Linear_Functions.py

# Linear Functions
'''
A linear function has one independent variable (x) and one dependent variable (y), and has the following form:
y = f(x) = ax + b 
This function is used to calculate a value for the dependent variable when we choose a value for the independent variable.

Explanation:
f(x) = the output (the dependant variable)
x = the input (the independant variable)
a = slope = is the coefficient of the independent variable. It gives the rate of change of the dependent variable
b = intercept = is the value of the dependent variable when x = 0. It is also the point where the diagonal line crosses the vertical axis.
'''

# Linear Function With One Explanatory Variable
 # - A function with one explanatory variable means that we use one variable for prediction.
 # For example:
  # Let us say we want to predict calorie burnage using average pulse. We have the following formula:  
  # f(x) = 2x + 80
'''
Here, the numbers and variables means:
f(x) = The output. This number is where we get the predicted value of Calorie_Burnage
x = The input, which is Average_Pulse
2 = Slope = Specifies how much Calorie_Burnage increases if Average_Pulse increases by one. It tells us how "steep" the diagonal line is
80 = Intercept = A fixed value. It is the value of the dependent variable when x = 0

'''
# Plotting a Linear Function
'''
Graph Explanations:
- The horizontal axis is generally called the x-axis. Here, it represents Average_Pulse.
- The vertical axis is generally called the y-axis. Here, it represents Calorie_Burnage.
- Calorie_Burnage is a function of Average_Pulse, because Calorie_Burnage is assumed to be dependent on Average_Pulse.
- In other words, we use Average_Pulse to predict Calorie_Burnage.
- The blue (diagonal) line represents the structure of the mathematical function that predicts calorie burnage.

'''