**Linear regression **is one of the most commonly used techniques in statistics. It is used to quantify the relationship between one or more predictor variables and a response variable.

The most basic form of linear is regression is known as simple linear regression, which is used to quantify the relationship between one predictor variable and one response variable.

If we have more than one predictor variable then we can use multiple linear regression, which is used to quantify the relationship between several predictor variables and a response variable.

This tutorial shares four different examples of when linear regression is used in real life.

**Linear Regression Real Life Example #1**

Businesses often use linear regression to understand the relationship between advertising spending and revenue.

For example, they might fit a simple linear regression model using advertising spending as the predictor variable and revenue as the response variable. The regression model would take the following form:

revenue = β_{0}+ β_{1}(ad spending)

The coefficient **β _{0}** would represent total expected revenue when ad spending is zero.

The coefficient **β _{1}** would represent the average change in total revenue when ad spending is increased by one unit (e.g. one dollar).

If β_{1} is negative, it would mean that more ad spending is associated with less revenue.

If β_{1} is close to zero, it would mean that ad spending has little effect on revenue.

And if β_{1} is positive, it would mean more ad spending is associated with more revenue.

Depending on the value of β_{1}, a company may decide to either decrease or increase their ad spending.

**Linear Regression Real Life Example #2**

Medical researchers often use linear regression to understand the relationship between drug dosage and blood pressure of patients.

For example, researchers might administer various dosages of a certain drug to patients and observe how their blood pressure responds. They might fit a simple linear regression model using dosage as the predictor variable and blood pressure as the response variable. The regression model would take the following form:

blood pressure = β_{0}+ β_{1}(dosage)

The coefficient **β _{0}** would represent the expected blood pressure when dosage is zero.

The coefficient **β _{1}** would represent the average change in blood pressure when dosage is increased by one unit.

If β_{1} is negative, it would mean that an increase in dosage is associated with a decrease in blood pressure.

If β_{1} is close to zero, it would mean that an increase in dosage is associated with no change in blood pressure.

If β_{1} is positive, it would mean that an increase in dosage is associated with an increase in blood pressure.

Depending on the value of β_{1}, researchers may decide to change the dosage given to a patient.

**Linear Regression Real Life Example #3**

Agricultural scientists often use linear regression to measure the effect of fertilizer and water on crop yields.

For example, scientists might use different amounts of fertilizer and water on different fields and see how it affects crop yield. They might fit a multiple linear regression model using fertilizer and water as the predictor variables and crop yield as the response variable. The regression model would take the following form:

crop yield = β_{0}+ β_{1}(amount of fertilizer) + β_{2}(amount of water)

The coefficient **β _{0}** would represent the expected crop yield with no fertilizer or water.

The coefficient **β _{1}** would represent the average change in crop yield when fertilizer is increased by one unit,

*assuming the amount of water remains unchanged.*

The coefficient **β _{2}** would represent the average change in crop yield when water is increased by one unit,

*assuming the amount of fertilizer remains unchanged.*

Depending on the values of β_{1} and β_{2}, the scientists may change the amount of fertilizer and water used to maximize the crop yield.

**Linear Regression Real Life Example #4**

Data scientists for professional sports teams often use linear regression to measure the effect that different training regimens have on player performance.

For example, data scientists in the NBA might analyze how different amounts of weekly yoga sessions and weightlifting sessions affect the number of points a player scores. They might fit a multiple linear regression model using yoga sessions and weightlifting sessions as the predictor variables and total points scored as the response variable. The regression model would take the following form:

points scored = β_{0}+ β_{1}(yoga sessions) + β_{2}(weightlifting sessions)

The coefficient **β _{0}** would represent the expected points scored for a player who participates in zero yoga sessions and zero weightlifting sessions.

The coefficient **β _{1}** would represent the average change in points scored when weekly yoga sessions is increased by one,

*assuming the number of weekly weightlifting sessions remains unchanged.*

The coefficient **β _{2}** would represent the average change in points scored when weekly weightlifting sessions is increased by one,

*assuming the number of weekly yoga sessions remains unchanged.*

Depending on the values of β_{1} and β_{2}, the data scientists may recommend that a player participates in more or less weekly yoga and weightlifting sessions in order to maximize their points scored.

**Conclusion**

Linear regression is used in a wide variety of real-life situations across many different types of industries. Fortunately, statistical software makes it easy to perform linear regression.

Feel free to explore the following tutorials to learn how to perform linear regression using different softwares:

How to Perform Simple Linear Regression in Excel

How to Perform Multiple Linear Regression in Excel

How to Perform Multiple Linear Regression in R

How to Perform Multiple Linear Regression in Stata

How to Perform Linear Regression on a TI-84 Calculator