# Difference Between T-test and Linear Regression

T-test and Linear regression are terms related to inferential statistics that is the statistical method that helps us in making generalizations and predictions about a population by taking a small but illustrative sample of that population.

## T-test vs Linear Regression

The main 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. While T-test is one of the tools of hypothesis tests applied on the slope coefficients or regression coefficients derived from a simple linear regression.

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 find out that the difference between the averages of two groups is remarkable or not that is, whether those differences may have happened by chance or not.

## 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 right.

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 is used to compare the average of a single set of observed data at different times.
3. One Sample T-test: It makes a comparison between the mean of a single set of data and a known mean.

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

## 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 that significantly affect the dependant or outcome variable?
3. And lastly, to what extent a change in these independent or explanatory variables affect the outcome or dependant variable?

Similarly, a relationship between the dependant and the independent variable is said to be a negative one 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 dependant variable induced by the independent variables.
3. For predicting future trends and values.

There are mainly two types of linear regressions: Simple Linear Regression which consists of one dependant variable and one independent variable and Multiple Linear Regression that comprises of dependant 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 thata Linear Regression is used to explain 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 sets of data but a T-test is suitable for only smaller data sets.

## Conclusion

Both T-test and Linear Regression fall within the broader framework of inferential statistics that are used to make assumptions on a particular population using a small sample.

While linear regression helps in making certain predictions about a particular sample e.g. customer behaviour, T-test helps in testing the applicability of a hypothesis to a sample population.

## References

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