# Statistical Models

The following outlines the variadic function definitions provided with the kdb Insights ML Analytics library for various statistical models. Full breakdowns of the algorithms represented can be found here, this includes, via examples the use of the function returns for prediction, this is not outlined below explicitly.

Note

All arguments marked with an asterisk are optional and can be input using the notation defined in the function calls section of the model monitoring documentation.

## Ordinary Least Squares(OLS) Regression

### .ml.kxi.stats.OLS.fit

Fit a Ordinary Least Squares(OLS) model

.ml.kxi.stats.OLS.fit[X;y]


Parameters:

name type description
X any Endogenous variable determined by it's relationship with others.
y any Exogenous variables which effect the endogenous variable.

options:

name type description default
trend boolean Is trend to be accounted for. 1b

Returns:

type description
dictionary All information collected during the fitting of a model, along with prediction functionality.

Examples:

Example 1: Fit a model using default configuration

// Generate data
q)endog:til 10
q)exog:3+2*til 10

// Fit model
q)show mdl1:.ml.kxi.stats.OLS.fit[endog;exog]
modelInfo| coefvariablesstatsDict!(-1.5 0.5;(+(,name)!,yInterceptx0)!+..
predict  | {[config;exog]
modelInfo:configmodelInfo;
trend:yIntercept i..
q)mdl1[modelInfo]variables
name      | coef stdErr       tStat         pValue C195
----------| ---------------------------------------------------
yIntercept| -1.5 2.571224e-16 -5.833798e+15 0      5.929253e-16
x0        | 0.5  1.93265e-17  2.587121e+16  0      4.456699e-17


Example 2: Fit a model modifying the default behavior

// Generate data
q)endog:til 10
q)exog:3+2*til 10

// Fit model
q)show mdl2:.ml.kxi.stats.OLS.fit[endog;exog;.var.kw[trend;0b]]
modelInfo| coefvariablesstatsDict!(,0.3983051;(+(,name)!,,x0)!+coefstd..
predict  | {[config;exog]
modelInfo:configmodelInfo;
trend:yIntercept i..
q)mdl2[modelInfo]variables
name| coef      stdErr     tStat    pValue       C195
----| -----------------------------------------------------
x0  | 0.3983051 0.01622758 24.54495 2.875458e-10 0.03742086


## Weighted Least Squares(WLS) Regression

### .ml.kxi.stats.WLS.fit

Fit a Weighted Least Squares(WLS) model

.ml.kxi.stats.WLS.fit[X;y]


Parameters:

name type description
X any Endogenous variable determined by it's relationship with others.
y any Exogenous variables which effect the endogenous variable.

options:

name type description default
weights float[] Weights to apply to X. ::
trend boolean Is trend to be accounted for. 1b

Returns:

type description
dictionary All information collected during the fitting of a model, along with prediction functionality.

Examples:

Example 1: Fit a model using default configuration

// Generate data
q)endog:til 10
q)exog:3+2*til 10

// Fit model
q)show mdl1:.ml.kxi.stats.WLS.fit[endog;exog]
modelInfo| coefvariablesstatsDictweights!(-1.5 0.5;(+(,name)!,yIntercep..
predict  | {[config;exog]
modelInfo:configmodelInfo;
trend:yIntercept i..
q)show each mdl1[modelInfo]variablesweights;
name      | coef stdErr       tStat         pValue C195
----------| ---------------------------------------------------
yIntercept| -1.5 5.126997e-15 -2.925689e+14 0      1.182288e-14
x0        | 0.5  3.853687e-16 1.297459e+15  0      8.886618e-16
130.4302 46.95487 23.95657 14.49224 9.701419 6.945986 5.217208 4.06184 3.2517..


Example 2: Fit a model modifying the default behavior

// Generate data
q)endog:til 10
q)exog:3+2*til 10

// Fit model
q)params:.var.kwargstrendweights!(0b;10?1f)
q)show mdl2:.ml.kxi.stats.WLS.fit[endog;exog;params]
modelInfo| coefvariablesstatsDictweights!(,0.4012137;(+(,name)!,,x0)!+..
predict  | {[config;exog]
modelInfo:configmodelInfo;
trend:yIntercept i..
q)show each mdl2[modelInfo]variablesweights;
name| coef      stdErr     tStat    pValue       C195
----| -----------------------------------------------------
x0  | 0.4012137 0.01625652 24.68018 2.723961e-10 0.03748759
0.5232126 0.6587993 0.4064619 0.3612185 0.6559165 0.6997534 0.5315412 0.89392..