Residual

TL;DR

• The leftover amount remaining after a calculation or process in contexts such as finance, statistics, and engineering.
• In finance, used as the estimated end-of-life value of an asset when calculating depreciation.
• In statistics, the per-observation difference between a model’s predicted value and the actual observed value; residuals are inspected (e.g., plotted) to assess model fit.

Definition

Residual refers to the remaining or leftover value or amount after certain calculations or processes have been completed. It can be used in a variety of contexts, including finance, statistics, and engineering.

Explanation

A residual is the portion that remains once a calculation or process has been applied. In finance, residuals commonly appear as a “residual value” for long-lived assets, representing the estimated value of the asset at the end of its useful life and affecting depreciation calculations. In statistics, residuals are the differences between predicted and actual values for each data point in a regression model; analyzing these residuals (residual analysis) helps visualize and evaluate the model’s overall fit. A good fit is represented by a patternless scatter of residuals around the zero line.

Examples

Finance (capital expenditures and depreciation)

Capital expenditures are money spent on long-term assets expected to have a useful life of more than one year. When calculating depreciation, a company may include a residual value, the estimated value of the asset at the end of its useful life.

Example from the source: A company purchases equipment for $100,000, estimates a useful life of 10 years and a residual value of$10,000. The company would depreciate the asset for $9,000 per year for the next 10 years ($100,000 - $10,000 =$90,000, $90,000 / 10 =$9,000).

The depreciation calculation can be expressed as: $\frac{100{,}000 - 10{,}000}{10} = 9{,}000$

Statistics (regression residuals)

In regression modeling, residuals are the difference between the predicted value of the dependent variable and the actual value for each data point. Residual analysis involves calculating these differences and plotting them to visualize model fit; a good fit appears as a patternless scatter of residuals around the zero line.

Use cases

• Finance: estimating residual value for capital expenditures and computing depreciation.
• Statistics: residual analysis in regression models to assess fit.
• Engineering: general reference to remaining or leftover amounts after calculations or processes.

Related terms

• Residual value
• Residual analysis
• Regression model
• Capital expenditures
• Depreciation