How to interpret a multiple linear regression table

Start with the outcome and the question

Multiple linear regression estimates how a quantitative outcome is associated with several predictors considered together. A coefficient describes an association conditional on the other predictors in that model. “Holding constant” is a model comparison, not evidence that a researcher experimentally controlled those variables. NIST describes the linear model as a sum of predictor terms and their coefficients.

Our advanced research example has 360 employees measured once. H2 models work engagement from supervisor support and job autonomy. All three scores are means of five items on a 1–5 scale. This observational study can describe adjusted associations; it cannot establish that changing support will cause a change in engagement.

Read the coefficients in their own units

The following H2 values come from the published canonical results and findings chapter. Rounding is for display.

For employees with the same autonomy score, a one-point higher support score is associated with an estimated 0.39-point higher engagement score. The autonomy coefficient is interpreted while holding support constant. These are score points, not percentages or guaranteed changes for individuals.

B uses the variables' original units. β uses standardized units; support's β of 0.38 expresses the fitted association in outcome standard deviations for a one-standard-deviation difference in support, conditional on autonomy. It is not “38% explained,” and its size alone does not prove which predictor is more important. Units, measurement and the included predictors matter.

Separate uncertainty from the estimate

A standard error describes sampling uncertainty around a coefficient, rather than the spread of employees' observed scores. In H2 the support coefficient has SE = 0.0465, rounded to 0.05 in the complete table. The R summary documentation distinguishes coefficient estimates, standard errors, t statistics and p values.

Support's 95% interval is approximately 0.30–0.48 score points under the fitted model and its assumptions. The R confidence-interval documentation describes t-based intervals for linear models. A confidence interval is not a range containing 95% of individual engagement scores or a guarantee about a future employee. Both H2 predictor p values are below .001; statistical significance does not establish practical importance or causality.

Read model fit without overstating prediction

H2 has R² = .278 and adjusted R² = .274. In this sample, the fitted model accounts for about 27.8% of observed engagement-score variation. This is not 27.8% prediction accuracy, and no performance on new employees was established here. The adjusted measure accounts for model size; neither number replaces diagnostics.

The overall test is F(2, 357) = 68.72, p < .001. It compares the two-predictor model with an intercept-only model. It does not, on its own, show that every predictor is associated with the outcome. Read each coefficient and its uncertainty separately.

What the additional model does and does not show

A1 is a separate, planned additional analysis that adds work arrangement and tenure group. It is not a fourth confirmatory hypothesis.

A larger raw R² does not demonstrate a statistically significant improvement over H2. The reported A1 overall F test compares A1 with an intercept-only model, not with H2; no dedicated comparison of the two fitted models is reported here. Tenure was entered as categories, with under two years as reference, not as a numeric trend.

Check the process behind the table

Review residual patterns, variance, collinearity and influential cases. NIST emphasizes graphical residual checks. A diagnostic flag requires investigation, not automatic deletion. The published diagnostics contain influence flags; this guide does not claim every assumption passed.

Compare the prepared data, study description and decisions report. For the wider reporting structure, read the results chapter guide. Statistical analysis describes possible deliverables within an agreed scope. Consultation and ordering remain closed; see service availability.

See the complete research examples

Follow the research questions through the input files, analysis plan and outputs. Each example includes the consultation report, itemized illustrative price and generated files.