# T-test vs Linear Regression: Difference and Comparison

T-test and Linear regression are terms related to inferential statistics. The statistical method helps us generalise and predict a population by taking a small but illustrative sample.

## Key Takeaways

1. A t-test is a statistical test used to compare the means of two groups. At the same time, linear regression is a method for modeling the relationship between a dependent variable and one or more independent variables.
2. T-tests help determine if differences between groups are significant, whereas linear regression can predict the value of a dependent variable based on independent variable values.
3. T-tests are limited to comparing means, while linear regression can model complex relationships and control for confounding variables.

## T-test vs Linear Regression

The difference between T-test and Linear Regression is that Linear Regression is applied to elucidate the correlation between one or two variables in a straight line. At the same time, T-test is one of the tools of hypothesis tests applied to the slope coefficients or regression coefficients derived from a simple linear regression.

/10

Education Quiz

1 / 10

What is the study of the physical universe called?

2 / 10

Which of the following is NOT one of the Seven Wonders of the Ancient World?

3 / 10

What is the study of plants called?

4 / 10

Who painted the famous artwork “The Starry Night”?

5 / 10

What is the name of the standardized test used for college admissions in the United States?

6 / 10

What is the study of government and political systems called?

7 / 10

What is the skill of speaking in front of an audience called?

8 / 10

Which is the first country to have a public education system?

9 / 10

What is the study of history called?

10 / 10

What is the basic unit of life?

While T-test is one of the tests used in hypothesis testing, Linear Regression is one of the types of regression analysis.

A T-test is one of the hypothesis tests conducted to determine whether the difference between the averages of two groups is remarkable or not, that is, whether those differences may have happened by chance.

## What is T-test?

A T-test is one of the instruments used in hypothesis testing for comparing two different sets of data and their means or averages.

It was used for the first time by William Sealy Gosset, a chemist who worked for a brewing company named Guinness, to monitor the consistent quality of the stout.

Gradually, it was upgraded, and now it refers to any hypothesis tests in which the data, when analyzed, is supposed to be equivalent to a t-distribution (a bell-shaped distribution curve with heavier tails) if the null hypothesis (the assumption that no relationship exists between the sets of data) proves to be correct.

There are three types of T-tests:

1. Independent Samples T-test: It is used to compare two different sets of observed data and their means.
2. Paired Sample T-test: It compares the average of a single set of observed data at different times.
3. One Sample T-test: It compares the mean of a single set of data and a known standard.

As an approach for testing the hypothesis, T-test is quite conservative. It can be applied to only two data sets and is suitable for only small ones.

## What is Linear Regression?

Linear Regression is a method of inferential statistics that tries to explain the correlation between a dependent variable(Y) and one or more independent variables(X) using a straight line.

1. Does a set of explanatory variables correctly predict the outcome variable?
2. If it does, then which are the most prominent independent or explanatory variables significantly affecting the dependent or outcome variable?
3. And lastly, to what extent does a change in these independent or explanatory variables affect the outcome or dependent variable?

Similarly, a relationship between the dependent and the independent variable is said to be harmful if the former decreases with an increase in the latter.

Linear Regression has three usages:

1. For deciding the strength of independent variables, i.e. to what extent they influence the independent variable.
2. For forecasting the change in the dependent variable induced by the independent variables.
3. For predicting future trends and values.

There are mainly two linear regressions: Simple Linear Regression which consists of one dependent variable and one independent variable, and Multiple Linear Regression, which comprises the dependent variable and two or more independent variables.

## Main Differences Between T-test and Linear Regression

1. The main difference between a Linear Regression and a T-test is that Linear Regression explains the correlation between a regressand and one or more regressors and the extent to which the latter influences the former.
2. Linear regression analysis can be done even with larger data sets, but a T-test is suitable for only smaller data sets.

References

Last Updated : 11 June, 2023

One request?

I’ve put so much effort writing this blog post to provide value to you. It’ll be very helpful for me, if you consider sharing it on social media or with your friends/family. SHARING IS ♥️

What do you think?
6
5
8
9
4
6

### 23 thoughts on “T-test vs Linear Regression: Difference and Comparison”

1. I’m not quite sure these concepts were explained well enough. It might be too complex for some readers to understand.

1. I respectfully disagree. I think the explanations were thorough and clear, catering to a wide audience.

2. The article provides a clear and informative explanation of both T-test and Linear Regression. It’s useful for anyone interested in inferential statistics.

1. I completely agree! It’s a very comprehensive explanation that can definitely benefit anyone who wants to learn more about inferential statistics.

3. Vanessa Reynolds

The article presents a well-structured comparison between T-tests and Linear Regression, making it easy for readers to grasp the key differences.

4. I found the article to be informative and well-written, providing valuable insights into the topics discussed.

5. The article seems a bit too simplistic and does not dive deep into the complexities of these statistical methods.

1. I can see how one might perceive it as simplistic, but sometimes a straightforward explanation is the best approach for such concepts.

2. I think the simplicity of the explanations is what makes this article effective. It’s not lacking in depth, but rather concise and comprehensible.

6. I find this article very enlightening and feel like I’ve learned a lot from it. Great job on explaining these complex terms in a simple manner!

1. Definitely! The author did a fantastic job of simplifying these concepts for the readers. It’s a valuable read.

1. I appreciate the thoroughness of the article. It’s important to ensure that all aspects are adequately explained.

2. I don’t think it’s verbose; it thoroughly covers the essential aspects of T-test and Linear Regression.

7. Finally, a well-explained article on T-tests and Linear Regression. The comparison table is especially helpful for understanding their differences.

1. Absolutely! The comparison table really simplifies the contrasting aspects of these statistical methods.

8. The article provides excellent insights into T-test and Linear Regression and their practical applications. A valuable resource indeed.

1. I couldn’t agree more! The practical applications provided here are very informative.

Want to save this article for later? Click the heart in the bottom right corner to save to your own articles box!