Several predictors, one continuous outcome, and coefficients that mean something more specific than most write-ups claim. What holding constant actually means, which assumptions decide the result, and how to report it in APA 7.
Linear regression predicts one continuous outcome from one or more predictors. Each coefficient, reported as B, is the expected change in the outcome for a one-unit increase in that predictor, with the other predictors in the model held constant.
That final clause carries the whole meaning and is where interpretation usually goes wrong. A coefficient is not the relationship between the predictor and the outcome. It is the relationship that remains after the other predictors have accounted for what they can. Add a correlated predictor and the coefficient changes, sometimes dramatically, sometimes reversing sign. Neither version is wrong; they answer different questions.
This is why a regression coefficient cannot be quoted without its model. The same predictor in two models is two different quantities, and comparing them across published studies with different covariate sets is not a like-for-like comparison.
The run opens with four figures across the top: R squared with adjusted R squared beneath it, the model F with both degrees of freedom, the model p, and n, the number of cases used. Those four are the model-level summary and they are the first thing to read.
The Coefficients card gives one row per term, starting with the intercept: B, SE, t, and p for each. Quanta prints exact relational p values, so a non-significant predictor reads as = .339 rather than as a bare ns.
A Readiness card states whether the setup produced automated cautions, such as sample-size or model-fit warnings. A clean run reports no automated cautions, which is a positive statement rather than an absence of output. It tells you the check ran.
Note what the coefficients table does not include: confidence intervals. APA 7 asks for them, so compute them from B and SE, or report B with its standard error and say so.
R squared is the proportion of variance in the outcome the model accounts for. It has one property worth knowing before you use it: adding any predictor increases it, even a column of random numbers.
Adjusted R squared penalizes for the number of predictors and can fall when a predictor earns nothing. That makes it the honest figure for a multi-predictor model, and Quanta prints it directly beneath R squared so both are in view. A five-predictor model at .362 and .349 has lost little to the adjustment, which means the predictors are largely earning their place.
A large R squared does not mean the model is correct, and a small one does not mean it is useless. In social and behavioral research, models explaining 15% of the variance in human behavior can be both true and important. Judge the figure against your field.
Linearity. Each predictor's relationship with the outcome is assumed to be a straight line. A curve there means the model is misspecified, and no amount of significance testing repairs it.
Independent errors. Violated by clustered data, where students sit within classrooms or patients within clinics. Standard errors come out too small and everything looks more significant than it is. Clustered designs need a multilevel model, not an OLS regression with a cluster dummy.
Constant variance of the residuals. When the spread of errors grows with the fitted value, coefficients stay unbiased but standard errors are wrong.
Multicollinearity. Not an assumption but a practical problem. Highly correlated predictors produce unstable coefficients with inflated standard errors, and the classic symptom is a model that is significant overall while no individual predictor is. Check the correlations among your predictors before modelling; a correlation matrix is the cheapest diagnostic available.
Enough cases per predictor. Rules of thumb run from ten to twenty cases per predictor. Small samples with many predictors produce models that fit this dataset and nothing else.
Lay the data out one row per case, with one column per predictor and one for the outcome.
Upload categorical predictors as text rather than numeric codes. A category stored as 1, 2, 3 will be read as a quantity, and a regression will happily treat three unordered groups as a linear scale. This is one of the quietest ways to produce a wrong model.
Configure the outcome and predictors on the right and the summary tiles, coefficients, and readiness check appear in the center panel.
Check your scale items are correctly scored first. A reverse-worded item that was never rescored enters the model with its sign flipped and its coefficient is uninterpretable. See reverse-coded items.
Decide the predictor set from theory before you run. Adding and removing predictors while watching p values is a search procedure, and the p values it produces no longer mean what they claim.
Use the action bar to add the result to a report, copy the table, or copy the APA text. Every result carries the ReliCheck Intelligence card for a plain-language explanation computed on your Mac.
Report the overall model with F, both degrees of freedom, p, and adjusted R squared, then the coefficients in a table.
The model accounted for a significant proportion of variance in job performance, F(5, 244) = 27.66, p < .001, R² = .36, adjusted R² = .35. Self-awareness item 2 was a significant positive predictor, B = 2.04, SE = 0.57, t(244) = 3.60, p < .001.
Give unstandardized coefficients with their standard errors, and add confidence intervals where your journal requires them.
State the full model. A coefficient without its covariate set is uninterpretable, and readers cannot reconstruct it from a results table alone.
Do not interpret the p values of control variables as findings. They were included to adjust, not to be tested.
Every result carries a ReliCheck Intelligence card with one action: explain this result in plain language. It runs entirely on your Mac with Apple Intelligence. No upload, no API key, nothing to configure. The model only explains the result Quanta has already computed and validated. It never computes a statistic, and it never applies a decision on your behalf.
From the action bar you can add the result to a report, copy the table, or copy the APA text. Exported reports carry the APA table, its note, and a caution specific to that analysis beneath it.
Quanta's linear regression is validated against the NIST Statistical Reference Datasets, matching certified coefficients, standard errors, and R squared to nine or ten digits. NIST publishes these datasets precisely because they break naive implementations. The engine is pure Swift with no R or Python at runtime. Full record on the validation page.
Regression is part of every Quanta subscription, $9.99 a month or $79.99 a year after the 30-day trial. One price for everyone. See pricing.
The analysis, the report builder, and the on-device explanations all work with the network off. Your dataset is never uploaded.
Logistic regression for a binary outcome · Poisson regression for counts · Pearson correlation for two variables without controls · the complete list on the analyses page.