bptest(y2 ~ x)

