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When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?

When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 4SGR
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**Understanding Extrapolation and Interpolation in Least-Squares Regression** When we use a least-squares line to predict \( y \) values for \( x \) values beyond the range of \( x \) values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions? *Explanation:* - **Extrapolation:** This occurs when we use a model to predict \( y \) values for \( x \) values that are outside the range of the data we originally used to create the model. - **Interpolation:** This refers to using the model to predict \( y \) values for \( x \) values that fall within the range of the original data. **Concerns about Extrapolation:** - Extrapolation can be problematic as it assumes that the pattern observed in the data continues beyond the observed range, which might not always be the case. - Predicting outside the data range can lead to large errors if the true relationship deviates from the pattern detected within the original data range. **Concerns about Interpolation:** - Interpolation is generally more reliable as it operates within the range of the data used to fit the model, hence it is less prone to large prediction errors.
Transcribed Image Text:**Understanding Extrapolation and Interpolation in Least-Squares Regression** When we use a least-squares line to predict \( y \) values for \( x \) values beyond the range of \( x \) values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions? *Explanation:* - **Extrapolation:** This occurs when we use a model to predict \( y \) values for \( x \) values that are outside the range of the data we originally used to create the model. - **Interpolation:** This refers to using the model to predict \( y \) values for \( x \) values that fall within the range of the original data. **Concerns about Extrapolation:** - Extrapolation can be problematic as it assumes that the pattern observed in the data continues beyond the observed range, which might not always be the case. - Predicting outside the data range can lead to large errors if the true relationship deviates from the pattern detected within the original data range. **Concerns about Interpolation:** - Interpolation is generally more reliable as it operates within the range of the data used to fit the model, hence it is less prone to large prediction errors.
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