Linear model

Definition

A linear model is a mathematical representation of a relationship between two variables that can be expressed with a linear equation, typically in the form $y = mx + b$. It is used to predict the value of one variable based on the value of another.

5 Must Know Facts For Your Next Test

1. The slope $m$ represents the rate of change of $y$ with respect to $x$.
2. The y-intercept $b$ is the value of $y$ when $x = 0$.
3. Linear models are often used for regression analysis to fit data points with a line that best represents their trend.
4. The coefficient of determination, denoted as $R^2$, measures how well the linear model fits the data.
5. Residuals are the differences between observed values and predicted values from the linear model.

Review Questions

Related terms

Slope:

The measure of steepness or incline of a line, representing the rate at which one variable changes with respect to another in a linear equation.

Y-intercept: The point where the line crosses the y-axis, representing the value of y when x equals zero in a linear equation.

$R^2$ (Coefficient of Determination): $R^2$ indicates how well data points fit a statistical model – specifically, it shows what proportion of variance in dependent variable is predictable from independent variable(s).