Regression analysis

Regression analysis is a statistical technique for quantifying how one variable responds to changes in others. The variable being predicted is the dependent variable, and the variables doing the predicting are independent variables. Simple regression uses one predictor; multiple regression uses several.

The most common form, simple linear regression, fits a straight line of the form y = a + bx through observed data using the least squares method, which minimizes the total squared vertical distance between the data points and the line. The intercept a is the predicted value of y when x is zero, and the slope b tells how much y changes for each one-unit change in x. In a cost-behavior setting, a represents fixed cost and b represents variable cost per unit of activity — so a fitted line like total cost = 5,000 + 12x estimates $5,000 of fixed cost plus $12 per unit produced.

Analysts judge a regression's usefulness with measures like the coefficient of determination (R²), which reports the share of variation in the dependent variable explained by the model. Regression generally produces better cost estimates than simpler tools like the high-low method because it uses every observation rather than just two, but its forecasts are only reliable within the range of the historical data and when past relationships persist.

The CMA Part 1 exam tests regression analysis in two places: as a forecasting technique for budgeting — including interpreting the intercept, slope, and R² — and within its technology and analytics section on statistical methods used in data analytics.