Regression Models Explained for Analysts
After ML Fundamentals: An Analyst's Perspective, regression is the analyst's toolkit for modelling a continuous output from one or more inputs. It matters in interviews because candidates are expected to know the core equations, choose the right regression variant, and interpret metrics and coefficients in a business setting like house-price prediction.
- Simple Linear Regression: y = ฮฒโ + ฮฒโx + ฮต, where y = output, x = input, ฮฒโ = intercept, ฮฒโ = slope, ฮต = error.
- Multiple Regression: y = ฮฒโ + ฮฒโxโ + ฮฒโxโ + ... + ฮฒโxโ + ฮต, with n input features - each ฮฒ represents the effect holding others constant.
- Rยฒ = 1 - (SS_residual / SS_total), the proportion of variance explained; Rยฒ = 0.72 means 72% of y variance explained by X.
- Adjusted Rยฒ = 1 - (1-Rยฒ)(n-1)/(n-k-1); it penalises adding irrelevant features - use this over Rยฒ for multiple regression.
- RMSE = โ[ ฮฃ(yแตข - ลทแตข)ยฒ / n ]; Root Mean Squared Error is in the same units as y and penalises large errors more.
- In the Bengaluru House Prices example, Adjusted Rยฒ = 0.74, meaning the model explains 74% of price variance.
Regression Models: The Big Picture
Regression starts with a target output y and one or more input features x. The core analyst task is to match the model to the relationship, check the key assumption, choose the right metric, and understand the limitation before translating coefficients into business insight.
Simple Linear Regression: y = ฮฒโ + ฮฒโx + ฮต. Multiple Regression: y = ฮฒโ + ฮฒโxโ + ฮฒโxโ + ... + ฮฒโxโ + ฮต.
Bengaluru House Prices: The Full Framework in One Business Problem
Bengaluru House Prices shows how a regression model moves from input features to a continuous target, then from metrics and coefficients to a business insight.
A shallow answer stops at the score. A complete regression answer explains the features, target, model, metric, coefficients, and the business signal.
How to Interpret the Key Regression Metrics
Rยฒ = 1 - (SS_residual / SS_total). It is the proportion of variance explained - Rยฒ = 0.72 means 72% of y variance explained by X.
Adjusted Rยฒ = 1 - (1-Rยฒ)(n-1)/(n-k-1). It penalises adding irrelevant features - use this over Rยฒ for multiple regression.
RMSE = โ[ ฮฃ(yแตข - ลทแตข)ยฒ / n ]. Root Mean Squared Error is in the same units as y and penalises large errors more.
Multicollinearity: Two or more predictor variables in a regression are highly correlated with each other. Problem: coefficients become unstable and uninterpretable (but predictions may still be accurate). Detection: VIF (Variance Inflation Factor) - VIF > 10 signals problematic multicollinearity; > 5 warrants investigation.
Choosing the Right Regression Variant
Use Simple Linear Regression when there is 1 predictor and a linear relationship. Use Multiple Linear Regression when there are multiple predictors and a continuous output, but remember that it is sensitive to multicollinearity and outliers.
Use Polynomial Regression for a non-linear but smooth relationship, while watching for overfitting at high degree. Ridge Regression (L2) is useful with many features and potential multicollinearity, while Lasso Regression (L1) is useful when feature selection is needed because it sets some coeff to zero.
XGBoost Regressor fits non-linear, complex interactions and tabular data. Its limitation is that it is less interpretable and needs tuning.
Structuring a Regression Models Explained for Analysts Interview Answer
"How would you choose between simple linear regression, multiple regression, Ridge, Lasso and XGBoost for house-price prediction?"
Do not stop at model accuracy. In a regression answer, connect the equation, assumptions, metric choice, coefficients and limitation to the business decision.
The most frequent error is using Rยฒ as the main proof of quality for multiple regression. Rยฒ can look better when irrelevant features are added, so Adjusted Rยฒ is preferred because it penalises adding irrelevant features.
Conclusion
Regression is most useful when an analyst can move from equation to model choice, from metric to limitation, and from coefficient to business insight. The strongest interview answers do not just report Rยฒ or RMSE - they explain what the model says and what decision it supports.