public class OLS
extends java.lang.Object
The OLS estimator is consistent when the independent variables are exogenous and there is no multicollinearity, and optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated. Under these conditions, the method of OLS provides minimumvariance meanunbiased estimation when the errors have finite variances.
There are several different frameworks in which the linear regression model can be cast in order to make the OLS technique applicable. Each of these settings produces the same formulas and same results, the only difference is the interpretation and the assumptions which have to be imposed in order for the method to give meaningful results. The choice of the applicable framework depends mostly on the nature of data at hand, and on the inference task which has to be performed.
Least squares corresponds to the maximum likelihood criterion if the experimental errors have a normal distribution and can also be derived as a method of moments estimator.
Once a regression model has been constructed, it may be important to confirm the goodness of fit of the model and the statistical significance of the estimated parameters. Commonly used checks of goodness of fit include the Rsquared, analysis of the pattern of residuals and hypothesis testing. Statistical significance can be checked by an Ftest of the overall fit, followed by ttests of individual parameters.
Interpretations of these diagnostic tests rest heavily on the model assumptions. Although examination of the residuals can be used to invalidate a model, the results of a ttest or Ftest are sometimes more difficult to interpret if the model's assumptions are violated. For example, if the error term does not have a normal distribution, in small samples the estimated parameters will not follow normal distributions and complicate inference. With relatively large samples, however, a central limit theorem can be invoked such that hypothesis testing may proceed using asymptotic approximations.
Constructor and Description 

OLS() 
Modifier and Type  Method and Description 

static LinearModel 
fit(Formula formula,
DataFrame data)
Fits an ordinary least squares model.

static LinearModel 
fit(Formula formula,
DataFrame data,
java.util.Properties prop)
Fits an ordinary least squares model.

static LinearModel 
fit(Formula formula,
DataFrame data,
java.lang.String method,
boolean stderr,
boolean recursive)
Fits an ordinary least squares model.

public static LinearModel fit(Formula formula, DataFrame data)
formula
 a symbolic description of the model to be fitted.data
 the data frame of the explanatory and response variables.
NO NEED to include a constant column of 1s for bias.public static LinearModel fit(Formula formula, DataFrame data, java.util.Properties prop)
prop
include
smile.ols.method
(default "svd") is a string (svd or qr) for the fitting method
smile.ols.standard.error
(default true) is a boolean. If true, compute the estimated standard
errors of the estimate of parameters
smile.ols.recursive
(default true) is a boolean. If true, the return model supports recursive least squares
formula
 a symbolic description of the model to be fitted.data
 the data frame of the explanatory and response variables.
NO NEED to include a constant column of 1s for bias.prop
 Training algorithm hyperparameters and properties.public static LinearModel fit(Formula formula, DataFrame data, java.lang.String method, boolean stderr, boolean recursive)
formula
 a symbolic description of the model to be fitted.data
 the data frame of the explanatory and response variables.
NO NEED to include a constant column of 1s for bias.method
 the fitting method ("svd" or "qr").stderr
 if true, compute the estimated standard errors of the estimate of parameters.recursive
 if true, the return model supports recursive least squares.