Simple Linear Regression
EVIDENCE LAB · 07
Simple Linear
Regression.
Regression summarises how an outcome changes with an explanatory variable. Learn to estimate the line, interpret its coefficients and respect what it cannot establish.
SLOPERESIDUALFIT
01 · THE REGRESSION MODEL
A line through data.
An economic interpretation.
Outcome
The dependent variable to be explained or predicted.
Intercept
Expected Y when X equals zero, if zero is meaningful and observed.
Slope
Expected change in Y associated with a one-unit increase in X.
Error term
All unobserved influences on Y not represented by X.
02 · FIT AND ERROR
The line predicts.
Residuals reveal what it misses.
Residual
êᵢ = Yᵢ − Ŷᵢ
The vertical difference between an observed outcome and its fitted value. Residual patterns diagnose neglected structure.
Coefficient of determination
R² = 1 − SSE / SST
The share of sample variation in Y accounted for by the fitted regression. High R² does not prove causality or correct specification.
INTERACTIVE REGRESSION LABORATORY
Estimate the line.
Read the coefficient.
Enter paired X and Y values. ECONORIA estimates ordinary least squares, plots the data and fitted line, and produces an economic reading.
ECONOMIST’S READING
03 · INTERPRETATION DISCIPLINE
A coefficient is conditional evidence.
Not automatic causation.
Units matter
Interpret one unit of X in the actual measurement scale of both variables.
Range matters
Avoid extrapolating the fitted line far beyond observed X values.
Design matters
OLS association becomes causal only under credible identifying assumptions.
