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

Description Usage Arguments Details Value Examples

The WREG.OLS function executes the multiple linear regression analysis using ordinary least-squares regression.

1	WREG.OLS(Y, X, transY, x0 = NA)

`Y`	The dependent variable of interest, with any transformations already applied.
`X`	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`.
`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.

This function follows the basic implementation of ordinary least-squares regression.

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). 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.

# Import some example data
peakFQdir <- paste0(
  file.path(system.file("exampleDirectory", package = "WREG"),
    "pfqImport"))
gisFilePath <- file.path(peakFQdir, "pfqSiteInfo.txt")
importedData <- importPeakFQ(pfqPath = peakFQdir, gisFile = gisFilePath)

# Run a simple regression
Y <- importedData$Y$AEP_0.5
X <- importedData$X[c("Sand", "OutletElev", "Slope")]
transY <- "none"
result <- WREG.OLS(Y, X, transY)