Statistics Foundation · Lesson 5.2
Simple linear regression.
Simple linear regression models how an outcome changes with one explanatory variable. This lesson develops the regression equation, slope, intercept, fitted values, prediction, residuals, least-squares logic and responsible interpretation.
Lesson route
Move from association to a fitted predictive line.
Regression gives structure to relationships. It estimates a line, interprets its coefficients and studies what the line fails to explain.
0–20 min
From association to regression
Understand why regression goes beyond correlation by modelling an outcome as a function of an explanatory variable.
20–45 min
The regression equation
Learn the simple linear regression model: predicted outcome equals intercept plus slope times x.
45–70 min
Slope and intercept
Interpret the slope as expected change in Y per one-unit increase in X and understand the role of the intercept.
70–95 min
Prediction
Use a fitted line to predict average outcomes and distinguish prediction from explanation.
95–120 min
Residuals
Study residuals as observed minus predicted values and use them to diagnose fit.
120–150 min
Limitations
Recognise extrapolation, nonlinearity, outliers, confounding and causal overinterpretation.
Mastery checklist
Students should interpret the line and its errors.
Write the simple linear regression model.
Interpret slope and intercept correctly.
Calculate fitted values.
Calculate residuals.
Explain least-squares logic.
Use regression for prediction cautiously.
Recognise extrapolation risk.
Avoid causal overinterpretation.