Sum Of Squares

AAA

DEFINITION of 'Sum Of Squares'

A statistical technique used in regression analysis. The sum of squares is a mathematical approach to determining the dispersion of data points. In a regression analysis, the goal is to determine how well a data series can be fitted to a function which might help to explain how the data series was generated. The sum of squares is used as a mathematical way to find the function which best fits (varies least) from the data.


In order to determine the sum of squares the distance between each data point and the line of best fit is squared and then all of the squares are summed up. The line of best fit will minimize this value.

INVESTOPEDIA EXPLAINS 'Sum Of Squares'

There are two methods of regression analysis which use the sum of squares: the linear least squares method and the non-linear least squares method. Least squares refers to the fact that the regression function minimizes the sum of the squares of the variance from the actual data points. In this way, it is possible to draw a function which statistically provides the best fit for the data. A regression function can either be linear (a straight line) or non-linear (a curving line).

RELATED TERMS
  1. Line Of Best Fit

    A straight line drawn through the center of a group of data points ...
  2. Least Squares Method

    A statistical technique to determine the line of best fit for ...
  3. Residual Sum Of Squares - RSS

    A statistical technique used to measure the amount of variance ...
  4. Stepwise Regression

    The step-by-step iterative construction of a regression model ...
  5. Hedonic Regression

    A method used to determine the value of a good or service by ...
  6. Multiple Linear Regression - MLR

    A statistical technique that uses several explanatory variables ...
Related Articles
  1. Investing Basics

    Calculating Beta: Portfolio Math For The Average Investor

    Beta is a useful tool for calculating risk, but the formulas provided online aren't specific to you. Learn how to make your own.
  2. Investing Basics

    Regression Basics For Business Analysis

    This tool is easy to use and can provide valuable information on financial analysis and forecasting. Find out how.
  3. Options & Futures

    Bettering Your Portfolio With Alpha And Beta

    Increase your returns by creating the right balance of both these risk measures.
  4. Active Trading

    The Linear Regression Of Time and Price

    This investment strategy can help investors be successful by identifying price trends while eliminating human bias.
  5. Budgeting

    The P/E Ratio: A Good Market-Timing Indicator

    Check out the returns this newer technical analysis tool would've yielded over the period from 1920 to 2003.
  6. Fundamental Analysis

    What is a Null Hypothesis?

    In statistics, a null hypothesis is assumed true until proven otherwise.
  7. Investing

    How to Use Stratified Random Sampling

    Stratified random sampling is a technique best used with a sample population easily broken into distinct subgroups. Samples are then taken from each subgroup based on the ratio of the subgroup’s ...
  8. Fundamental Analysis

    Lognormal and Normal Distribution

    When and why do you use lognormal distribution or normal distribution for analyzing securities? Lognormal for stocks, normal for portfolio returns.
  9. Investing Basics

    Using Normal Distribution Formula To Optimize Your Portfolio

    Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk.
  10. Technical Indicators

    The Normal Distribution Table, Explained

    The normal distribution formula is based on two simple parameters - mean and standard deviation

You May Also Like

Hot Definitions
  1. Asset Class

    A group of securities that exhibit similar characteristics, behave similarly in the marketplace, and are subject to the same ...
  2. Fiat Money

    Currency that a government has declared to be legal tender, but is not backed by a physical commodity. The value of fiat ...
  3. Interest Rate Risk

    The risk that an investment's value will change due to a change in the absolute level of interest rates, in the spread between ...
  4. Income Effect

    In the context of economic theory, the income effect is the change in an individual's or economy's income and how that change ...
  5. Price-To-Sales Ratio - PSR

    A valuation ratio that compares a company’s stock price to its revenues. The price-to-sales ratio is an indicator of the ...
  6. Hurdle Rate

    The minimum rate of return on a project or investment required by a manager or investor. In order to compensate for risk, ...
Trading Center