Regressions

The regressions this instance offers: what each is for, the questions it answers and when to reach for something else. Operators are sorted by name; each name links to its detail block below.

Operators

REG_BAYES_LINEAR

Fits a straight-line model of a numeric outcome under a prior, reporting each coefficient’s posterior mean and credible interval.

Level: advanced

Also known as: bayesian linear regression

Questions it answers:

• Given the data and our prior belief, what range of values is plausible for the price coefficient?
• How do the coefficients shift when last year’s estimates are used as the prior?

Use cases by domain:

• survey: Fit a key-driver model on a small wave, using the previous wave’s coefficients as the prior mean.
• ops: Relate cost per order to volume when only a few weeks of data exist.
• science: Combine a small new study with earlier estimates of a dose-response slope.

Assumptions:

• Rows are independent of each other: repeated rows for the same customer, or values over time, make the reported uncertainty too small.
• The outcome changes linearly with each predictor, with normal residuals of constant spread (the model’s likelihood).
• The prior is conjugate Normal-Inverse-Gamma: each coefficient is normal around prior_mu (zeros by default, intercept first) with one shared precision for every coefficient, intercept included, measured relative to the residual variance: each coefficient’s prior standard deviation is σ / sqrt(prior_precision), so the prior’s strength changes with the noise level. The residual variance is inverse-gamma.
• The default prior is weak (precision 0.001), so with enough rows the coefficients sit close to REG_OLS. Its pull depends on each predictor’s units: a coefficient that is large because its predictor’s units are small is pulled harder toward prior_mu.
• Credible intervals are probability statements about each coefficient given the prior and the model; a wrong prior or a wrong model makes them wrong too.
• A coefficient describes association with the outcome, holding the other predictors fixed; it shows a causal effect only when the design supports one (for example random assignment), never from the fit alone, and a predictor left out of the model can drive both.
• Strongly related predictors (multicollinearity) make coefficients unstable; the prior keeps even an exactly collinear set solvable, but then the prior, not the data, decides how the shared association is split between them.
• Predictors must be numeric: encode a category as 0/1 columns first (FEAT_ONE_HOT) and leave one level out, or the columns are collinear with the intercept.
• Rows with a null target or predictor are dropped before fitting (listwise deletion); n_obs counts the rows used.

Use something else:

• REG_OLS when you want p-values, resampled standard errors or stepwise predictor selection (none run on this type).
• REG_GLM when the outcome is yes/no (0/1) or a count.
• TEST_PEARSON_R when you only want how closely two numeric fields follow a straight line together.

Glossary: credible-interval, heteroscedasticity, independence, listwise-deletion, multicollinearity, normal-distribution, posterior, prior, r-squared, regression-coefficient, residual

Skill: op-reg-bayes-linear

REG_GLM

Fits a generalized linear model: logistic regression for yes/no outcomes, Poisson for counts, gamma for positive skewed amounts.

Level: advanced

Also known as: generalized linear model, logistic regression, poisson regression, glm

Questions it answers:

• Which customer traits are associated with the chance of churning, holding the others fixed?
• How does the expected number of support tickets change with account size?

Use cases by domain:

• survey: Relate a yes/no answer (would recommend) to respondent attributes.
• ops: Model the count of incidents per site from traffic and staffing.
• science: Relate the probability of a response to dose and age.

Assumptions:

• Rows are independent of each other: repeated rows for the same customer, or values over time, make the reported uncertainty too small.
• The family must match the outcome: binomial needs a 0/1 (or packed_bool) target, Poisson non-negative counts, gamma positive values.
• Only the canonical link runs for each family (logit for binomial, log for Poisson, inverse for gamma); the predictors act linearly on that link scale.
• Each p-value is a Wald z test of the null hypothesis that its coefficient is 0 given the other predictors, with the dispersion fixed at 1. Overdispersed counts (variance above the mean) make Poisson p-values too small; gamma data rarely have dispersion 1, so gamma standard errors and p-values are unreliable, and the gamma path is not yet checked against a reference implementation.
• If a predictor separates the 0s from the 1s perfectly in a logistic model, the fit cannot converge and Pulse refuses it.
• A coefficient describes association with the outcome, holding the other predictors fixed; it shows a causal effect only when the design supports one (for example random assignment), never from the fit alone, and a predictor left out of the model can drive both.
• Strongly related predictors (multicollinearity) make coefficients unstable and their uncertainty large; Pulse refuses an exactly collinear set.
• Predictors must be numeric: encode a category as 0/1 columns first (FEAT_ONE_HOT) and leave one level out, or the columns are collinear with the intercept.
• Rows with a null target or predictor are dropped before fitting (listwise deletion); n_obs counts the rows used.

Use something else:

• REG_OLS when the outcome is a numeric measure with roughly symmetric, constant-spread residuals.
• TEST_PROP_Z when you only want to know whether a yes/no rate differs between two groups.
• TEST_CHISQ when the outcome and the single predictor are both categories.

Glossary: deviance, generalized-linear-model, independence, link-function, listwise-deletion, logistic-regression, multicollinearity, null-hypothesis, odds-ratio, overdispersion, p-value, pseudo-r-squared, regression-coefficient, skew, standard-error

Skill: op-reg-glm

REG_OLS

Fits a straight-line model that predicts a numeric outcome from one or more numeric predictors, by least squares.

Level: intermediate

Also known as: linear regression, ordinary least squares, lm

Questions it answers:

• Which of price, discount and season are associated with weekly sales, holding the others fixed?
• How much does predicted order value change per extra visit, with the other predictors held fixed?
• How much of the variation in satisfaction do these attribute ratings account for together?

Use cases by domain:

• survey: Relate overall satisfaction to several attribute ratings at once (often called key-driver analysis, though it shows which ratings go with satisfaction, not which ones drive it).
• ops: Model ticket handling time from queue length and agent tenure.
• science: Estimate how a measured response changes with dose while adjusting for body weight.

Assumptions:

• Rows are independent of each other: repeated rows for the same customer, or values over time, make the reported uncertainty too small.
• The outcome changes linearly with each predictor; model a curve by adding transformed predictors (FEAT_POLY, FEAT_LOG).
• Residuals have roughly constant spread: Pulse reports classic standard errors, not heteroscedasticity-robust ones. With few rows the residuals should also be roughly normal for the p-values to hold.
• Each p-value tests the null hypothesis that its coefficient is 0 given the other predictors, on a t distribution with n - p - 1 degrees of freedom (p predictors).
• A coefficient describes association with the outcome, holding the other predictors fixed; it shows a causal effect only when the design supports one (for example random assignment), never from the fit alone, and a predictor left out of the model can drive both.
• Strongly related predictors (multicollinearity) make coefficients unstable and their uncertainty large; Pulse refuses an exactly collinear set.
• Penalized fits (l1, l2, elasticnet) shrink coefficients toward 0 by design, so their p-values lose the usual reading; l1 and elasticnet standard errors are approximate and Pulse warns.
• Predictors must be numeric: encode a category as 0/1 columns first (FEAT_ONE_HOT) and leave one level out, or the columns are collinear with the intercept.
• Rows with a null target or predictor are dropped before fitting (listwise deletion); n_obs counts the rows used.

Use something else:

• REG_GLM when the outcome is yes/no (0/1) or a count.
• REG_BAYES_LINEAR when you want intervals that combine the data with prior knowledge about the coefficients.
• TEST_PEARSON_R when you only want how closely two numeric fields follow a straight line together.
• TEST_ANOVA_F when the predictor is a set of groups and you want to know whether the group averages differ.
• ATTR_REG_RESIDUAL when you want each row’s residual, to check the residual assumptions or find rows the model fits badly.

Glossary: adjusted-r-squared, degrees-of-freedom, heteroscedasticity, independence, listwise-deletion, multicollinearity, normal-distribution, null-hypothesis, outlier, overfitting, p-value, r-squared, regression-coefficient, residual, standard-error

Skill: op-reg-ols