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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

xyy = x
11y = x = 1
22y = x = 2
33y = x = 3
44y = x = 4
55y = x = 5

Results from f(x) = 2x

xyy = 2x
12y = 2x = 2
24y = 2x = 4
36y = 2x = 6
48y = 2x = 8
510y = 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.