Regression for Analytics

• Fit and interpret linear regression coefficients
• Validate assumptions and spot common breakdowns
• Choose between linear and regularized models for prediction vs explanation

• It moves analysis from 'are these related?' to 'how much does this move that?'
• Controls for confounding variables that naive comparisons miss.
• It is the bridge between statistics and the machine-learning models you will use later.

The output changes by the dial's gain while every other dial stays put — exactly how a coefficient works at constant held features.

• Choose the outcome Y and the predictors X that theory says should move it.
• Fit coefficients that minimize squared error between predictions and observed outcomes.
• Each coefficient is the expected change in Y per one-unit change in that predictor, holding others constant.
• Check R-squared, p-values, and residuals to judge fit and validity.

• Pricing analytics estimates price elasticity from historical price experiments and natural variation.
• Growth teams quantify the marginal revenue effect of a feature roll-out while controlling adoption.
• Forecasting teams use lagged predictors in regression to project demand.

• Interpret coefficients in the units of the business, not the regression output.
• Report coefficients together with their uncertainty (standard errors or confidence intervals).
• Prefer few, well-chosen predictors over kitchen-sink models when explaining.

• Interpreting regression as proof of causation, ignoring confounding and omitted variables.
• Reading the coefficient of a collinear predictor as if it were independent.
• Extrapolating predictions far outside the range of the training data.

• If signs flip when you add a variable, suspect multicollinearity — variables are fighting each other.
• If predictions are systematically wrong at the edges, check outliers and nonlinear relationships.