`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 comma-separated list of column names Rows are in the same group if their values for all of the columns listed in `G` are the same. If `G` is omitted, all rows are considered to be in the same group. If any of the columns listed in `G` contain N/A, the N/A value is considered a valid grouping value.
`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 `S` is omitted, all rows will be considered by the function (subject to any prior row selections). If any of the values in `S` are neither 1 nor 0, an error is returned.
`Y`	integer or decimal	A column name denoting the dependent variable
`XX`	integer or decimal	A space- or comma-separated list of column names denoting the independent variable(s) `XX` may also include the special value `1` for the constant (intercept) term in the linear model.

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.

The model that g_lsq returns can be used as an argument to the following functions:

param(M;P;I) to extract the regression model parameters
score(XX;M;Z) to score data points according to the regression model

Note: 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).

Assuming M is the column containing the result of g_lsq, use the following function calls to obtain the desired information:

param(M;'b';N): Nth coefficient of the model (corresponding to the Nth data column in XX)
param(M;'p';N): p-value associated with the Nth coefficient of the model
param(M;'g';N): Nth diagonal value of (X^TX)^-1, where X is the matrix of input values
param(M;'valcnt';): Count of valid observations (those where XX and Y are all non-N/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 (R²) for the model
param(M;'adjr2';): Adjusted R² for the model
score(XX;M;): Predicted Y for data points XX according to the model

The standard error of the estimate for the Nth 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"/>