Intercept

TL;DR

• The intercept is where the regression line crosses the y-axis and gives a baseline predicted value.
• It represents the predicted value of the dependent variable when predictor variables are at their minimum values.
• Do not treat the intercept as evidence of causation; it can change when predictors are added or removed.

Definition

Intercept in regression analysis refers to the point at which the regression line crosses the y-axis. This is the point at which the predicted value of the dependent variable is zero, even when all predictor variables are at their minimum values.

Explanation

The intercept provides a baseline prediction for the dependent variable when the predictor variables are at their minimum values. It can be interpreted as a minimum or baseline level of the outcome in the contexts described by the model. However, the intercept does not imply a causal relationship between predictors and the dependent variable. The numeric value of the intercept can also be influenced by which predictor variables are included in the model.

Examples

Studying time and final exam score

Consider a regression analysis of the relationship between the amount of time spent studying and the final exam score. The intercept in this case would represent the predicted final exam score when no time is spent studying. This could be interpreted as the minimum score that a student could achieve without studying at all.

Company size and profitability

Consider a regression analysis of the relationship between the size of a company and its profitability. The intercept in this case would represent the predicted profitability of a company when its size is zero. This could be interpreted as the minimum profitability that a company could achieve without having any size.

Use cases

• Determining the minimum effort required to achieve a certain exam score (from the studying-time example).
• Determining the minimum size required to achieve a certain level of profitability (from the company-size example).

Notes or pitfalls

• The intercept should not be interpreted as a causal relationship between predictor and dependent variables; it only represents a predicted value when predictors are at their minimum values.
• The intercept can be influenced by the inclusion or exclusion of other factors that impact the dependent variable (for example, industry or management in the profitability example).

Related terms

• Regression analysis
• Regression line
• Predictor variable
• Dependent variable
• y-axis