# What is Linear Regression?

Linear regression is a statistical method that predicts a variable’s value based on another variable’s value. The method is a valuable data science tool that empowers companies to uncover hidden trends in their data. Companies use this information to forecast business outcomes.

### How Linear Regression Works

The idea of linear regression is that one can use a line (or multiple lines) to connect a pair of points and predict how those two points will move in relation to each other over time. To show this relationship, you first build what is called a model. The variable of interest is called the response variable. The variables that affect the response are called predictor values.

To use linear regression, you first define a relationship between the two variables you want to predict. For example, you might want to know how much money a person makes each year in relation to how much education they have. In this case, you’d need to measure both education and income and then construct a line connecting the two points. You can then use the slope of that line to calculate how much money you’ll make each year if you have more education than someone else, and vice versa.

The next step is to determine the prediction error for each possible combination of predictor variables and response variables. This value shows the difference between the actual response and the predicted response when the prediction is correct. The prediction error should be low if the combination is accurate at predicting the response.

The benefit of simple linear regression is that it provides easy-to-understand results as it only deals with two variables. Additionally, regression accounts for measurement error, so it can provide meaningful results even when data is noisy or inaccurate.

#### Linear Regression Example

Ordinal regression is a form of linear regression that estimates the relationship between two variables by comparing their ranks or order. For example, ordinal regression can be used to estimate the association between a person’s weight and height. This relationship is linear because there are clear differences in weight values between people with different heights. However, there is no obvious difference between someone who weighs 99 pounds and someone who weighs 100 pounds.

The advantage of using ordinal regression is that it does not require statistically significant data. It also does not assume a constant relationship between variables, which makes it more robust in situations when there may be other factors influencing results. However, it is harder to interpret than linear regression because there are inherent assumptions about how variables are ordered that need to be validated to make valid predictions.

#### Multiple Variable Linear Regression

Multiple variable linear regression is a statistical technique used to predict the value of one or more dependent variables given the values of one or more independent variables. It is used to predict one response variable given many predictor variables that describe different aspects of the same phenomenon. These are called independent variables because they have no effect on the dependent variable.

In this case, the response variable is usually some kind of quantity, such as income level or sales volume. The predictor variables describe aspects of the phenomenon being predicted, such as education level or weather conditions. This type of linear regression has many uses in business. For example, consider the following:

- Independent variable (product feature A) has a 10% effect on sales.
- Independent variable (feature B) has a 20% effect on sales.

You can then use multiple regression to see if both features combined impact sales. If so, you can conclude that something about having both features at the same time has an impact.

Multivariable linear regression can also be used for hypothesis testing. This means you can use it to test whether one or more predictor variables impact the response variables. If a predictor variable impacts response variables, then it’s possible that its impact is due to some other cause. For example, if you find that gender impacts sales, it’s possible that gender is causing other factors, such as age or number of employees. If you find no impact from one or more independent variables, then it’s highly unlikely that their impact is due to other causes.

### Linear Regression: Key to Finding Hidden Meaning in Data

Linear regression is a valuable tool with many use cases. The method pairs well with data mining to uncover hidden relationships in data which is valuable to informed-decision making.

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