Linear model

Definition

A linear model is a mathematical representation of a relationship between two variables using a straight line. The general form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

5 Must Know Facts For Your Next Test

1. The slope ($m$) indicates the rate of change between the dependent and independent variables.
2. The y-intercept ($b$) represents the value of $y$ when $x$ equals zero.
3. Linear models are used to predict values within or outside the range of data points.
4. Least squares regression is a common method for fitting linear models to data.
5. The correlation coefficient ($r$) measures how well the linear model fits the data.

Review Questions

• What does the slope in a linear model represent?
• How do you interpret the y-intercept in a linear model?
• What method is commonly used to fit a linear model to data?

Related terms

Slope: The measure of steepness or incline of a line, defined as rise over run.

Y-Intercept: The point where the line crosses the y-axis, indicating the value of $y$ when $x=0$.

Correlation Coefficient: $r$, a statistical measure that indicates how well data points fit a linear model.