Linear regression

Definition

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data. It aims to predict the value of the dependent variable based on the values of the independent variables.

5 Must Know Facts For Your Next Test

1. The equation for simple linear regression is $Y = \beta_0 + \beta_1X + \epsilon$, where $Y$ is the dependent variable, $X$ is the independent variable, $\beta_0$ is the intercept, $\beta_1$ is the slope, and $\epsilon$ represents error terms.
2. The coefficient of determination, denoted as $R^2$, measures how well the regression line approximates real data points.
3. Assumptions of linear regression include linearity, independence, homoscedasticity (equal variance), and normal distribution of errors.
4. Residuals are differences between observed values and predicted values; they help in diagnosing model fit.
5. Outliers can significantly affect the results of a linear regression analysis by skewing the fitted line.

Review Questions

• What does the slope ($\beta_1$) in a simple linear regression represent?
• How do you interpret an $R^2$ value close to 1?
• What are residuals in the context of linear regression?

Related terms

Correlation Coefficient:

A measure that indicates the extent to which two variables fluctuate together. The value ranges from -1 to +1.

Scatter Plot: A graphical representation that uses dots to represent values obtained for two different variables – one plotted along the x-axis and one plotted along the y-axis.

Multiple Linear Regression: An extension of simple linear regression that models the relationship between a dependent variable and multiple independent variables using a linear equation.