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What Is Mathematical Regression?

Regression is the method you use to create a mathematical model from a data set. Nowadays, you will always be using digital tools to accomplish this. When you perform a regression, you want to find the function that best matches the set of data points you have been given. Graphically, you can imagine that you have obtained numbers from reality and drawn these as points in a coordinate system. Through regression, you find a graph that is very close to those points. The image below shows a regression that follow the points reasonably well. (Remember: A mathematical model is rarely perfect when compared to reality).

Graph of a quadratic regression

Graph of a quadratic regression

Different sets of data can look quite distinct from one another. You need to know various types of functions, whose graphs are shaped differently in order to fit these different types of data sets. To get a good model with few flaws, it’s important to choose the right type of function. The most common models are described here:

Theory

The Most Common Models for Regression

Linear model:

y = ax + b

Quadratic model:

y = ax2 + bx + c

Exponential model:

y = aekx

Trigonometric model:

y = A sin(cx + ϕ) + d

You want to find a model with a graph that is fairly close to the data points you have. You can see a linear model that fits the data points kind of alright below:

Graph of a linear regression

Graph of a linear regression

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