Mastering Linear Regression: Your Essential Guide for Machine Learning Interviews

Introduction: Why Linear Regression Matters in Interviews

What Linear Regression Really Does

The Famous Assumptions (and Why They Matter)

How Linear Regression Learns

Making Sense of the Coefficients

Evaluating Your Model

Practical Tips & Common Pitfalls

10 Common Interview Questions on Linear Regression

Conclusion: The Backbone of Machine Learning

Mastering Linear Regression: Your Essential Interview Guide

When it comes to machine learning interviews, Linear Regression almost always shows up. It’s one of those algorithms that looks simple at first, and that’s exactly why interviewers love it. It’s like the “hello world” of ML: easy to understand on the surface, but full of details that reveal how well you actually know your fundamentals.

Many candidates dismiss it as “too basic,” but here’s the truth: if you can’t clearly explain Linear Regression, it’s hard to convince anyone you understand more complex models. So, in this post, I’ll walk you through everything you really need to know—assumptions, optimization, evaluation metrics, and those tricky pitfalls that interviewers love to probe. Think of this as your practical, no-fluff guide to talking about Linear Regression with confidence.

What Linear Regression Really Does

At its heart, Linear Regression is about modeling relationships. Imagine you’re trying to predict someone’s weight from their height. You know taller people tend to weigh more, right? Linear Regression turns that intuition into a mathematical equation; it draws the best-fitting line that connects height to weight.

The simple version looks like this:

[ y = \beta_0 + \beta_1 x + \epsilon ]

Here, (y) is what you want to predict, (x) is your input, (\beta_0) is the intercept (value of (y) when (x=0)), (\beta_1) is the slope (how much (y) changes when (x) increases by one unit), and (\epsilon) is the error, the stuff the line can’t explain.

In real-world data, you often have multiple features, leading to:

[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \ldots + \beta_n x_n + \epsilon ]

Now you’re fitting a hyperplane in multi-dimensional space. Each coefficient tells you how much that feature contributes to the target, holding everything else constant. This is why interviewers like asking about it: it tests whether you understand what your model is doing, not just whether you can run .fit() in scikit-learn.

The Famous Assumptions (and Why They Matter)

Linear Regression rests on key assumptions. In interviews, bonus points often go to candidates who can name them and explain why they matter or how to check them.

1. Linearity: The relationship between features and the target should be linear.

   • Test it: Plot residuals vs. predicted values; if you see patterns, it’s not linear.
   • Fix it: Try transformations, polynomial terms, or switch to a non-linear model.

2. Independence of Errors: Errors shouldn’t be correlated, which can be problematic in time-series work.

   • Test it: Use the Durbin-Watson test (values around 2 = good).
   • Fix it: Consider ARIMA or add lag variables.

3. Homoscedasticity: Errors should have constant variance.

   • Test it: A “funnel shape” in residuals indicates heteroscedasticity.
   • Fix it: Transform the dependent variable or use Weighted Least Squares.

4. Normality of Errors: Residuals should be roughly normally distributed (important for inference).

   • Test it: Histogram or Q-Q plot.
   • Fix it: With a large enough dataset, this matters less due to the Central Limit Theorem.

5. No Multicollinearity: Predictors shouldn’t be too correlated with each other.

   • Test it: Check VIF scores (values >5 or 10 are red flags).
   • Fix it: Drop redundant features or use Ridge/Lasso regression.

In practice, these assumptions are rarely perfect. Knowing how to test and address them is key; that separates theory from applied understanding.

How Linear Regression Learns

Once you set up the equation, how does the model learn those coefficients? The goal is simple: find β values that minimize the differences between predicted and actual values.

The most common method is Ordinary Least Squares (OLS), which minimizes the sum of squared errors (the differences between actual and predicted values).

Two Main Methods:

1. Closed-form solution (analytical):
   [
   \hat{\beta} = (X^TX)^{-1}X^Ty
   ]
   This is exact and fast for small datasets but doesn’t scale well with a large number of features.

2. Gradient Descent (iterative):
   For large datasets, gradient descent takes small steps towards minimizing error, making it highly scalable. This approach is the foundation of how neural networks learn today.

Making Sense of the Coefficients

Each coefficient tells you how much the target changes when that feature increases by one unit, assuming all others remain constant. For example, if you’re predicting house prices and the coefficient for “square footage” is 120, it means that (roughly) every extra square foot adds $120 to the price, holding other features constant.

This interpretability is why interviewers love it. It tests if you can explain models in plain English, a key skill in data roles.

Evaluating Your Model

After training, you’ll want to know how good it is. Here are key metrics:

• MSE (Mean Squared Error): Average of squared residuals, penalizing big errors heavily.
• RMSE (Root MSE): Square root of MSE, in the same units as your target.
• MAE (Mean Absolute Error): Average of absolute differences, more robust to outliers.
• R² (Coefficient of Determination): Measures how much variance your model explains.

The closer R² is to 1, the better, but it can be misleading; adding features can inflate it. That’s why Adjusted R² is preferable—it penalizes adding irrelevant predictors.

There’s no “best” metric; it depends on your problem. If large mistakes are more damaging, go with RMSE. If you want robustness against outliers, MAE is your go-to.

Practical Tips & Common Pitfalls

A few things can make or break your regression model:

• Feature scaling: Not strictly required, but essential with regularization (Ridge/Lasso).
• Categorical features: Use one-hot encoding but drop one dummy to avoid multicollinearity.
• Outliers: Check residuals; they can heavily distort results.
• Overfitting: Too many predictors? Use regularization techniques. Ridge shrinks coefficients, while Lasso can eliminate unimportant ones.

And remember, Linear Regression doesn’t imply causation. Just because a coefficient is positive doesn’t mean changing that variable will cause the target to rise. Interviewers appreciate candidates who acknowledge this nuance.

10 Common Interview Questions on Linear Regression

1. What are the key assumptions of linear regression, and why do they matter?
2. How does ordinary least squares estimate coefficients?
3. What is multicollinearity and how do you detect and handle it?
4. What is the difference between R² and Adjusted R²?
5. Why might you prefer MAE over RMSE as an evaluation metric?
6. What happens if residuals are not normally distributed?
7. How do you detect and handle heteroscedasticity?
8. What happens if you include irrelevant variables in a regression model?
9. How would you evaluate a regression model when errors have different costs?
10. How do you handle missing data in regression?

If you can confidently answer those, you’re already ahead of most candidates.

Conclusion

Linear Regression may be old-school, but it remains the backbone of machine learning. Mastering it isn’t about memorizing formulas; it’s about understanding why it works, when it fails, and how to fix it. Once you’ve nailed that, everything else—from logistic regression to deep learning—starts to make a lot more sense.

About the Author

Karun Thankachan is a Senior Data Scientist specializing in Recommender Systems and Information Retrieval. He has worked in E-Commerce, FinTech, PXT, and EdTech industries and holds several published papers and patents in Machine Learning. Currently, he works at Walmart E-Commerce, improving item selection and availability.

Karun also serves on the editorial board for IJDKP and JDS, and is a Data Science Mentor on Topmate. He has been awarded the Top 50 Topmate Creator Award in North America (2024) and the Top 10 Data Mentor in the USA (2025), and is a Perplexity Business Fellow. He writes to over 70k followers on LinkedIn and is the co-founder of BuildML, a community for weekly research paper discussions and monthly project development cohorts.