Week_5_Assignment_ITCS_6500

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University of North Carolina, Charlotte *

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6500

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Statistics

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Feb 20, 2024

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docx

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How Do You Differentiate Between an Error and a Residual Error? In statistics and data analysis, the terms "error" and "residual error" are often used, but they have distinct meanings: Error:  Represents the unobserved true difference between a data point and its true value. This true value is often impossible to know perfectly, leading to the concept of error.  Can arise from various sources, including measurement errors, random noise, inherent variation in the population, and limitations of the model being used.  Usually denoted by the Greek letter ε (epsilon) . Residual Error:  Represents the difference between a predicted value and the actual observed value for a data point.  Obtained during the process of fitting a model to the data. It essentially tells you how much the model's prediction deviates from the actual observation.  Usually denoted by e (lowercase epsilon) . Key Differences:  Scope: Error refers to the unobserved difference from the true value, while residual error is specific to the predictions made by a particular model for the observed data.  Observability: Error is unobservable, while residual error can be calculated based on the model and the data.  Information: Error carries information about all potential sources of discrepancy, while residual error reflects the model's ability to fit the data. Example: Imagine measuring the heights of people. The true height of each person might differ slightly from the measured value due to rounding, measurement instrument limitations, or posture. This difference represents the error . If we then fit a regression model to predict heights based on other factors, the residual error for each person would be the difference between their actual measured height and the height predicted by the model. In simpler terms:  Error is the hidden truth you can't fully grasp.  Residual error is the model's attempt to capture that truth, leaving a gap between prediction and reality.

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