elasticNetBasic
Syntax
elasticNetBasic(Y, X, [mode], [alpha], [l1Ratio], [intercept], [normalize],
[maxIter], [tolerance], [positive], [swColName], [checkInput])
Details
Perform elastic net regression.
Minimize the following objective function:
Parameters
Y is a numeric vector indicating the dependent variable.
X is a numeric vector/tuple/matrix/table indicating the independent variable.
-
When X is a vector/tuple, it must be of the same length as Y.
-
When X is a matrix/table, the number of rows must be the same as the length of Y.
modeis an integer indicating the contents in the output. It can be:
-
0 (default): a vector of the coefficient estimates.
-
1: a table with coefficient estimates, standard error, t-statistics, and p-values.
-
2: a dictionary with the following keys: ANOVA, RegressionStat, Coefficient, and Residual.
|
Source of Variance |
DF (degree of freedom) |
SS (sum of square) |
MS (mean of square) |
F (F-score) |
Significance |
|---|---|---|---|---|---|
| Regression | p | sum of squares regression, SSR | regression mean square, MSR=SSR/R | MSR/MSE | p-value |
| Residual | n-p-1 | sum of squares error, SSE | mean square error, MSE=MSE/E | ||
| Total | n-1 | sum of squares total, SST |
|
Item |
Description |
|---|---|
| R2 | R-squared |
| AdjustedR2 | The adjusted R-squared corrected based on the degrees of freedom by comparing the sample size to the number of terms in the regression model. |
| StdError | The residual standard error/deviation corrected based on the degrees of freedom. |
| Observations | The sample size. |
|
Item |
Description |
|---|---|
| factor | Independent variables |
| beta | Estimated regression coefficients |
| StdError | Standard error of the regression coefficients |
| tstat | t statistic, indicating the significance of the regression coefficients |
Residual: the difference between each predicted value and the actual value.
alpha(optional) is a floating number representing the constant that multiplies the L1-norm. The default value is 1.0.
intercept (optional) is a Boolean value indicating whether to include the intercept in the regression. The default value is true.
normalize (optional) 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 (optional) is a positive integer indicating the maximum number of iterations. The default value is 1000.
tolerance (optional) 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.
solver (optional) is a string indicating the solver to use in the computation. It can be either 'svd' or 'cholesky'. It ds is a list of data sources, solver must be 'cholesky'.
swColName (optional) is a STRING indicating a column name of ds. The specified column is used as the sample weight. If it is not specified, the sample weight is treated as 1.
Returns
Depends on the mode parameter.