Fitted Value

TL;DR

• Values a statistical model assigns to observations after fitting (the model’s predictions for the input data).
• Used to make predictions and to assess model performance.
• Common in regression (predicted outcomes per observation) and time series forecasting (predicted values per time period).

Definition

Fitted values are values predicted or estimated by a statistical model for a given set of input data.

Explanation

A fitted value is the prediction a model provides for each observation based on the model’s fitted line or curve. After fitting a statistical model to observed data, the model yields fitted values that represent its estimate of the outcome for those inputs. These fitted values can be used to make predictions about future observations or to assess how well the model captures the relationship between input variables and the output variable.

Examples

Regression example

Suppose we model the relationship between a person’s age and their income. We collect a sample of individuals’ ages and incomes and use a linear regression model to fit a line to the data. The fitted values are the predicted income for each individual in the sample based on their age.

Time series example

Suppose we forecast the sales of a product over the next year. We collect sales data from the past few years and use a time series model to fit a curve to the data. The fitted values are the predicted sales for each time period in the forecast.

Use cases

• Making predictions or estimates about future values.
• Assessing the accuracy of a fitted statistical model.
• Informing decisions based on model outputs (for example, decisions about hiring and salary in the regression example, or inventory and production planning in the time series example).

Related terms

• Regression analysis
• Linear regression
• Time series analysis
• Statistical model
• Forecast