Developer Guide for Intel® Data Analytics Acceleration Library 2018
Given a data set X = (x i ) that contains vectors of input variables x i = (x i1, …, x ip ), respective responses z i = (z i1, …, z ik ) computed at the prediction stage of the linear regression model defined by its coefficients β ht , h = 1, ..., k, t = 1, ..., p, and expected responses y i = (y i1, …, y ik ), i = 1, ..., n, the problem is to evaluate the linear regression model by computing the root mean square error, variance-covariance matrix of beta coefficients, various statistics functions, and so on. See Linear Regression for additional details and notations.
For linear regressions, the library computes statistics listed in tables below for testing insignificance of beta coefficients:
The statistics are computed given the following assumptions about the data distribution:
For more details, see [Hastie2009].
The library uses the following quality metrics:
Quality Metric |
Definition |
---|---|
Root Mean Square (RMS) Error |
|
Vector of variances
|
|
A set of variance-covariance matrices C = C 1, ..., C k for vectors of betas β jt , j = 1, ..., k |
|
Z-score statistics used in testing of insignificance of a single coefficient β jt |
![]() |
Confidence interval for β jt |
![]() |
The library uses the following quality metrics:
Quality Metric |
Definition |
---|---|
Mean of expected responses, ERM = (ERM 1, ..., ERM k ) |
|
Variance of expected responses, ERV = (ERV 1, ..., ERV k ) |
|
Regression Sum of Squares RegSS = (RegSS 1, ..., RegSS k ) |
|
Sum of Squares of Residuals ResSS = (ResSS 1, ..., ResSS k ) |
|
Total Sum of Squares TSS = (TSS 1, ..., TSS k ) |
|
Determination Coefficient ![]() |
|
F-statistics used in testing insignificance of a group of betas F = (F 1, ..., F k ) |
![]() |