ridgeBasic(Y, X, [mode=0], [alpha=1.0], [intercept=true], [normalize=false], [maxIter=1000], [tolerance=0.0001], [solver='svd'], [swColName])


Perform Ridge regression.

Minimize the following objective function:



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)


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



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.



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.