A function with one explanatory variable means using a single variable to make predictions.
For example, if we want to predict calorie burnage based on average pulse, we can use the following formula:
In this formula, the numbers and variables represent the following:
- f(x): The output, which gives the predicted value of Calorie_Burnage.
- x: The input, which is the Average_Pulse.
- 2: The slope, indicating how much Calorie_Burnage increases when Average_Pulse increases by one. It describes the steepness of the line.
- 80: The intercept, a fixed value representing the dependent variable when x = 0.
Plotting a Linear Function
The term “linearity” refers to a “straight line.” When you graph a linear function, the result will always be a straight line, which can slope upwards, downwards, or in some cases, be horizontal or vertical.
Below is a graphical representation of the mathematical function described earlier:
Graph Explanations:
- The horizontal axis is typically referred to as the x-axis, representing Average_Pulse in this case.
- The vertical axis is called the y-axis, which represents Calorie_Burnage.
- Calorie_Burnage is considered a function of Average_Pulse because it is assumed to depend on Average_Pulse.
- In other words, Average_Pulse is used to predict Calorie_Burnage.
- The blue (diagonal) line illustrates the structure of the mathematical function used to predict Calorie_Burnage.
