g_lsq(G;S;Y;XX)
Returns a model corresponding to the multiple least squares regression of one or more independent variables against a given dependent variable.
Function type
Vector only
Syntax
g_lsq(G;S;Y;XX)
Input
Argument  Type  Description 

G 
any  A space or commaseparated list of column names Rows are in the same group
if their values for all of the columns listed in If If any of the columns listed in 
S 
integer  The name of a column in which every row evaluates to a 1 or 0, which determines
whether or not that row is selected to be included in the calculation If
If any of the values in

Y 
integer or decimal  A column name denoting the dependent variable 
XX 
integer or decimal  A space or commaseparated list of column names denoting
the independent variable(s)

Return Value
For every row in each group defined by G
(and for those rows where
S
=1, if specified), g_lsq
computes a multiple least squares regression for the independent variable(s)
XX
against the dependent variable Y
and returns a
special type representing a model for each group in the data.
g_lsq
returns can be used as an argument to the following
functions:param(M;P;I)
to extract the regression model parametersscore(XX;M;Z)
to score data points according to the regression model
g_lsq
may be much slower if there is significant multicollinearity in
the data (i.e., if two or more of the independent variables XX
are nearly
perfectly correlated with each other).M
is the column containing the result of g_lsq
,
use the following function calls to obtain the desired information:param(M;'b';N)
N
th coefficient of the model (corresponding to theN
th data column inXX
)param(M;'p';N)
 pvalue associated with the
N
th coefficient of the model param(M;'g';N)
N
th diagonal value of (X
^{T}X
)^{1}, whereX
is the matrix of input valuesparam(M;'valcnt';)
 Count of valid observations (those where
XX
andY
are all nonN/A) in the data param(M;'ybar';)
 Mean of the valid dependent variable observations
Y
in the data param(M;'chi2';)
 Residual sum of squares
param(M;'df';)
 Degrees of freedom of the model
param(M;'r2';)
 Coefficient of determination (R^{2}) for the model
param(M;'adjr2';)
 Adjusted R^{2} for the model
score(XX;M;)
 Predicted
Y
for data pointsXX
according to the model
The standard error of the estimate for the N
th regression coefficient can
be calculated as the square root of the mean squared error multiplied by
param(M;'g';N)
, where the mean squared error is equal to the residual sum
of squares, param(M;'chi2';)
, divided by the number of degrees of freedom,
param(M;'df';)
.
Example
The following example uses g_lsq(G;S;Y;XX)
to perform a least squares
regression on a data set containing the returns of a number of international stock exchanges
(pub.demo.mleg.uci.istanbul). It then uses the
score(XX;M;Z)
function to obtain the predicted value of the linear
model.
<base table="pub.demo.mleg.uci.istanbul"/> <willbe name="model" value="g_lsq(;;ise2;1 sp dax ftse nikkei bovespa eu em)"/> <willbe name="pred" value="score(1 sp dax ftse nikkei bovespa eu em;model;)" format="dec:7"/>