WREG.WLS: Weighted-Multiple-Linear Regression Program (WREG)
In USGS-R/WREG: USGS WREG v. 2.02

Description Usage Arguments Details Value Examples

The WREG.WLS function executes the multiple linear regression analysis using weighted least-squares regression.

1	WREG.WLS(Y, X, recordLengths, LP3, transY, x0 = NA)

`Y`	A numeric vector of the dependent variable of interest, with any transformations already applied.
`X`	A numeric matrix of the independent variables in the regression, with any transformations already applied. Each row represents a site and each column represents a particular independe variable. (If a leading constant is used, it should be included here as a leading column of ones.) The rows must be in the same order as the dependent variables in `Y`.
`recordLengths`	A numeric vector whose rows are in the same order as `Y` and represent the at-site record length.
`LP3`	A numeric matrix containing the fitted Log-Pearson Type III standard deviate, standard deviation and skew for each site. The columns of the matrix represent S, K, G, and an option regional skew value `GR` required by WREG.GLS with regSkew = TRUE. The order of the rows must be the same as `Y`.
`transY`	A required character string indicating if the the dependentvariable was transformed by the common logarithm ('log10'), transformed by the natural logarithm ('ln') or untransformed ('none').
`x0`	A vector containing the independent variables (as above) for a particular target site. This variable is only used for ROI analysis.

In this implementation, the weights for weighted least-squares regression are defined by record lengths. See manual for details.

All outputs are returned as part of a list. The elements of the list depend on the type of regression performed. The elements of the list may include:

`Coefs`	A data frame composed of four variables: (1) `Coefficient` contains the regression coefficeints estimated for the model, (2) `Standard Error` contains the standard errors of each regression coefficient, (3) `tStatistic` contains the Student's T-statistic of each regression coefficient and (4) `pValue` contains the significance probability of each regression coefficient.
`ResLevInf`	A data frame composed of three variables for each site in the regression. `Residual` contains the model residuals. `Leverage` contains the leverage of each site. `Influence` contains the influence of each site.
`LevLim`	The critical value of leverage. See `Leverage`
`InflLim`	The critical value of influence. See `Influence`
`LevInf.Sig`	A logical matrix indicating if the leverage (column 1) is significant and the influence (column 2) is significant for each site in the regression.
`PerformanceMetrics`	A list of not more than ten elements. All regression types return the mean squared error of residuals (`MSE`), the coefficient of determination (`R2`), the adjusted coefficient of determination (`R2_adj`) and the root mean squared error (`RMSE`, in percent). The pseudo coefficient of regression (`R2_pseudo`), the average variance of prediction (`AVP`), the standard error of prediction (`Sp`, in percent), a vector of the individual variances of prediction for each site (`VP.PredVar`), the model-error variance (`ModErrVar`) and the standardized model error variance (`StanModErr`, in percent) are also returned. Details on the appropriateness and applicability of performance metrics can be found in the WREG manual.
`X`	The input predictors.
`Y`	The input observations.
`fitted.values`	A vector of model estimates from the regression model.
`residuals`	A vector of model residuals.
`Weighting`	The weighting matrix used to develop regression estimates.
`Input`	A list of input parameters for error searching. Currently empty.