How To Find The Sum Of The Squared Residuals

What is Sum of Squares?

Sum of squares (SS) is a statistical tool that is used to identify the dispersion of information likewise as how well the data can fit the model in regression analysis Regression Analysis Regression analysis is a set of statistical methods used to estimate relationships between a dependent variable and ane or more than independent variables. . The sum of squares got its proper noun because it is calculated by finding the sum of the squared differences.

Sum of Squares Diagram

This epitome is but for illustrative purposes.

The sum of squares is 1 of the most important outputs in regression analysis. The general rule is that a smaller sum of squares indicates a better model, equally at that place is less variation in the data.

In finance, agreement the sum of squares is important because linear regression models Forecasting Methods Summit Forecasting Methods. In this article, we will explain four types of revenue forecasting methods that financial analysts use to predict future revenues. are widely used in both theoretical and applied finance.

Types of Sum of Squares

In regression analysis, the iii chief types of sum of squares are the total sum of squares, regression sum of squares, and residual sum of squares.

1. Full sum of squares

The total sum of squares is a variation of the values of a dependent variable Dependent Variable A dependent variable is a variable whose value will change depending on the value of some other variable, called the contained variable. from the sample mean of the dependent variable. Substantially, the total sum of squares quantifies the total variation in a sample. It tin can be determined using the following formula:

Total Sum of Squares

Where:

y_i– the value in a sample
ȳ– the mean value of a sample

2. Regression sum of squares (likewise known every bit the sum of squares due to regression or explained sum of squares)

The regression sum of squares describes how well a regression model represents the modeled data. A college regression sum of squares indicates that the model does not fit the data well.

The formula for calculating the regression sum of squares is:

Regression Sum of Squares

Where:

ŷ_i– the value estimated past the regression line
ȳ – the mean value of a sample

3. Remainder sum of squares (also known as the sum of squared errors of prediction)

The residue sum of squares essentially measures the variation of modeling errors. In other words, it depicts how the variation in the dependent variable in a regression model cannot be explained by the model. Generally, a lower residual sum of squares indicates that the regression model tin amend explicate the data, while a higher rest sum of squares indicates that the model poorly explains the data.

The residual sum of squares tin be institute using the formula below:

Residual Sum of Squares

Where:

y_i– the observed value
ŷ_i– the value estimated by the regression line

The human relationship between the three types of sum of squares can be summarized by the post-obit equation:

Additional Resources

Give thanks you for reading CFI's guide to Sum of Squares. To continue learning and advancing your career, the following CFI resources will exist helpful:

Guide to Financial Modeling Free Fiscal Modeling Guide This financial modeling guide covers Excel tips and best practices on assumptions, drivers, forecasting, linking the three statements, DCF analysis, more
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