Artificial Intelligence
Linear Functions
- Linear means straight
- A linear function is a straight line
- A linear graph represents a linear function
Linear Functions
A Function is special relationship where each input has an output.
A function is often written as f(x) where x is the input:
Results from f(x) = x
| x | y | y = x |
|---|---|---|
| 1 | 1 | y = x = 1 |
| 2 | 2 | y = x = 2 |
| 3 | 3 | y = x = 3 |
| 4 | 4 | y = x = 4 |
| 5 | 5 | y = x = 5 |
Results from f(x) = 2x
| x | y | y = 2x |
|---|---|---|
| 1 | 2 | y = 2x = 2 |
| 2 | 4 | y = 2x = 4 |
| 3 | 6 | y = 2x = 6 |
| 4 | 8 | y = 2x = 8 |
| 5 | 10 | y = 2x = 10 |
Linear Equations
A Linear Equation is an equation for a straight line:
- y = x
- y = x*2
- y = x*2 + 7
- y = ax + b
- 5x = 3y
- y/2 = 6
Non-Linear Equations
A Linear Equation can NOT contain exponents or square roots:
- y = x**2
- y = Math.sqrt(x)
- y = Math.sin(x)
Linear Regression
A Linear regression tries to model the relationship between two variables by fitting a linear graph to data.
One variable (x) is considered to be data, and the other (y) is considered to be dependent.
For example, a Linear Regression can be a model to relate the price of houses to their size.
Linear Least Squares
Linear algebra is used to solve Linear Equations.
Linear Least Squares (LLS) is a set of formulations for solving statistical problems involved in Linear Regression.
