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Mathematical functions are important to know as a data scientist, because we want to make predictions and interpret them
In mathematics a function is used to relate one variable to another variable.
Suppose we consider the relationship between calorie burnage and average pulse. It is reasonable to assume that, in general, the calorie burnage will change as the average pulse changes - we say that the calorie burnage depends upon the average pulse.
Furthermore, it may be reasonable to assume that as the average pulse increases, so will the calorie burnage. Calorie burnage and average pulse are the two variables being considered.
Because the calorie burnage depends upon the average pulse, we say that calorie burnage is the dependent variable and the average pulse is the independent variable.
The relationship between a dependent and an independent variable can often be expressed mathematically using a formula (function).
This function is used to calculate a value for the dependent variable when we choose a value for the independent variable.
Explanation:
A function with one explanatory variable means that we use one variable for prediction.
Let us say we want to predict calorie burnage using average pulse. We have the following formula:
Here, the numbers and variables means:
The term linearity means a "straight line". So, if you show a linear function graphically, the line will always be a straight line. The line can slope upwards, downwards, and in some cases may be horizontal or vertical.
Here is a graphical representation of the mathematical function above:
Graph Explanations: