Understanding the Question

When an interviewer asks, "What are the main assumptions of linear regression?" during a job interview for a Quantitative Analyst position, they're probing your understanding of foundational statistical methods. Linear regression is a fundamental tool in the quantitative analyst's toolkit, used for predicting a quantitative response based on one or more predictor variables. It's crucial not only to know how to perform these analyses but also to understand the assumptions underlying them, as these assumptions affect the validity of the results.

Interviewer's Goals

The interviewer's primary goal with this question is to assess:

• Your technical knowledge: Do you understand the basic principles that underpin linear regression analysis?
• Your critical thinking skills: Can you identify when these assumptions might be violated and what impact this could have on your analysis?
• Your practical application skills: Are you capable of applying this knowledge in real-world scenarios, including checking for these assumptions and addressing any violations?

How to Approach Your Answer

In formulating your response, aim to succinctly explain each assumption, why it matters, and how you might check for it in your analysis. It's beneficial to include examples from your experience where relevant, showing that you not only know the theory but also how to apply it.

Example Responses Relevant to Quantitative Analyst

Here are example responses that could resonate well in an interview for a Quantitative Analyst position:

1. Linearity: "The first assumption is that there is a linear relationship between the independent variables and the dependent variable. In practice, I check this by plotting scatter plots of the independent variables against the dependent variable and looking for a linear pattern. If the relationship isn't linear, I might consider transforming the variables or using a different analytical approach."

2. Homoscedasticity: "Another assumption is homoscedasticity, meaning the variance of error terms is constant across all levels of the independent variables. Violations of this assumption, known as heteroscedasticity, can lead to inefficient estimates. I typically use scatter plots of the residuals against predicted values or independent variables to look for constant variance."

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3. Independence of observations: "The assumption of independence states that the observations are independent of each other. In time series data, for example, this assumption can be violated due to autocorrelation. I would check for independence by looking at the Durbin-Watson statistic or using plots of residuals against time order."

4. Normal distribution of error terms: "Linear regression assumes that the error terms are normally distributed, particularly important for hypothesis testing. I assess this assumption by examining a histogram or Q-Q plot of the residuals. If the residuals are not normally distributed, transformations or non-parametric methods might be necessary."

5. No multicollinearity: "Finally, the model assumes that there is no perfect multicollinearity, meaning that the independent variables are not too highly correlated with each other. High correlation among predictors can make it difficult to distinguish their individual effects on the dependent variable. I check for multicollinearity using Variance Inflation Factor (VIF) scores, where a VIF above 10 indicates a potential problem."

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Tips for Success

• Be Concise but Comprehensive: While you want to cover each assumption, it's also important to keep your answers to a reasonable length. Aim for clarity and succinctness.
• Use Examples: If you have personal experience identifying and dealing with these assumptions in your work, share those examples. This demonstrates practical knowledge and problem-solving skills.
• Understand the Implications: Be ready to discuss not just what each assumption is, but also what it means if an assumption is violated and how you might address it.
• Stay Updated: Linear regression is a well-established method, but new techniques and best practices for assumption testing and mitigation continue to evolve. Showing that you're up-to-date with the latest methods can set you apart.

By thoroughly understanding the assumptions of linear regression and preparing detailed, example-rich responses, you demonstrate not only your technical proficiency but also your ability to apply critical analysis in practical scenarios—a key skill for any Quantitative Analyst.