# elasticNet

**Syntax**

elasticNet(ds, yColName, xColNames, [alpha=1.0], [l1Ratio=0.5], [intercept=true], [normalize=false], [maxIter=1000], [tolerance=0.0001], [positive=false])

**Arguments**

ds is an in-memory table or a data source usually generated by the sqlDS function.

yColName is a string indicating the column name of the dependent variable in *ds*.

xColNames is a string scalar/vector indicating the column names of the independent variables in *ds*.

alpha is a floating number representing the constant that multiplies the L1-norm. The default value is 1.0.

l1Ratio is a floating number between 0 and 1 indicating the mixing parameter. For l1Ratio = 0 the penalty is an L2 penalty; for l1Ratio = 1 it is an L1 penalty; for 0 < l1Ratio < 1, the penalty is a combination of L1 and L2. The default value is 0.5.

intercept is a Boolean value indicating whether to include the intercept in the regression. The default value is true.

normalize is a Boolean value. If true, the regressors will be normalized before regression by subtracting the mean and dividing by the L2-norm. If intercept=false, this parameter will be ignored. The default value is false.

maxIter is a positive integer indicating the maximum number of iterations. The default value is 1000.

tolerance is a floating number. The iterations stop when the improvement in the objective function value is smaller than tolerance. The default value is 0.0001.

positive is a Boolean value indicating whether to force the coefficient estimates to be positive. The default value is false.

**Details**

Linear regression with combined L1 and L2 priors as regularizer.

Minimize the following objective function:

**Examples**

```
$ y = [225.720746,-76.195841,63.089878,139.44561,-65.548346,2.037451,22.403987,-0.678415,37.884102,37.308288]
$ x0 = [2.240893,-0.854096,0.400157,1.454274,-0.977278,-0.205158,0.121675,-0.151357,0.333674,0.410599]
$ x1 = [0.978738,0.313068,1.764052,0.144044,1.867558,1.494079,0.761038,0.950088,0.443863,-0.103219]
$ t = table(y, x0, x1)
$ elasticNet(t, `y, `x0`x1);
```

If t is a DFS table, then the input should be a data source:

```
$ elasticNet(sqlDS(<select * from t>), `y, `x0`x1);
```