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Chapter 13: Problem 9

Explain the meaning and concept of SSE. You may use a graph for illustration purposes.

Short Answer

Expert verified
Sum of Squared Errors (SSE) is a measurement used to quantify the discrepancy between observed data and predicted values by a model. The SSE is calculated as the sum of the squares of the differences (errors) between each observed value and its predicted counterpart. Graphically, SSE can be understood as the total area of the squares that illustrate the deviation (error) of each actual data point from the predictive line/model.

Step by step solution

01

Define SSE

SSE stands for Sum of Squared Errors. This is a common statistical tool used to measure the overall discrepancy between a set of observed data and the values predicted by an estimation model.
02

Formula of SSE

The SSE is calculated using the formula \( SSE = \Sigma_{}(Y - Y')^2 \) where \( Y \) represents an observed value, \( Y' \) represents the forecasted value, and \( \Sigma \) implies the summation of all the observations. The outcome of each observed and predicted value difference is squared and all these squared values are added together to get the SSE.
03

Explain graphically

On a graph, SSE is represented by the area that is between the actual data points and the estimation model or line. Each point of the observed data has a corresponding point on the estimation line. The vertical distance between these points is an error. This error being squared is represented graphically as a square (hence, 'squared error') and the SSE constitutes the total area of these squares, illustrating the total error.

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