Regression line

Definition

A regression line is a straight line that best fits the data points on a scatter plot, showing the relationship between two variables. 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 equation of a regression line is typically written as $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept.
2. The slope ($m$) indicates the rate of change of the dependent variable with respect to the independent variable.
3. The y-intercept ($b$) represents the value of the dependent variable when the independent variable is zero.
4. Regression lines minimize the sum of squared differences between observed values and predicted values, known as least squares method.
5. Correlation coefficient (r) measures how well data points fit on a regression line, with $r = 1$ or $r = -1$ indicating perfect fit.

Review Questions

• What does the slope in a regression line represent?
• How do you interpret the y-intercept in a regression line equation?
• What method is used to find the best-fitting regression line?

Related terms

Slope: The rate at which one variable changes in relation to another; represented by $m$ in the equation $y = mx + b$.

Y-Intercept: The point where the regression line crosses the y-axis; represented by $b$ in $y = mx + b$, indicating value when x=0.

Correlation Coefficient: $r$, a statistical measure that describes the strength and direction of a linear relationship between two variables.