Linear Model

TL;DR

• Predicts a dependent variable from one or more independent variables using a linear relationship.
• Useful for estimating how factors affect the dependent variable and for prediction.
• Relies on the assumption of linearity; if the true relationship is nonlinear, predictions may be inaccurate.

Definition

A linear model is a mathematical model that represents the relationship between a dependent variable and one or more independent variables by using a linear equation. The model assumes that the relationship between the dependent and independent variables is linear, meaning the change in the dependent variable is directly proportional to the change in the independent variable.

Explanation

A linear model expresses the dependent variable as a linear function of the independent variables via a linear equation. Because it assumes proportional change, an increase (or decrease) in an independent variable corresponds to a directly proportional change in the dependent variable. Linear models are simple, intuitive, and widely used for predicting the dependent variable from observed inputs and for identifying and estimating the effects of factors that influence the dependent variable.

Examples

Weight and volume

Consider the relationship between the weight of an object and its volume. The weight of an object is directly proportional to its volume, which means that if the volume of the object increases, the weight of the object will also increase. This relationship can be represented by a linear equation, where the weight is the dependent variable and the volume is the independent variable.

Price and demand

Another example of a linear model is the relationship between the price of a product and its demand. The price of a product is directly proportional to its demand, which means that if the price of a product increases, the demand for the product will decrease. This relationship can also be represented by a linear equation, where the price is the dependent variable and the demand is the independent variable.

Use cases

• Applied across fields such as economics, engineering, and statistics.
• Predicting the behavior of a dependent variable based on values of independent variables.
• Identifying factors that affect a dependent variable and estimating their effects.

Notes or pitfalls

• The primary limitation is the assumption of linearity, which may not hold in real-world situations.
• If the true relationship between variables is nonlinear, a linear model may produce inaccurate predictions or estimates.

Related terms

• Linear equation
• Dependent variable
• Independent variables
• Proportionality