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Regression is a statistical tool that is leveraged in many different disciplines to help determine the strength and direction of the relationship between different variables; independent and dependent:
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There are two basic types of regression:
It is important to note that the aforementioned regressions are methods of linear regression and cannot be used for non-linear data. Linear regression involves relating variables with a straight line while nonlinear regression relates the variables in a nonlinear (curved) relationship. For more complicated data and analysis, there are other methods of non-linear regression.
Simple linear regression involves using one independent variable (x) to explain the outcome of the dependent variable (y).
The formula for simple linear regression is:
Y = a + bX + u
To understand when the appropriate use of linear regression, let’s consider the following example:
If we were to assume height as the singular determinant of body weight, we could use the simple linear regression model to predict or explain the impact of a change in height on weight.
Multiple linear regression involves using two or more independent variables (x) to explain the outcome of the dependent variable (y).
The formula for multiple linear regression is as follows:
Y = a + b1X1 + b2X2 + b3X3 + … + btXt + u
Multiple linear regression is used when simple linear regression is not enough to account for the multiple real-life factors that influence the outcome of a dependent variable.
Let’s continue with the previous example involving height and weight. Realistically, height is not the only determinant of weight. There are a lot of different factors that influence a person’s weight, such as diet and exercise, and therefore a more realistic model would contain multiple x variables (independent variable).
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Overfitting is a modelling error that occurs quite frequently in regression analysis. It takes place when a function or a model is too complex for the data and too many parameters are being estimated from a sample size that is too small. Although an overfitted model may fit your data well, it won’t align with additional test samples or the overall target population.
When a model is overfitted, its p-values, R-Squared, and regression coefficients are likely to be very misleading. So how can we avoid overfitting?
These are a few ways in which you can avoid overfitting your data:
Regression refers to the approach of modelling the relationship between variables to determine the strength and direction of their relationship.
The two main types of linear regression are simple linear regression and multiple linear regression.
Simple linear regression involves modelling the relationship between one independent variable (x) and one dependent variable (y). It is used when a dependent variable only has one determinant.
Multiple linear regression involves modelling the relationship between two or more independent variables (x) and one dependent variable (y). It is used when a dependent variable has multiple determinants.
Linear regression involves relating variables with a straight line while nonlinear regression relates the variables in a nonlinear (curved) relationship.
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