Analyzing data is vital in today’s era of computers. There is tremendous scope for data scientists and data analysis in the industry today. The companies recruiting these data scientists would naturally interview them to understand their capability. One of the favorite topics on which the interviewers ask questions is ‘Linear Regression.’ Here are some of the common Linear Regression Interview Questions that pop up in interviews all over the world.

## Linear Regression Interview Questions – Fundamental Questions

Let us begin with a fundamental Linear Regression Interview Questions

### 1. What is a Linear Regression?

In simple terms, linear regression is adopting a linear approach to modeling the relationship between a dependent variable (scalar response) and one or more independent variables (explanatory variables). In case you have one explanatory variable, you call it a simple linear regression. In case you have more than one independent variable, you refer to the process as multiple linear regressions.

### 2. Can you list out the critical assumptions of linear regression?

There are three crucial assumptions one has to make in linear regression. They are,

- It is imperative to have a linear relationship between the dependent and independent A scatter plot can prove handy to check out this fact.
- The independent variables in the dataset should not exhibit any multi-collinearity. In case they do, it should be at the barest minimum. There should be a restriction on their value depending on the domain requirement.
- Homoscedasticity is one of the most critical It states that there should be an equal distribution of errors.

### 3. What is Heteroscedasticity?

Heteroscedasticity is the exact opposite of homoscedasticity. It entails that there is no equal distribution of the error terms. You use a log function to rectify this phenomenon.

### 4. What is the primary difference between R square and adjusted R square?

In linear regression, you use both these values for model validation. However, there is a clear distinction between the two. R square accounts for the variation of all independent variables on the dependent variable. In other words, it considers each independent variable for explaining the variation. In the case of Adjusted R square, it accounts for the significant variables alone for indicating the percentage of variation in the model. By significant, we refer to the P values less than 0.05.

### 5. Can you list out the formulas to find RMSE and MSE?

The most common measures of accuracy for any linear regression are RMSE and MSE. MSE stands for Mean Square Error whereas RMSE stands for Root Mean Square Error. The formulas of RMSE and MSE are as hereunder.

## Linear Regression Interview Questions – Complex Questions

We have seen some of the basic interview questions on linear regression. As we move further into the article, we shall look at some of the complex linear regression interview questions as well.

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### 6. Can you name a possible method of improving the accuracy of a linear regression model?

You can do so in many ways. One of the most common ways is ‘The Outlier Treatment.’

Outliers have great significance in linear regression because regression is very sensitive to outliers. Therefore, it becomes critical to treat outliers with appropriate values. It can also prove useful if you replace the values with mean, median, mode or percentile depending on the distribution.

### 7. What are outliers? How do you detect and treat them?

An outlier is an observation point distant from other observations. It might be due to a variance in the measurement. It can also indicate an experimental error. Under such circumstances, you need to exclude the same from the data set. If you do not detect and treat them, they can cause problems in statistical analysis.

You can see that 3 is the outlier in this example.

There is no strict mathematical calculation of how to determine an outlier. Deciding whether an observation is an outlier or not, is itself a subjective exercise. However, you can detect outliers through various methods. Some of them are graphical and are known as normal probability plots whereas some are model-based. You have some hybrid techniques such as Boxplots.

Once you have detected the outlier, you should either remove them or correct them to ensure accurate analysis. Some of the methods of eliminating outliers are the Z-Score and the IQR Score methods.

### 8. How do you interpret a Q-Q plot in a linear regression model?

As the name suggests, the Q-Q plot is a graphical plotting of the quantiles of two distributions with respect to each other. In other words, you plot quantiles against quantiles.

Whenever you interpret a Q-Q plot, you should concentrate on the ‘y = x’ line. You also call it the 45-degree line in statistics. It entails that each of your distributions has the same quantiles. In case you witness a deviation from this line, one of the distributions could be skewed when compared to the other.

### 9. What is the importance of the F-test in a linear model?

The F-test is a crucial one in the sense that it tests the goodness of the model. When you reiterate the model to improve the accuracy with the changes, the F-test proves its utility in understanding the effect of the overall regression.

### 10. What are the disadvantages of the linear regression model?

One of the most significant demerits of the linear model is that it is sensitive and dependent on the outliers. It can affect the overall result. Another notable demerit of the linear model is overfitting. Similarly, underfitting is also a significant disadvantage of the linear model.

### 11. What is the curse of dimensionality? Can you give an example?

When you analyze and organize data in high-dimensional spaces (usually in thousands), various situations can arise that usually do not do so when you analyze data in low-dimensional settings (3-dimensional physical space). The curse of dimensionality refers to such phenomena.

Here is an example.

All kids love to eat chocolates. Now, you bring a truckload of chocolates in front of the kid. These chocolates come in different colors, shapes, tastes, and price. Consider the following scenario.

The kid has to choose one chocolate from the truck depending on the following factors.

- Only taste – There are usually four tastes, sweet, salty, sour, and bitter. Hence, the child will have to try out only four chocolates before choosing one to its liking.
- Taste and Color – Assume there are only four colors. Hence, the child will now have to taste a minimum of 16 (4 X 4) before making the right choice.
- Taste, color, and shape – Let us assume that there are five shapes. Therefore, the child will now have to eat a minimum of 80 chocolates (4 X 4 X 5).

What will happen to the child if it tries out 80 chocolates at a time? It will naturally become sick. Hence, it will not be in a position to try out the chocolates. This example is the perfect one to explain the curse of dimensionality. The more the options you have, the more the problems you encounter.

## Linear Regression Interview Questions – Multiple Choice Questions

Let us now look at some multiple-choice linear regression interview questions.

### 1. In regression analysis, which of the statements is true?

- The mean of residuals is always equal to Zero
- The Mean of residuals is less than Zero at all times
- The Mean of residuals is more than Zero at all times
- You do not have any such rule for residuals.

The correct answer is A. In regression analysis, the sum of the residuals in regression is always equal to Zero. Thus, it implies that the mean will also be Zero if the sum of the residuals is Zero.

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### 2. Which of the statements is correct about Heteroscedasticity?

- Linear regression with different error terms
- Linear regression with constant error terms
- Linear regression with no error terms
- None of the above

The solution is the option A. When you have a non-constant variance in the error terms, it results in Heteroscedasticity. Such non-constant variance occurs because you have outliers.

### 3. Which of the following plots is best suited to test the linear relationship of independent and dependent continuous variables?

- Scatter Plot
- Bar Chart
- Histograms
- None of the above options

The answer is A. The Scatter plot is the best way to determine the relationship between continuous variables. You can find out how one variable changes with respect to the other.

### 4. If you have only one independent variable, how many coefficients will you require to estimate in a simple linear regression model?

- One
- Two
- No idea

The answer is B. Consider the simple linear regression with one independent variable. Y = a + bx. You can see that you need two coefficients.

### Conclusion

We segregated the Linear Regression Interview Questions on the basis of fundamental, complex and multiple-choice questions.

Hopefully, you must have understood the above mentioned Linear Regression Interview Questions thoroughly.

We have seen the importance of linear regression through some interview questions on linear regression. Data scientists need to master this aspect as linear regression is usually a favorite topic with the interviewers. You can refer to the official website of Digital Vidya to learn more about the important aspects of Data Science.

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