How to read a regression table

Read every table in this order, and write down one sentence for each step.

1. What is being explained, and in what units? The dependent variable, which is the unit every coefficient is measured in.
2. Who is in the sample? The number of observations n, and what each one is: a household, a country, a year.
3. What do the coefficients say? Sign and size, in the units of x and of y. For a dummy it is a difference between groups. For a logged variable the units change (lesson 6).
4. How precise are they? The standard error, the t statistic (coefficient ÷ standard error) and the p-value. A t above about 2 in absolute value, or p below 0.05, means distinguishable from zero.
5. How well does it fit? R², adjusted R², and s, the standard error of the regression: the typical size of a residual, in the units of y.
6. Do the regressors matter together? The F statistic and its p-value, which test that every slope is zero at once.

Then ask what the table cannot say: it does not prove cause, it can hide one odd observation, and its standard errors assume things that may not hold. Chapter 4 shows each of these on this very table.

Life expectancy at birth, in years, for 186 economies in 2019 (every economy for which the World Bank reports all four series), regressed on the natural log of GDP per head (PPP, constant 2021 international dollars), current health spending as a share of GDP, and the urban share of the population. The year is chosen to precede the pandemic, which cut life expectancy sharply and unevenly in 2020 and 2021. The data were read from the World Bank’s API on 2026-10-24. This is a description of a cross-section, not an estimate of a cause.

1. Explained and units. Life expectancy at birth, in years.
2. Sample. 186 economies, one observation each, in 2019.
3. Coefficients. The coefficient on ln GDP per head is 5.9. A log is a proportional change, so a doubling of income per head, which adds ln 2 = 0.693 to the log, goes with 4.1 more years of life expectancy, holding health spending and urbanisation fixed. Health spending has a coefficient of 0.114 years per percentage point of GDP, and urbanisation 0.004 years per percentage point.
4. Precision. The t statistic for ln GDP is 15.2, enormous. For health spending it is 1.09 (p = 0.28) and for urbanisation 0.2 (p = 0.84). Those two cannot be told apart from zero once income is in the regression.
5. Fit. R² = 0.717: the three variables account for about 72% of the variation in life expectancy across these economies. The standard error of the regression is 4.31 years: a typical economy’s actual life expectancy is about 4.3 years from its predicted value. The adjusted R², 0.712, is almost the same, because n is large and k is small.
6. Joint test. F = 153.6 on (3, 182) degrees of freedom, p below 0.001: the regressors matter together. Almost all of that is income, as the t statistics show.

A table is a summary, and each of these is invisible in it. All four can be checked from the same data.

• One odd observation. The lowest life expectancy in the data is 31.53 years, for Central African Republic, as published by the World Bank for 2019. The next lowest is 52.99. One point so far below the rest can pull a coefficient. Drop it, and the coefficient on ln GDP per head moves from 5.9 to 5.48, and R² from 0.717 to 0.74. The conclusion survives, but the number depends on one economy. An exam question will not show you this, and a researcher always checks.
• Unequal spread. The standard errors assume the errors have the same variance everywhere. Here the average size of a residual is 3.94 years in the 39 economies with income below $5,000 per head, against 2.13 years in the 56 above $30,000. Poorer economies are harder to predict. That is heteroscedasticity, and it makes the reported standard errors unreliable (lesson 9).
• Overlapping regressors. Urbanisation looks irrelevant, but the correlation between ln GDP per head and the urban share is 0.69. Urbanisation tends to come with wealth, so once income is in the regression there is little left for it to add. “Not significant here” means “no additional information given income”, not “does not matter”.
• Association is not cause. The table says richer economies have longer-lived people. It does not say that raising income by a given amount adds 4.1 years: health, schooling and institutions move with income and with life expectancy.