Chapter 7

Linear Model

Linear Model

A mathematical equation that describes the relationship between two or more variables using a straight line, typically used to predict the value of a dependent variable based on one or more independent variables.

Model

A simplified representation of a real-world process or system, using mathematical, statistical, or computational methods to describe and analyze the relationships between variables.

Predicted Value

The estimated value of the dependent variable based on a given set of independent variables and a specified model, often denoted by ŷ

Residuals

The differences between observed values of the dependent variable and the values predicted by the model, indicating the error or discrepancy between the actual data and the model's predictions.

Least Squares

A method used in regression analysis to determine the best-fitting line by minimizing the sum of the squared differences between observed values and predicted values.

Slope

The measure of the steepness or incline of the regression line, representing the change in the dependent variable for a one-unit change in the independent variable.

Intercept

The point at which the regression line crosses the y-axis, representing the value of the dependent variable when all independent variables are equal to zero.

Regression To The Mean

The phenomenon where extreme values in a data set tend to be closer to the mean in subsequent measurements, often observed in repeated measurements or over time.

Regression Line (Line Of Best Fit)

The straight line that best represents the data in a scatter plot, determined by minimizing the sum of the squared residuals, often used to make predictions based on the linear relationship between variables.

Standard Deviation Of The Residuals

A measure of the spread of residuals around the regression line, indicating the average distance between observed values and predicted values, often denoted by 𝑠ₑ