Handbook of Regression Modeling in People Analytics

1. 1Build your model iteratively: start with a base model, add candidate inputs, and inspect the significance of each coefficient from the summary output.
2. 2Identify non-significant inputs (those whose effect on the outcome is not statistically distinguishable from zero) and mark them as candidates for removal.
3. 3Remove non-significant variables one at a time — 'gradual safe elimination' — rerun the model, and confirm the remaining coefficients and fit have not materially changed after each removal.
4. 4Assess explanatory power appropriate to the model type: R-squared for linear regression, and goodness-of-fit tests (e.g., the Hosmer-Lemeshow test) plus pseudo-R-squared measures for logistic regression.
5. 5Compute AIC for each competing model iteration using AIC() and compare values — the lowest AIC indicates the most parsimonious model among the candidates.
6. 6Cross-check that the lowest-AIC model is not also a poor-fitting model: run the goodness-of-fit tests separately, because AIC ranks parsimony, not absolute quality.
7. 7When inputs are numerous and unavoidable, apply coefficient regularization such as LASSO regression to shrink the effective input set rather than hand-pruning everything.
8. 8Watch for measurement problems that grow with input count — check for multicollinearity before finalizing, since more inputs raise its risk.

In the binomial logistic regression promotion example, three model iterations are compared by AIC. The sales-only model returns an AIC of 76.49508, the model with sales and customer rating returns 71.13145, and the full model with all inputs returns 76.37433. The two-input model limited to the significant predictors (sales and customer rating) has the lowest AIC and is therefore judged the most parsimonious. Fit is separately confirmed: almost all goodness-of-fit tests, including the Hosmer-Lemeshow test, suggest the model fits. The decision is to keep sales and customer rating and drop the non-significant inputs, because dropping them lowered AIC while preserving fit — the same logic that drove variable removal in both the linear and logistic approaches.

• If a variable's coefficient shows no significant effect on the outcome, then drop it — a model carrying information that doesn't serve the inference objective is more complex than needed.
• If two models achieve the same or very close fit, then prefer the one with fewer inputs (Occam's Razor).
• If comparing log-likelihood models like logistic regression, then rank candidates by AIC and select the lowest — but only after confirming acceptable fit.
• If the lowest-AIC model still fails goodness-of-fit tests, then do not treat it as good — AIC measures parsimony, not model quality or confidence.
• If the number of inputs is large and unavoidable, then use LASSO-style regularization instead of relying only on manual elimination.

• Treating the lowest AIC as proof of a good model — the tell: reporting AIC without ever running Hosmer-Lemeshow or a pseudo-R-squared, so a poor-fitting model gets shipped.
• Removing multiple non-significant variables in one pass rather than gradually — the tell: after a bulk cut, remaining coefficients or fit shift unexpectedly and you can't attribute the change.
• Padding the model with derived inputs to impress a stakeholder — the tell: new variables are mathematical transforms of measures already in the model, inflating complexity with no analytic gain.
• Letting inputs approach or exceed the number of observations — the tell: unstable coefficients, and a model too complex to interpret.
• Ignoring multicollinearity as input count rises — the tell: coefficients with implausible signs or huge standard errors after adding correlated predictors.

• ▸Model iteration label: name each candidate (e.g., sales only, sales + customer rating, all inputs).
• ▸Inputs included: list the variables in this iteration.
• ▸Non-significant inputs flagged: note any coefficient not distinguishable from zero.
• ▸Fit measure: record R-squared / pseudo-R-squared for this model.
• ▸Goodness-of-fit test result: record Hosmer-Lemeshow (or equivalent) pass/fail.
• ▸AIC value: enter the computed AIC for this iteration.
• ▸Multicollinearity check: note any correlated inputs or unstable coefficients.
• ▸Selection decision: mark keep/drop and the reason (lowest AIC with acceptable fit).

1. 1Fix the four interlocking quantities before you collect data: significance level (alpha, the Type I error rate), desired power (1 minus the Type II error rate), the effect size you consider meaningful, and the required sample size — power analysis solves for whichever one you leave open, typically sample size.
2. 2Match the power method to the model you intend to run: use simple hypothesis-test power analysis (Chapter 11.2) for a t-test or correlation, linear-regression power analysis (11.3) for continuous outcomes, log-likelihood power analysis (11.4) for logistic/multinomial outcomes, and hierarchical power analysis (11.5) when data are nested.
3. 3Set the effect size from something defensible — a prior study, a pilot, or the smallest effect that would change a people decision — rather than defaulting to a 'medium' convention, because the required n scales sharply with how small an effect you insist on detecting.
4. 4When your data have a latent hierarchy or grouping (employees within teams, repeated events per person), plan power under the hierarchical/mixed framework, since the effective sample size is smaller than the raw row count once you account for within-group correlation.
5. 5Run the calculation before fieldwork: input alpha (commonly 0.05), target power (commonly 0.80), and the expected effect size to get the minimum n; if the number exceeds your available population, either widen the effect size you will commit to detecting, reduce the number of predictors, or accept lower power and state it.
6. 6Recompute after you know your realistic sample: given the n you can actually obtain, back out the smallest effect your study can reliably detect, so you know in advance which effects you will and will not be able to see.
7. 7In people analytics specifically, treat small employee populations as a binding constraint — if the required n is unreachable, choose a method appropriate to small samples rather than forcing a model your data cannot power, and report the limitation.
8. 8Reproduce the same power computation in Python (11.6) if that is your stack, so the sample-size logic travels with the modeling code.

Suppose you want to test whether a learning program raises performance ratings, and you plan a Welch's t-test comparing trained versus untrained employees. Before pulling data, you decide alpha = 0.05 and target power = 0.80, meaning you accept a 5% chance of a false positive and want an 80% chance of detecting the effect if it is real. From a prior cohort you estimate the difference in mean ratings corresponds to a modest effect size, so you run a power analysis for a simple hypothesis test (Chapter 11.2), which returns a minimum n per group. If that n exceeds the number of trained employees available — a common squeeze in people analytics where populations are relatively small — you either commit only to detecting a larger effect, which lowers the required n, or you accept that with your available sample the study can only detect a large program effect and you document that ceiling. This keeps you from running the model, finding a non-significant result, and wrongly concluding the program does nothing when the study was simply underpowered.

• If the outcome is continuous, then use linear-regression power analysis (11.3); if it is binary or categorical, then use log-likelihood power analysis (11.4).
• If the data are nested (employees within groups, repeated events), then compute power under the hierarchical/mixed framework (11.5), never with a flat single-level formula.
• If the required n exceeds your available population, then either raise the minimum effect size you commit to detecting or reduce predictors — do not silently proceed at low power.
• If you cannot justify an effect size from prior data or a pilot, then state the assumption explicitly and report the smallest detectable effect for your actual n.
• If your employee population is small, then let power analysis pick the method — prefer a simpler test your data can power over a richer model it cannot.

• Running the model first and doing power analysis never — the tell is a non-significant result reported as evidence of 'no effect' with no statement of what effect the sample could have detected.
• Using the raw row count as the sample size in nested data — the tell is a hierarchical structure (repeated measures, teams) modeled as if every row were independent, inflating claimed power.
• Plugging in a conventional 'medium' effect size with no source — the tell is a suspiciously round required n and no reference to a pilot or prior study.
• Ignoring the small-population constraint typical of people analytics — the tell is a required n far larger than the organization's headcount, waved away rather than resolved.
• Optimizing only Type I error (chasing p < 0.05) while never setting a power target — the tell is alpha stated but power (1 minus Type II error) absent from the plan entirely.

• ▸Research question and outcome type: state the outcome and whether it is continuous, binary, or categorical.
• ▸Model to be run: name the method (t-test, linear, logistic, hierarchical) and matching power section (11.2–11.5).
• ▸Data structure: note any nesting/grouping and the expected within-group correlation.
• ▸Alpha (Type I error rate): set the significance level, e.g. 0.05.
• ▸Target power (1 − Type II error): set desired power, e.g. 0.80.
• ▸Effect size and its source: record the value and the pilot/prior study/decision threshold it comes from.
• ▸Required sample size: enter the n returned by the power calculation.
• ▸Available sample and gap: state the n you can actually obtain and whether it meets the requirement.
• ▸Smallest detectable effect at available n: if the gap is negative, record the effect ceiling and the decision to proceed, adjust, or switch methods.

1. 1Frame the inference as a claim about the population Ω, not the sample S: you are using the relationship between measured data X and outcome y to describe a relationship between constructs and outcome that holds to a high degree of statistical certainty beyond your data.
2. 2Define the model form explicitly as y = f(X) + ϵ, and decide parametric vs non-parametric. If you assume a formula (e.g. linear), you have committed to assumptions that must be checked before the inference is trustworthy.
3. 3Confirm the outcome satisfies the basic condition for your regression type (e.g. a continuous outcome for linear regression) before generalizing anything.
4. 4Run a power analysis to estimate the minimum sample size needed to detect the effect size of interest at your chosen error rate — do this before or alongside modeling, since people analytics data sets are rarely large.
5. 5Interpret each coefficient in its own terms and test its significance; drop or re-specify terms that are not significant (as with the Yr1 variable removed when it was not significant linearly).
6. 6Distinguish coefficient magnitude from importance and standardize your reasoning: larger coefficients (e.g. dummy variable coefficients) do not imply greater importance.
7. 7Validate the fitted relationship against alternatives (e.g. compare a quadratic term against the linear fit) and, in any predictive use, test on new data to guard against overfitting.
8. 8State the generalization limit explicitly: report which elements of the relationship can be carried from S to Ω and to what degree of statistical certainty.

Testing whether a quadratic term improves a linear model shows the discipline of valid inference in miniature. The author had already removed Yr1 from the model because it was not significant when modeled linearly. Rather than assume that a curved relationship might exist, he explicitly trialed a polynomial term using I() in the R formula notation so the ^ symbol is interpreted literally as 'the square of Yr1'. The resulting fit measure of 0.5304198 was compared against the prior fit, and the conclusion was that modeling Yr1 as a quadratic makes no difference. The inference held: no new term was retained because the data gave no evidence for one. Contrast this with the interaction model, where someone scoring very low in both Year 2 and Year 3 was awarded an unreasonably high score due to the intercept — a fit too tightly aligned to past data to generalize.

• If the outcome variable fails the basic condition for the model (e.g. not continuous for linear regression), then do not use that regression type — choose a variant matched to the outcome.
• If your sample size is below the minimum from a power analysis, then treat the inference as underpowered and do not generalize it to the population.
• If a term is not statistically significant, then remove it or refrain from claiming it as a driver — as with Yr1 modeled linearly.
• If a coefficient is large, then check whether it is a dummy variable or on a different scale before treating it as more important than smaller coefficients.
• If the model is used to predict rather than explain, then validate on new data, because a tight fit to past data (like the interaction model's inflated low-low score) signals overfitting rather than a generalizable relationship.

• Running multivariate models without understanding the underlying mathematics — the tell is being unable to explain why a coefficient or fit statistic means what it claims.
• Treating higher coefficients as more important — the tell is ranking drivers by raw coefficient size while ignoring scale and dummy-variable effects.
• Ignoring power — the tell is confidently generalizing from a small people-analytics data set that was never large enough to support the inference.
• Overfitting and then generalizing — the tell is nonsensical fitted values, like the interaction model awarding an unreasonably high score to someone scoring very low in both years.
• Adding terms without testing them against alternatives — the tell is keeping a quadratic or interaction term that produces no improvement in fit (e.g. no movement from 0.5304198).

• ▸Population Ω claim: one sentence on what relationship you want to generalize beyond the sample
• ▸Outcome condition: state outcome type and confirm it fits the chosen regression
• ▸Model form: write y = f(X) + ϵ; mark parametric or non-parametric
• ▸Assumptions to check: list each assumption the model form commits you to
• ▸Power/sample size: required minimum n from power analysis vs actual n
• ▸Significance results: list each term and whether it is significant (keep/drop)
• ▸Coefficient interpretation: note scale and dummy status before ranking importance
• ▸Alternative tested: which competing specification was compared and the fit difference
• ▸Generalization statement: which elements transfer from S to Ω and to what certainty

1. 1Start from the stakeholder's people decision, not the model: name the outcome O (e.g., hired) and the input constructs C the decision maker actually cares about before running anything.
2. 2Choose inference over prediction when the data set is small and the decision affects individuals — stakeholders will not bear consequences of a black box they cannot understand, so pick regression models that yield explainable coefficients.
3. 3Translate coefficients into ranked drivers and shares of variance explained: state which inputs are the strongest drivers, which have no significant relationship, and which have a negative relationship.
4. 4Quote effect direction, significance, and magnitude in plain language tied to the outcome, not statistical jargon (avoid presenting raw p-values as the headline).
5. 5Use dimension reduction (e.g., structural equation modeling with latent variables) when the regression problem is complex, to produce more intuitive and interpretable results for stakeholders.
6. 6Document the analysis in a reproducible integrated document (R Markdown) so the code and narration are easily obtained and rerun — undocumented work has limited impact and lifetime.
7. 7Check the analytic traps in steps 1-6 (reliable measurement of O, valid measures for C, collinearity) before generalizing any inference to the population, because a flawed inference misleads the decision.

In the recruiting data set, a stakeholder claims the aptitude test is a waste of time because its information is already in applicants' SAT scores and GPA. Rather than argue from opinion, you build a model regressing aptitude test score on SAT and GPA to see how much of the aptitude score those two explain, and you check for collinearity among SAT, GPA, and apttest. Separately you model the hired outcome using all inputs — interview ratings int1, int2, int3, apttest, SAT, and GPA — using logistic regression because hired is binary, then reduce to the most parsimonious set. If the aptitude test adds significant explanatory power to the hiring decision beyond SAT and GPA, you tell the stakeholder the test earns its place; if it does not, you have evidence to drop it. In the politics_survey example the same logic produces the clear stakeholder message: policies, habit, and interest in local issues are the three strongest drivers and explain roughly 70% of variance, interest in the environment is a significant negative driver, and interest in the economy has no significant relationship.

• If the data set is small or the decision has real impact on individuals, then choose an inferential regression model over a predictive one so stakeholders can understand and trust the output.
• If the outcome is binary (e.g., hired), then use a model appropriate for that type rather than forcing linear regression.
• If two inputs plausibly carry the same information (e.g., SAT and GPA vs. aptitude test), then test for collinearity and test incremental explanatory power before recommending you keep or drop a measure.
• If the regression problem has many correlated inputs and stakeholders need an intuitive story, then use latent variable / structural equation modeling to reduce dimensions and rank drivers.
• If a group difference is suspected (e.g., hiring by gender), then run the specific hypothesis test that isolates where in the process the difference arises rather than reporting only the overall gap.

• Running multivariate models without basic understanding of the underlying mathematics — the tell is being unable to answer or defend against critique of your method.
• Presenting predictive output to people-decision stakeholders with no explanation of how predictions are generated — the tell is stakeholders refusing to act on results they don't trust.
• Ignoring collinearity between inputs like SAT, GPA, and aptitude test — the tell is unstable or counterintuitive coefficients that flip when a variable is added or removed.
• Leaving analysis undocumented and non-reproducible — the tell is that no one else can obtain or rerun your code, so the insight dies quickly.
• Treating steps 1-6 (defining O, reliable measures for C, cleaning) as trivial and jumping to modeling — the tell is a technically clean model built on invalid measures, producing a confident but wrong inference.

• ▸Decision to inform: the specific people decision this analysis supports
• ▸Outcome O: the measured outcome and confirmation it has reliable data
• ▸Input constructs C: the drivers stakeholders care about and their data measures
• ▸Model type + why: chosen model and reason it fits (inference need, binary outcome, size)
• ▸Strongest drivers: ranked significant inputs with direction and variance explained
• ▸Non-significant / negative findings: inputs with no relationship or negative relationship, stated plainly
• ▸Collinearity check: variable pairs at risk and result of the test
• ▸Plain-language recommendation: the evidence-based action, no jargon
• ▸Reproducibility link: where the documented code (R Markdown) lives

1. 1Inspect the outcome column y first: check its data type, count of distinct values, and whether values are numeric, labeled categories, or a time/event pair. This single inspection dictates the entire model family.
2. 2If y is numeric and can take any value on a continuous scale, route to linear regression (Chapter 4) and plan to test its assumptions: linearity/additivity, constant error variance, normally distributed errors, and low multicollinearity.
3. 3If y has exactly two categories, route to binomial logistic regression (Chapter 5); model the log odds rather than the raw probability, then convert coefficients to odds and, where needed, to probabilities.
4. 4If y has three or more unordered categories, route to multinomial logistic regression (Chapter 6): pick a reference level and estimate one binomial-style contrast per remaining category against it.
5. 5If y has three or more ordered categories, route to proportional odds logistic regression (Chapter 7) and explicitly test the proportional odds assumption using stratified binomial coefficients and the Brant-Wald test before trusting the model.
6. 6If y is a singular event measured over time (with censoring), route to survival analysis: fit a Cox proportional hazard model (Chapter 9) and check the proportional hazard assumption; add a frailty term if grouped observations share unobserved risk.
7. 7If observations are nested in explicit groups (hierarchy), add random effects via a mixed model (Chapter 8.1); if the construct itself is latent and measured by multiple indicators, use a structural equation model (Chapter 8.2).
8. 8Confirm the same technique is available in your language of choice (R or Python via statsmodels OLS, logistic, multinomial, SEM, survival) before committing, so implementation matches the outcome type.

Consider the salespeople data set, which records sales, average customer ratings and performance ratings. If you model 'sales' (a continuous numeric column) as the outcome, linear regression is appropriate: you fit y = f(X) + ε with a linear f, interpret each coefficient as the change in sales per unit of input, and then check constant error variance and normally distributed errors. If instead you recode the outcome to whether a salesperson was promoted (yes/no), the outcome is now binary, so you switch to binomial logistic regression and interpret coefficients as log odds. If the outcome were an ordered performance rating (low/medium/high), you would move again to a proportional odds model and test that assumption with the Brant-Wald test. The same X columns feed all three, but the measurement nature of y forces three different techniques.

• If y is continuous, then use linear regression and validate the four assumptions before interpreting coefficients.
• If y has two categories, then use binomial logistic regression and model log odds, not raw probability.
• If y has unordered categories ≥3, then use multinomial logistic regression with a chosen reference level; if the categories are ordered, then use proportional odds logistic regression instead.
• If y is a time-to-event with censoring, then use a Cox proportional hazard model and verify the proportional hazard assumption.
• If observations are nested in known groups or the construct is latent, then add random effects (mixed model) or move to an SEM rather than a flat single-level regression.

• Treating an ordinal outcome as nominal (multinomial) and discarding the ordering — the tell is coefficients that trend monotonically across categories, signaling proportional odds would fit more parsimoniously.
• Fitting a proportional odds model without testing the assumption — the tell is divergent coefficients across stratified binomial models and a failed Brant-Wald test.
• Running linear regression on a binary or count outcome — the tell is predicted probabilities outside 0–1 and non-constant error variance in residual plots.
• Ignoring censoring by modeling time-to-event as a plain continuous outcome — the tell is systematically biased time estimates because incomplete follow-up is treated as the event time.
• Fitting a flat model when data are hierarchically grouped — the tell is underestimated standard errors and correlated residuals within groups that a mixed model or frailty term would absorb.

• ▸Outcome column name: name the single y column you are modeling.
• ▸Data type: record numeric, categorical-labeled, or time+event pair.
• ▸Distinct value count: count unique outcome values.
• ▸Ordered?: state whether categories have a natural order (yes/no).
• ▸Censoring present?: note if any observations are incomplete over time (yes/no).
• ▸Grouping structure: list any nesting or repeated-measure groups in the data.
• ▸Selected technique: write the routed model (linear / binomial / multinomial / proportional odds / Cox / mixed / SEM).
• ▸Assumption to test: name the key assumption for that technique (e.g., proportional odds, proportional hazard, constant error variance).

1. 1Produce a statistical and structural overview of the data before choosing a model: inspect data types, check scales across variables (e.g. different years scored on 0–100, 0–200, 0–300), and confirm whether NA counts appear in the summary to detect missingness.
2. 2Plot variables pairwise to read the diagonal distributions and the off-diagonal correlation statistics; note which pairs are strongly correlated (Yr3–Final), moderately correlated (Yr2–Final), and which are relatively independent.
3. 3Test the independence assumption explicitly: ask whether one observation's outcome could be influenced by another's (salespeople serving the same customers), because if so the data is not independent and identically distributed and you must adjust techniques.
4. 4When observations cluster within an explicit grouping (repeated measures, shared customers, nested units), route to a mixed model that separates fixed effects from random effects rather than using ordinary linear regression.
5. 5When many measured items are believed to reflect a smaller set of unmeasured constructs (survey items reflecting engagement), route to a structural equation model: first run and assess the measurement model, then run and interpret the structural model.
6. 6Check collinearity implications for interpretation: rescale numerical inputs onto common scales so scaled coefficients rank construct importance, and remember single terms outrank two-way interactions which outrank three-way interactions in coefficient hierarchy.
7. 7Verify residual independence as a downstream check of the structure assumptions: plot residuals against fitted values and against each input variable, looking for a random distribution with no discernible pattern.

You are given the ugtests data for 975 graduates with Yr1 (0–100), Yr2 and Yr3 (0–200), and Final (0–300) scores. A summary confirms all four columns read as numeric, the different scales match what you were told, means show Year 2 was the hardest, and no NA counts appear, so there is no missing data. A pairplot shows relatively normal distributions on the diagonal and, off-diagonal, a strong Yr3–Final correlation, a moderate Yr2–Final correlation, and relative independence elsewhere. Because each student's scores are their own and not influenced by other students, the independence assumption holds and ordinary linear regression is appropriate here. This structural read tells you Yr3 will carry the model, Yr1 may drop out as insignificant, and that interaction and quadratic terms can be trialed to capture trajectory effects between years.

• If one observation's outcome can be influenced by another's (shared customers, nested groups), then treat the data as hierarchical and adjust techniques rather than assuming i.i.d.
• If the hierarchy is explicit (observations grouped by a known clustering variable), then use a mixed model with fixed and random effects; if the hierarchy is latent (many items reflecting hidden constructs), then use a structural equation model.
• If the summary shows NA counts, then resolve missingness before modeling; a clean summary with no NA is your confirmation the data is complete.
• If an interaction term is significant, then automatically regard the single terms inside it as significant and retain them.
• If inputs are on different scales and you need ranked importance, then rescale onto common scales so coefficients are comparable.

• Assuming independence when observations share drivers — tell: individuals' outcomes are proportions of the same shared total (salespeople splitting one customer's sales), yet you fit a flat regression.
• Missing latent hierarchy — tell: you regress dozens of survey items directly on an outcome instead of modeling the underlying constructs they reflect via a measurement model.
• Overloading interactions — tell: interpretability collapses as you add many interaction combinations, and coefficients no longer read cleanly against the single-term hierarchy.
• Ignoring differing scales — tell: coefficients look incomparable and you misrank input importance because variables run 0–100 versus 0–300 and were never rescaled.
• Skipping the residual independence check — tell: residuals plotted against fitted values or an input show a clear pattern, signaling the structure or linearity assumption is violated.

• ▸Data types & scales: list each variable's type and measurement range
• ▸Missingness: record NA counts per column from the summary
• ▸Pairwise correlations: note strong / moderate / independent variable pairs
• ▸Independence check: can any observation influence another? yes/no + reason
• ▸Explicit hierarchy: name any grouping/clustering variable present
• ▸Latent hierarchy: list items suspected to reflect a hidden construct
• ▸Rescaling needed: mark variables to put on a common scale
• ▸Chosen approach: linear / mixed model / SEM + one-line justification
• ▸Residual check plan: fitted-vs-residual and per-input residual plots to run

1. 1Classify the outcome variable first. Determine whether it is continuous (e.g., compensation, engagement score), binary (attrition yes/no), nominal with 3+ unordered categories (product choice A/B/C), ordered categorical, or time-to-event with censoring.
2. 2For a continuous outcome, select linear regression (Chapter 4) and plan to test its assumptions: linearity/additivity, constant error variance, normally distributed errors, and absence of high collinearity.
3. 3For a binary outcome, select binomial logistic regression (Chapter 5), which models the log odds through a logistic function rather than the raw outcome.
4. 4For a nominal outcome with more than two unordered categories, select multinomial logistic regression (Chapter 6); confirm whether you will run stratified binomial models (one category versus others) as the building block.
5. 5For an ordered-category outcome, use proportional odds; for a time-to-event outcome such as attrition timing with censored cases, use Cox proportional hazard regression (Chapter 9), and consider frailty models when grouped observations share unobserved risk.
6. 6Check the data structure alongside outcome type: if observations are nested or grouped, plan for a mixed model; if you are measuring latent constructs from survey items (e.g., employee engagement), plan for structural equation modeling (Chapter 8).
7. 7Confirm you have adequate sample size before committing. People analytics populations are often small, which can limit the methods available; run a power analysis (Chapter 11) to estimate the minimum sample needed for meaningful inference.
8. 8Remember the primary aim in most people analytics work is explanation, not prediction, so favor a method whose coefficients you can interpret and defend under critique over a black-box alternative.

A team wants to understand employee attrition. Because the interest is whether an employee leaves or stays, the outcome is binary, so binomial logistic regression fits—modeling the log odds of leaving from inputs like tenure and compensation. If instead the question shifts to how long employees stay before leaving, the outcome becomes time-to-event with censoring (some employees have not yet left at the study's end), which the book handles with Cox proportional hazard regression using employee attrition as its walkthrough. If employees are grouped within teams that share unmeasured attrition risk, a frailty model extends the Cox approach. The same attrition data thus routes to different methods purely because the outcome definition changed from a binary state to a timed event. Selecting the wrong one—say linear regression on a 0/1 leave flag—produces predicted probabilities outside 0–1 and violates the constant-error-variance and normal-error assumptions.

• If the outcome is continuous, then use linear regression and test its four assumptions before interpreting.
• If the outcome is binary, then use binomial logistic regression rather than linear regression so predictions stay in probability space.
• If the outcome has 3+ unordered categories, then use multinomial logistic regression; if the categories are ordered, then use proportional odds instead.
• If the outcome is time-to-event with censored cases, then use Cox proportional hazard regression, adding frailty terms when observations are grouped.
• If you are measuring latent variables from survey items or observations are nested, then use structural equation modeling or a mixed model respectively rather than a standard single-level model.

• Running a multivariate model with no grasp of its underlying mathematics—the tell is inability to answer basic critique about why coefficients behave as they do.
• Applying linear regression to a binary or categorical outcome—the tell is fitted probabilities below 0 or above 1 and failed error-variance/normality checks.
• Ignoring censoring and treating time-to-event data as a continuous or binary outcome—the tell is dropping or mislabeling employees who have not yet experienced the event.
• Choosing a method without checking sample size in small employee populations—the tell is unstable coefficients and wide confidence intervals that no power analysis was run to anticipate.
• Optimizing for prediction accuracy when the stakeholder question is 'why'—the tell is a well-scoring but uninterpretable model that cannot support an evidence-based recommendation.

• ▸Outcome variable: name it and state its measurement type (continuous / binary / nominal / ordinal / time-to-event).
• ▸Number of outcome categories: enter 2, 3+, and whether ordered.
• ▸Censoring present: yes/no — any observations without the event by study end?
• ▸Data structure: flat, nested/grouped, or latent-from-survey-items.
• ▸Primary aim: explanation or prediction — which does the stakeholder need?
• ▸Sample size: record N and note if population is small.
• ▸Candidate method: linear / binomial / multinomial / proportional odds / mixed / SEM / Cox.
• ▸Assumption/power check: list checks required for the chosen method before interpretation.

1. 1State the model type first, because interpretation rules differ: linear regression coefficients read as change in the outcome per one unit of input; binomial logistic coefficients are on the log-odds scale and must be exponentiated to become odds ratios before you speak them plainly.
2. 2For each continuous input, define the unit explicitly (a dollar, a year, a point) and phrase the coefficient as 'holding all other inputs constant, a one-unit increase in X changes the outcome by [coefficient] units'.
3. 3For each categorical input, identify the reference level, then read every dummy coefficient as the effect of a 'switch' from that reference to the named category, comparing two observations otherwise identical (same manufacturing cost, same make).
4. 4Check the sign to state direction (positive raises the outcome, negative lowers it), then attach the significance test from the coefficient confidence output to decide whether you assert the relationship at all.
5. 5For logistic output, exponentiate the log-odds coefficient to get an odds ratio; report an odds ratio above 1 as increased odds and below 1 as decreased odds, and keep odds distinct from probability.
6. 6Refuse to rank inputs by raw coefficient size — normalize the comparison by unit scale before making any claim about relative influence.
7. 7Close by verifying model assumptions (linearity, additivity) hold, since a violated assumption makes the coefficient statement inaccurate regardless of how cleanly you word it.

Take the vehicle data set predicting retail price, with make encoded as dummy variables and Audi set as the reference. The manufacturing cost coefficient is read as: comparing two cars of the same make, each extra dollar spent on manufacturing changes retail price by that coefficient's number of dollars. The Ford dummy coefficient is read as: comparing a Ford with an Audi of the same manufacturing cost, we expect a difference in retail price of that coefficient. The Toyota dummy reads the same way against Audi at equal manufacturing cost. Note the dummy coefficients will typically look much larger than the manufacturing-cost coefficient, because a dummy flips a binary all-or-nothing state while a unit of manufacturing cost is one dollar out of many thousands. This scale difference is exactly why you cannot rank the inputs by coefficient value — a bigger number here does not mean greater importance.

• If the outcome is continuous and modeled by OLS, then interpret coefficients directly in outcome units; if binary and modeled by logistic regression, then exponentiate to odds ratios before interpreting.
• If the input is a dummy variable, then always phrase the effect as a switch from the reference level between two otherwise-identical observations.
• If two coefficients differ in raw magnitude, then do not infer relative importance until you account for the differing unit scales of each input.
• If a coefficient's significance test does not clear your threshold, then withhold any claim of a real relationship rather than reporting the point estimate as fact.
• If the linearity or additivity assumption fails, then do not translate the coefficient into a meaningful statement until the model form is corrected.

• Ranking inputs by coefficient value — the tell is a summary that calls the dummy variable 'the biggest driver' simply because its number is large, ignoring that a dollar-scale input will always show a smaller coefficient.
• Reading logistic coefficients as if they were on the outcome scale — the tell is a statement about probability change when the raw coefficient is actually log-odds and was never exponentiated.
• Omitting the reference level when interpreting dummies — the tell is a claim about 'the effect of being a Ford' with no comparison group named.
• Confusing odds with probability — the tell is treating an odds ratio of 2 as 'twice as likely' in probability terms.
• Stating a coefficient without defining its unit — the tell is 'a one-unit increase' where the reader cannot tell if a unit is a dollar, a year, or a category flip.

• ▸Model type: linear or logistic (sets whether you exponentiate).
• ▸Input variable name: the coefficient you are interpreting.
• ▸Unit of the input: one dollar, one year, one point, or a category switch.
• ▸Reference level (categorical only): the level all dummy switches are measured against.
• ▸Coefficient value and scale: raw number, plus odds ratio if logistic.
• ▸Direction: positive raises / negative lowers the outcome.
• ▸Significance verdict: passes or fails your threshold — assert only if passes.
• ▸Plain-language statement: 'holding others constant, a one-[unit] change in [input] changes [outcome] by [value].'
• ▸Ranking caution flag: note the input's scale so no false importance comparison is made.

1. 1After fitting a linear model, test linearity and additivity: plot residuals against each continuous input and against fitted values; a random band around zero confirms linearity, any curve or systematic bend signals you need a quadratic/polynomial term (section 4.6.2) or interaction (4.6.1).
2. 2Test constant error variance (homoscedasticity) by inspecting the residuals-vs-fitted plot for a fanning or funnel shape; widening spread across fitted values means the constant-error-variance assumption is violated.
3. 3Test normally distributed errors by examining the distribution of residuals (e.g., a Q-Q plot); departures in the tails tell you inferences on coefficients may be unreliable.
4. 4Check collinearity among inputs before trusting coefficient confidence intervals; high correlation between inputs inflates standard errors so you cannot separate individual effects — drop or combine collinear inputs.
5. 5For proportional odds logistic regression, test the proportional odds assumption explicitly: sight the coefficients of stratified binomial models to see whether slopes are stable across category cutoffs, then confirm with the Brant-Wald test.
6. 6For a Cox model, check the proportional hazard assumption before reporting hazard ratios; if hazards are not proportional over the study period the single hazard ratio is misleading.
7. 7When an assumption fails, move to the documented alternative rather than forcing the model: add polynomial/interaction terms for nonlinearity, or use an alternative to proportional odds models (section 7.3.3) when parallel slopes do not hold.

You are an analyst for a sports broadcaster examining player discipline across 2000+ players, with an ordered outcome discipline (None, Yellow, Red). Because the outcome is ordered, you choose proportional odds logistic regression, whose core assumption is that no input has a disproportionate effect on a specific level of the outcome — the 'slope' of the logistic function is the same for all category cutoffs (the parallel regression assumption). Before trusting any statement like 'each unit increase in x raises the odds of higher discipline by a fixed ratio,' you validate this. You first fit stratified binomial models (None-vs-rest, and Red-vs-rest) and sight whether the coefficients are similar across the cutoffs. You then run the Brant-Wald test as a formal check. If the coefficients diverge and Brant-Wald flags a violation, you cannot reduce the model to a single coefficient set and the approach fails, so you turn to an alternative to proportional odds models rather than reporting invalid ratios.

• If residuals-vs-fitted shows a curve, then add quadratic/higher-order or interaction terms instead of reporting the linear fit.
• If the residual spread fans out across fitted values, then the constant-error-variance assumption is violated and coefficient inference is untrustworthy.
• If two inputs are highly correlated, then their inflated standard errors mean you should not interpret their individual coefficients — combine or drop one.
• If the Brant-Wald test flags a violation or stratified binomial slopes differ across cutoffs, then abandon the single proportional odds model for a documented alternative.
• If the Cox proportional hazard check fails, then do not report a single hazard ratio as if it holds across the whole study period.

• Reporting coefficients and p-values without ever plotting residuals — the tell is a clean-looking output table but no linearity/homoscedasticity/normality diagnostics in the workflow.
• Interpreting individual coefficients under high multicollinearity — the tell is large standard errors and unstable signs when inputs are added or removed.
• Running a proportional odds model and skipping the Brant-Wald test — the tell is a single coefficient set presented with no parallel-slopes verification.
• Fitting a Cox model and citing hazard ratios without checking proportional hazards — the tell is a hazard ratio quoted as constant over time with no diagnostic.
• Treating small people-analytics samples (populations are often relatively smaller) as if large-sample assumptions hold — the tell is using z-based reasoning on samples under ~50 where the t-distribution matters.

• ▸Model chosen: name the method and why the outcome type fits it
• ▸Linearity/additivity: describe residual-vs-input pattern and any polynomial/interaction fix
• ▸Constant error variance: note residual spread across fitted values (funnel? yes/no)
• ▸Normality of residuals: record Q-Q or distribution check result
• ▸Collinearity: list highly correlated input pairs and action taken
• ▸Proportional odds: record stratified slope comparison and Brant-Wald result (if ordinal)
• ▸Proportional hazards: record Cox PH check result (if survival)
• ▸Decision on violations: state which alternative model or term you adopted
• ▸Inference confidence: sample size and t vs z choice noted