A focus in this release is on regression enhancements, although other important features have been added as well. Release 4.10 contains the following new features:

**Polynomial Regression**

A new **Polynomial Regression **data analysis tool has been added.

In addition, the following new functions are supported which provide similar support to that is provided by the new data analysis tool. Here, Rx and Ry are column arrays containing *x* and y data values and *deg* is the degree/order of the polynomial

**PolyDesign**(Rx, *deg, ones*) – returns an array consisting of *x*, *x*^{2}, …, *x*^{deg} columns. If *ones* = TRUE, then the output is 1, *x*, *x*^{2}, …, *x*^{deg}

**PolyCoeff**(Rx, Ry, *deg*) – returns a column array consisting of the polynomial regression coefficients and their standard errors

**PolyRSquare**(Rx, Ry, *deg*) = R-square value for the polynomial regression

**PolyDeg**(Rx, Ry, *max**deg*) = the highest degree polynomial ≤ *maxdeg* which produces a significantly different R-square value

**Least Absolute Deviation **(**LAD**)** Regression**

A new **Least Absolute Deviation Regression **data analysis tool has been added.

In addition, the following new functions are supported which provide similar support to that provided by the new data analysis tool. Here, Rx is an *n × k* array containing *x* data values, Ry is an *n ×* 1 array containing y data values and *iter* is the number of iterations used in the **iteratively reweighted least squares algorithm** (default = 25).

**LADRegCoeff**(Rx, Ry, *iter*) = *k *×* *2 range consisting of the regression coefficient vector followed by vector of standard errors of these coefficients

**LADRegWeights**(Rx, Ry, *iter*) = *n *×* *1 column range consisting of the weights calculated from the iteratively reweighted least squares algorithm

Note, that in addition to describing the iteratively reweighted least squares algorithm, the website will also describe the **Simplex method** for calculating the LAD regression coefficients.

**New Extracting Columns from a Data Range Data Analysis Tool**

The existing **Extracting Columns from a Data Range** data analysis tool has been completely revised. In addition to more easily selecting which columns you want to retain from a data range, you will now have the option to create (1) tag/dummy or categorical codes for selected columns, (2) interactions between the variables (e.g. *x*y) representing selected columns and (3) powers of variables in selected columns (*x*^{2}, *x*^{3}, etc.).

**Simplifications to Regression Data Analysis Tools**

The **Multiple Regression** data analysis tool has been simplified by the elimination of the Tag/dummy coding options. These capabilities are now provided, in a simpler-to-use way, by the **Extract Columns from a Data Range** data analysis tool.

The** Logistic Regression** data analysis tool has also been simplified by the elimination of the Categorical coding and the Deletion of variables options. These capabilities are now provided, in a simpler-to-use way, by the **Extract Columns from a Data Range** data analysis tool.

**Stepwise Regression Capabilities**

A** Stepwise Regression** option has been added to the **Multiple Regression** data analysis tool. When this option is selected an automatic selection of a subset of variables is made that produces a regression model that fits the data which is in some sense similar to that of the full regression model containing all the variables.

The output from this data analysis tool shows how the stepwise selection of variable was made along with the regression analysis using these variables.

In addition, the following new functions are supported which are used by the new data analysis tool. Here, Rx is an *n × k* array containing *x* data values, Ry is an *n ×* 1 array containing y data values and Rv is a 1 *× k* array containing a non-blank symbol if the corresponding variable is in the regression model and an empty string otherwise.

**RegRank**(Rx, Ry, Rv) – returns a 1 *× k* array containing the p-value of each* x* coefficient that can be added to the regression model defined by Rx, Ry and Rv.

**RegCoeffP**(Rx, Ry, Rv) – returns a 1 *× k* array containing the p-value of each* x* coefficient in the regression model defined by Rx, Ry and Rv.

**RegStepwise**(Rx, Ry) – returns a 1 *× k* array Rv where each non-blank elements in Rv corresponds to an *x* variable that should be retained in the stepwise regression model. Actually the output is a 1 *× k+*1 array where the last element is a positive integer equal to the number of steps performed in creating the stepwise regression model.