Regression output looks intimidating the first time you see it — a table full of numbers with labels like "Std. Error" and "Adj. R-squared." Whether it's R regression output or SPSS regression interpretation, you actually only need to look at four numbers first to understand what's going on.
The four numbers to check first
- The coefficient — how much the outcome changes for each 1-unit increase in the predictor.
- The p-value for that coefficient — whether the relationship is statistically significant, or could plausibly be due to chance.
- R² — what percentage of the variation in your outcome variable the model explains.
- The standard error — how precisely the coefficient is estimated (smaller is more precise).
Reading the coefficient
The coefficient tells you the direction and size of the relationship. A coefficient of 3.2 for "hours studied" predicting exam score means: for each additional hour studied, the model predicts a 3.2-point increase in score, holding everything else in the model constant.
Is the relationship statistically significant?
Check the p-value attached to that specific coefficient (not the overall model p-value, which is a different number). If it's below 0.05, the relationship is unlikely to be due to chance alone — the same logic as any other hypothesis test.
How much does the model actually explain?
R² ranges from 0 to 1 and tells you what proportion of the variation in your outcome the model accounts for. An R² of 0.45 means the model explains 45% of the variation in the outcome — the rest is due to factors outside the model, or random variation. A statistically significant coefficient doesn't automatically mean the model is a strong one; check R² separately.
Worked example
A simple regression predicts exam score from hours studied. The output shows: coefficient = 3.2, p < 0.001, R² = 0.45.
Interpretation: for each additional hour studied, predicted exam score increases by 3.2 points on average. This relationship is highly statistically significant (p < 0.001). The model explains 45% of the variation in exam scores — a moderate amount, meaning other factors besides study hours are also influencing scores.
Common mistakes
Treating a significant coefficient as proof of causation. Regression shows association, not causation, unless the data comes from a controlled experiment. "Hours studied predicts score" doesn't rule out other explanations.
Ignoring R² entirely. A highly significant p-value with a very low R² means the relationship is real but weak — both numbers matter together, not just one.
Stuck on a stats problem right now?
Tell us what you're working on and get matched with a tutor who explains the reasoning, not just the answer — free quote by email or WhatsApp.
Get a free quote