OLSRegression

Create the regression data from a data frame. The data frame must have a column with the response name responseName and columns with the names in the list predictorNames. The data type of these columns must be Double. hasIntercept indicates if the regression should include an intercept term. The default is true. The data in the data frame does not need to have a column for estimating the intercept.

This is the adjusted R-squared = 1 - ((1 - R-squared)*(n-1)/(n-p)) where n is the number of observations and p is the number of parameters estimated (including the intercept).

An estimate of the variance of the (residual) errors. This is MSE = SSE/(n-p)

Indicates true if the regression model includes an intercept term.

The hat matrix is defined in terms of the design matrix X by

$X(X^{T}X)^{-1}X^{T}$

The total number of observations (y_1, y_2, ..., y_n), where n = the number of observations.

Number of parameters in the model (including the intercept, if estimated)

An array containing the estimated parameters of the regression. The b_0, b_1_,..., b_k, where b_0 is the intercept term and k is the number of parameters estimated, so p = k + 1 is the total number of parameters (including the intercept term).

The standard error estimate for each regression coefficient.

Estimates for the variance of the regression parameters. The variance-covariance matrix of the regression parameters

The names of the predictor variables

An estimate of the variance of Y. The sample variance of the dependent variable.

The average distance that the observed values fall from the regression line. It tells you how wrong the regression model is on average using the units of the response variable. Smaller values are better because it indicates that the observations are closer to the fitted line. The standard deviation of the errors in the regression model. Sometimes called the standard error of the estimate. This is the square root of MSE.

The array of residual errors, e_i = (y_i - yHat_i)

This is SSE (sum of squared residual error).

The response values, the regressand values, the Y's

The name of the response variable

This is the coefficient of multiple determination. R-squared = SSR/SST = 1 - SSE/SST, where SSE is the sum of squared residuals, SST is the total sum of squares, and SSR is the sum of squares for the regression. Note that SST = SSR + SSE.

The array of standardize residuals

The SST total sum of squares. Sum of squared deviations of Y from its mean.

Loads a new dataset for performing the regression analysis.

The data associated with the named predictor. The name must exist as a predictor name.