| Library: | stats |
| See also: | gls linregfs linregres doglm |
| Quantlet: | linreg | |
| Description: | Computes the Generalized Least Squares estimate for the coefficients of a linear model. |
| Usage: | {beta,bse,bstan,bpval} = linreg (x, y {,opt, om}) | |
| Input: | ||
| x | n x p x d1 x ... x dn array, explanatory variables | |
| y | n x 1 x d1 x ... x dn array, dependent variables | |
| opt | optional string vector, options are: "notext" - no text output is generated, "display" - a special display window is generated showing the results instead of the output window itself, "nointercept" - the intercept is not included in the estimation, "omega" - the covariance matrix "om" is specified. | |
| om | optional n x n x d1 x ... x dn array, covariance matrix | |
| Output: | ||
| beta | p x 1 x d1 x ... x dn array, parameter estimates | |
| bse | p x 1 x d1 x ... x dn array, standard errors of b | |
| bstan | p x 1 x d1 x ... x dn array, standardized parameter estimates | |
| bpval | p x 1 x d1 x ... x dn array, p-values corresponding to bstan | |
By default, an ANOVA table is shown in the output window. If it is not desired you can use the option "notext". In this case linreg only shows: the parameter estimates "b", the standard errors of the estimates "bse", the standardized estimate "bstan" and the respective p-values "bpval".
library("stats")
setenv("outputstringformat", "%s")
randomize(1964)
n = 500
x = normal(n,3)
beta = #(10, 2, 3)
u = 0.5 * normal(n)
y = x*beta .+ u
{beta,se,betastan,p} = linreg(x,y)
Contents of out [ 1,] [ 2,] A N O V A SS df MSS F-test P-value [ 3,] _________________________________________________________________________ [ 4,] Regression 61494.937 3 20498.312 80164.745 0.0000 [ 5,] Residuals 126.828 496 0.256 [ 6,] Total Variation 61621.765 499 123.491 [ 7,] [ 8,] Multiple R = 0.99897 [ 9,] R^2 = 0.99794 [10,] Adjusted R^2 = 0.99793 [11,] Standard Error = 0.50567 [12,] [13,] [14,] PARAMETERS Beta SE StandB t-test P-value [15,] ________________________________________________________________________ [16,] b[ 0,]= -0.0058 0.0227 0.0000 -0.254 0.6001 [17,] b[ 1,]= 10.0019 0.0215 0.9501 465.977 0.0000 [18,] b[ 2,]= 1.9906 0.0221 0.1839 90.263 0.0000 [19,] b[ 3,]= 3.0249 0.0231 0.2667 130.817 0.0000
library("stats")
randomize(1964)
n = 50
x = normal(n,3)
beta = #(10, 2, 3)
u = 0.5 * normal(n)
y = x*beta .+ u
covar =(0.5.*x[,2] .+ 0.3.*x[,3]+ 0.2*x[,1]).^2
y = x*beta .+ sqrt(covar).*u
{beta,se,betastan,p} = linreg(x, y,"nointercept"|"display"|"omega",diag(covar))
You see the display:
A N O V A SS df MSS F-test P-value
_________________________________________________________________________
Regression 4872.988 3 1624.329 8876.339 0.0000
Residuals 8.601 47 0.183
R^2 = 0.98388
Standard Error = 0.42778
PARAMETERS Beta SE
______________________________________
b[ 1,]= 10.0297 0.0637
b[ 2,]= 2.0544 0.0512
b[ 3,]= 2.9838 0.0698