ridgeBasic

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.

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.

A vector, table, or dictionary, depending on the mode parameter

Example 1: Set mode=0 to output a coefficient estimate vector.

Y = [225.72, -76.20, 63.09, 139.45, -65.55]
X0 = [2.24, -0.85, 0.40, 1.45, -0.98]
X1 = [0.98, 0.31, 1.76, 0.14, 1.87]

coefficients = ridgeBasic(Y, [X0, X1], mode=0, alpha=0.5, intercept=true)
coefficients

// Output：[7.940468476954727, 88.20426761349431, 9.380634942436586]

Example 2: Set mode=1 to output a dictionary containing ANOVA (analysis of variance), RegressionStat, Coefficient, and Residual.

Y = [1.5, 2.3, 4.7, 3.2, 5.1]
X = matrix([1.1, 2.2, 3.1, 2.8, 4.0], [0.5, 0.8, 1.2, 1.0, 1.5])

result = ridgeBasic(Y, X, mode=2, alpha=0.8, solver='svd')

View analysis of variance.

result[`ANOVA]

View regression statistics.

result[`RegressionStat]

View regression coefficients.

result[`Coefficient]

View residuals.

result[`Residual]
// Output: [-0.06612025001746513, -0.5218539263508712, 0.7814669006299755, -0.32309620576716735, 0.12960348150553003]