About
A linear equation represents a linear function that forms a straight line.
A common form of a linear equation in the two variables (two dimensions) x and y is
<math> y= mx + b </math>
where:
- m is a constant named the slope or gradient of the line
- b is a constant named the intercept. It determines the point at which the line crosses the y-axis, otherwise known as the y-intercept.
In Statistics, it's the basic of a regression
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Assumptions
Terms of linear equations cannot contain:
- products of distinct or equal variables,
- nor any power (other than 1)
- or other function of a variable, equations involving terms such as xy, x2, y1/3, and sin(x)
Linear Equation in
Vector
In linear algebra, a linear equation can be expressed as an equation stating the value of the dot-product of:
- a coefficient vector (a vector whose entries are the coefficients)
- and a vector of unknowns variables.
Therefore a linear equation (function) is an equation of the form
<math>a . x = \beta</math>
where:
Type
Homogeneous
A linear equation a · x = 0 with zero right-hand side is a homogeneous linear equation. A system of homogeneous linear equations is called a homogeneous linear system.
Functions
Oracle:
- Slope: REGR_SLOPE(Y,X)
- Intercept: REGR_INTERCEPT(Y,X)