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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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R chart, or range chart, is a fundamental tool in statistical process control used to monitor the variability within a process. It complements the X-bar (x̄) chart by focusing on the range of the data, rather than individual values, providing a clear picture of the process dispersion over time.
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RR-plot: a descriptive tool for regression observations.

Xiaohui Liu1,2, Yang He1,2

  • 1School of Statistics, Jiangxi University of Finance and Economics, Nanchang Jiangxi, People's Republic of China.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary
This summary is machine-generated.

We introduce the regression depth versus regression depth plot (RR-plot) for analyzing regression data. This novel visualization tool aids in hypothesis testing and comparing regression models effectively.

Keywords:
RR-plotcharacterizationdescriptive statisticshalfspace regression depth

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Regression analysis is a fundamental statistical technique.
  • Assessing regression model performance and hypothesis testing are critical.
  • Existing methods for visualization and comparison can be limited.

Purpose of the Study:

  • To introduce a new visualization tool, the regression depth versus regression depth plot (RR-plot).
  • To demonstrate the utility of the RR-plot for hypothesis testing on regression coefficients.
  • To showcase its application in comparing regression observations across different models.

Main Methods:

  • The proposed method utilizes halfspace regression depth.
  • A novel plot, the RR-plot, is constructed using regression depth values.
  • Characterization theorems are developed to support the theoretical foundation.

Main Results:

  • The RR-plot provides a clear visualization for regression analysis.
  • It effectively visualizes hypothesis tests concerning regression coefficients.
  • It facilitates direct comparison of regression observations from diverse models.

Conclusions:

  • The RR-plot is a valuable and versatile tool for regression analysis.
  • It enhances the interpretability of regression models and tests.
  • Further applications in statistical modeling and data analysis are anticipated.