Least squares regression

Definition

Least squares regression is a statistical method used to determine the best-fitting linear relationship between two variables by minimizing the sum of the squares of the vertical distances (errors) between observed and predicted values.

5 Must Know Facts For Your Next Test

1. The least squares regression line has the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
2. The slope $m$ in least squares regression represents the rate of change of the dependent variable with respect to the independent variable.
3. The y-intercept $b$ in least squares regression represents the value of the dependent variable when the independent variable is zero.
4. The goal of least squares regression is to minimize the sum of squared residuals, which are differences between observed and predicted values.
5. The coefficient of determination, $R^2$, measures how well the regression line fits the data; it ranges from 0 to 1.

Related terms

Linear Function:

A function that creates a straight line when graphed, typically described by an equation of the form $y = mx + b$.

Residual: The difference between an observed value and its corresponding predicted value from a regression model.

$R^2$ (Coefficient of Determination): $R^2$ indicates how well data points fit a statistical model. It explains what proportion of variance in a dependent variable can be explained by an independent variable.