20 Linear Regression Interview Questions and Answers 2024

Linear Regression is probably one of the most well-known machine learning algorithms. It essentially involves modeling the relation between the given or derived parameters and the target to be learned. Therefore, any machine Learning job interview would be incomplete without a peppering of Linear Regression questions.

These linear regression interview questions and answers will help you prepare for your machine learning interview. We will cover all the crucial linear regression machine learning interview questions that you will most likely be asked in your machine learning interview.

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Top 20 Linear Regression Machine Learning Interview Questions and Answers

1. Describe a well-known law or natural phenomena that you could model with linear regression.

Many common laws have proportional relations and can be described by linear relationships. These can therefore be modeled with linear regression. A few famous examples are Ohm's law-related by V=IR or Newton's second law given by F=ma. On close observation, it is apparent that each of these laws has the form y=mx+c where c=0, or are essentially described by lines that pass through the origin.

2. Is it necessary to visualize the data when you have fitted a line? Why or why not?

It is crucial to visualize the data when you fit a line because numerically fitting a line is easy with pure numerical analysis or methods like Least Squares regression. But determining whether these fitted lines make any sense requires further analysis of which visualizing the data is one of the easiest ways.

To underscore this point, let us consider Anscombe's quartet, the four datasets with almost identical simple statistical properties but appear wildly different in distribution when plotted.

These four datasets result in a regression line with a slope of 0.50 and an intercept of 3.00. However, on plotting this line with the datasets, it becomes apparent that although fitted for datasets with almost identical results through quantitative analysis, the resultant line does not make any sense.

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3. Does correlation imply causation? Why or why not?

No, while correlation is popularly used to provide information on the extent and direction of the linear relationship between two variables and can be used to determine whether a variable can be used to predict another, a high correlation does not imply causation.

For instance, you might find a correlation between umbrella malfunctions and a carpenter's income. As you can imagine, it is unlikely that there is a direct relation between the two, except that people tend to open up their umbrellas during the rainy season and that wooden doors swell due to high humidity. In this case, there is a hidden cause, rain, that causes both the phenomena as mentioned above and consequently the high correlation between them. 

4. Is linear regression suitable for time series analysis?

While linear regression can be used for time series analysis and generally yield workable results, the performance is not particularly remarkable. The two main factors for this are :

• Time series generally have seasonal or periodic trends (such as peak seasons or even peak hours), which might be treated as outliers in linear regression and hence not appropriately accounted for.

• Future prediction is a generally sought-after use case in time series analysis, which will require extrapolation and rarely results in good predictions.

ARIMA, ARCH, and LSTM are widely used and better performing algorithms for time series analysis.

5. Is Feature Engineering necessary for even simple linear regression? Explain with an example.

Yes, Feature Engineering could be helpful even with the most straightforward linear regression problems. Say, for instance, you are trying to predict the Cost of a chocolate bar given the following

Here you might find a workable relationship between the Length and the Cost or the Breadth and the Cost. However, on multiplying the Length and the Breadth to derive the Size, you will see that this is a much better indicator of the Cost and will fit the resulting linear regression model better.

6. Are there any risks to extrapolation? Explain with an example when you would and would not use this.

Extrapolation is essentially predicting values of the target function for parameter values outside the range of those observed during training. While extrapolation could reasonably work well in some cases, such as predicting the voltage in Ohm's law, it can also result in meaningless results.

One easy example to explain this can be to extrapolate the decreasing rainfall trend at the end of the rainy season. If the extrapolation is done unchecked, the model could predict negative rain after a period that is about as nonsensical as it gets!

7. Can linear regression be used for representing quadratic equations? 

Yes, paradoxically, a multiple linear regression model can be used to represent quadratic equations. For more complex linear regression models, we use multiple independent variables to predict the dependent variable. Such a linear regression model is called a multiple linear regression model.

A linear model with multiple dependent variables x1, x2, ..., xn can be written as 

y=1x1+2x2+...+nxn.

For a quadratic function given by, say, y=ax2+bx+c, we can use x1=x2, x2=x, and x3=1, effectively representing the desired quadratic equation. Similarly, linear regression models can be used to describe higher-order polynomials as well.

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8. Give an example scenario where a multiple linear regression model is necessary. 

Consider an example where you are considering customer satisfaction for a particular brand of cereal. This would usually be decided by several factors, including cost, nutritional value, and taste. Say you are given all the above parameters and choose x1, x2, and x3 to represent them.

If these are the only three dependent variables, then your linear regression model, in this case, would be a multiple linear regression model that can be represented in the form

y=1x1+2x2+3x3

9. Is Overfitting a possibility with linear regression?

Yes, Overfitting is possible even with linear regression. This happens when multiple linear regression is used to fit an extremely high-degree polynomial. When the parameters of such a model are learned, they will fit too closely to the training data, fitting even the noise, and thereby fail to generalize on test data. 

10. Is it necessary to remove outliers? Why or why not?

Yes, it is necessary to remove outliers as they can have a huge impact on the model's predictions. Take, for instance, plots 3 and 4 for the Anscombe's quartet provided above. It is apparent from these plots that the outliers have caused a significant change in the best fit line in comparison to what it would have been in their absence.

11. How do you identify outliers?

An outlier is an observation that is unlikely to have occurred in a data set under ordinary circumstances. Its values are so widely different from the other observations that it is most likely a result of noise or a rare exceptional case.

Box plots are a simple, effective, and hence commonly used approach to identifying outliers. Besides this, scatter plots, histograms and Z-scores are other methods used whenever feasible.

12. Is the vertical offset, horizontal offset, or the perpendicular offset minimized for least-square fitting, assuming that the vertical axis is the dependent variable? Why is this so?

In most cases, the vertical offsets from a line (or a surface) are minimized instead of the perpendicular offsets (or the horizontal offset). The resultant fitting function for the independent variables that predict the dependent variable allows uncertainties of the data points to be represented in a simple manner. Further, compared to a fit based on perpendicular offsets, this practice allows for a much simpler analytic form for the fitting parameters.

13. How do residuals help in determining the quality of a model?

Residuals are the deviations of the observed values from a fitted line. Checking the residuals is an important step to ascertain whether our assumptions of the regression model are valid. Suppose there is no apparent pattern in the plot of residuals versus fitted values, and the ordered residuals result in an almost normal distribution. In that case, we can conclude that there are no apparent violations of assumptions. On the other hand, if there is a relationship between the residuals and our fitted values, it is an indicator that the model is not good.

14. What is scaling? When is it necessary?

The technique to standardize the features in the data set to fit within a fixed range is called Feature Scaling. It is performed during the preprocessing stage and helps avoid the dominance of certain features due to high magnitudes.

When using the analytical solution for Ordinary Least Square, feature scaling is almost useless. However, when using gradient descent as an optimization technique, the data scaling results can be valuable. It can help to ensure that the gradient descent moves smoothly towards the global minimum and that the gradient descent steps update at the same rate for all the features.

15. If your training error is 10% and your test error is 70%, what do you infer?

A low error in training error while the test data yields a significantly higher error is a strong indicator of Overfitting. Such an observation strongly suggests that the model has learned so well over the training set that it hardly makes any mistakes during prediction over training data but cannot generalize over the unseen test set.

16. If you have two choices of hyperparameters, one resulting in a training and test error of 10% and another with a training and test error of 20%, which one of the two would you prefer and why?

Given that both the training and the test set are yielding an error of 10% in case 1 and an error of 20% in case 2, it is pretty easy to opt for the hyperparameters of case 1 for our machine learning problem as it is always desirable to have a lower error in predictions.

17. If your training error is high despite adjusting the hyperparameter values and increasing the number of iterations, what is most likely to be the issue? How can you resolve this problem?

High training error despite hyperparameter adjustment and a significant number of iterations strongly indicates that the model is unable to learn the problem it is presented with despite its best effort, or in other words, that it is underfitting. Reducing the regularisation and using more complex models can be some ways used to address this problem.

18. If the deviations of the residuals from your model are extremely small, does it suggest that the model is good or bad?

Residuals are essentially how much the actual data points vary from the fitted line and are hence indicators of deviation or error. Therefore, the smaller the deviation of the residuals from the fitted line, the better the model is likely to be.

19. What scenario would you prefer to use Gradient Descent instead of Ordinary Least Square Regression and why?

Ordinary Least Square Regression is computationally very expensive. Therefore, while it performs well with small data sets, it is infeasible to use this approach for significant machine learning problems. Consequently, for problems with larger data sets, Gradient Descent is the preferred optimization algorithm.

20. If you observe that the test error is increasing after a certain number of iterations, what do you infer is most likely to be occurring? How do you address this problem?

Observing an increase in error on the validation set after a certain number of iterations can indicate that the model is Overfitting. We can arrive at this diagnosis because we expect the error to decrease with more optimized parameters. While simplifying the model is one way to address this problem, early stopping is another commonly used solution.

Early stopping is probably one of the most commonly used forms of regularization. Unlike a weight decay used in the cost function, which helps to arrive at less complex models by explicit regularization, early stopping can be considered as a form of implicit regularization.

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A computer science graduate with over four years of writing experience in various fields. His passion for technology and knack for clear communication enables him to simplify complex topics for readers. Fun fact: Badr has a mixed-breed dog named

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