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Related Concept Videos

Scatter Plot01:15

Scatter Plot

The most common and easiest way to display the relationship between two variables, x and y, is a scatter plot. A scatter plot shows the direction of a relationship between the variables. A clear direction happens when there is either:
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

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
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Survival Tree01:19

Survival Tree

Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
 Building a Survival Tree
Constructing a survival tree begins...
Correlation and Regression00:53

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...
Outliers and Influential Points01:08

Outliers and Influential Points

An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the vertical...
Survival Curves01:18

Survival Curves

Survival curves are graphical representations that depict the survival experience of a population over time, offering an intuitive way to track the proportion of individuals who remain event-free at each time point. These curves are widely used in fields such as medicine, public health, and reliability engineering to visualize and compare survival probabilities across different groups or conditions.
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...

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Related Experiment Video

Updated: Jun 26, 2026

Cutoff Value of Phase Angle by Bioelectrical Impedance Analysis at Admission as a Prognostic Factor in Patients with Acute Heart Failure
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Cutoff Value of Phase Angle by Bioelectrical Impedance Analysis at Admission as a Prognostic Factor in Patients with Acute Heart Failure

Published on: June 10, 2025

Quantile regression and restricted cubic splines are useful for exploring relationships between continuous variables.

Ruth Ann Marrie1, Neal V Dawson, Allan Garland

  • 1Faculty of Medicine, University of Manitoba, Manitoba, Canada.

Journal of Clinical Epidemiology
|January 13, 2009
PubMed
Summary

Quantile regression and restricted cubic splines (RCS) reveal complex relationships between continuous variables, going beyond linear assumptions. This powerful combination uncovers heterogeneity and nonlinearity often missed by ordinary least squares regression.

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Establishing a Competing Risk Regression Nomogram Model for Survival Data

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04:57

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Area of Science:

  • Statistics
  • Biostatistics
  • Data Analysis

Background:

  • Ordinary least squares (OLS) regression assumes linear relationships between continuous variables.
  • Analyzing only the mean may miss complex or nonlinear associations.
  • The true nature of variable relationships can be obscured by standard regression methods.

Purpose of the Study:

  • To demonstrate the utility of quantile regression combined with restricted cubic splines (RCS).
  • To reveal the complex and potentially nonlinear relationships between continuous variables.
  • To illustrate how these methods capture nuances missed by traditional linear regression.

Main Methods:

  • Review of methodologic concepts for quantile regression and RCS.
  • Application of the combined methods to two real-world data sets.
  • Analysis of relationships between cognition and disease duration (multiple sclerosis).
  • Analysis of length of stay (LOS) and severity of illness in the intensive care unit (ICU).

Main Results:

  • Quantile regression indicated heterogeneous relationships in both analyzed data sets.
  • Restricted cubic splines (RCS) identified nonlinearity in the relationship between illness severity and LOS.
  • The combined approach highlighted complex associations not evident with OLS regression.

Conclusions:

  • Quantile regression and RCS offer a powerful analytical strategy.
  • These methods effectively explore intricate relationships between continuous variables.
  • The combination enhances understanding beyond standard linear modeling.