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 minimizes the sum of the squared differences between observed values and the line's predicted values.

5 Must Know Facts For Your Next Test

1. The equation of a regression line is typically written as $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.
2. The slope ($m$) of the regression line indicates the rate at which $y$ changes with respect to $x$.
3. The y-intercept ($b$) is the value of $y$ when $x=0$.
4. Least squares method is commonly used to determine the best-fitting regression line.
5. The coefficient of determination, denoted as $R^2$, measures how well the regression line explains the variation in the dependent variable.

Review Questions

• What does the slope of a regression line represent?
• How is the best-fitting regression line determined?
• What does an $R^2$ value close to 1 indicate?

Related terms

Slope: The rate at which one variable changes with respect to another; in a linear equation, it corresponds to 'm' in $y = mx + b$.

Y-intercept: The point where a graph crosses the y-axis; in a linear equation, it corresponds to 'b' in $y = mx + b$.

Coefficient of Determination ($R^2$): A statistical measure that explains how much of the variance in a dependent variable can be explained by an independent variable or variables.