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Related Concept Videos

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...
Modified Boxplots00:57

Modified Boxplots

A standard box and whisker plot informs us about the spread of the data in a given sample. One can identify the minimum value, maximum value, first quartile value, second quartile or median value, and third quartile.
However, the box plot does not tell the reader about outliers - values that lie far from the center of the data. We can modify the standard box and whisker plot to identify the outliers and visualize the actual spread of the data in a sample.
Initially, we calculate the adjusted...
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:
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...
Boxplot01:12

Boxplot

Box plots (also called box-and-whisker plots or box-whisker plots) give an excellent graphical image of the concentration of the data. They also show how far the extreme values are from most data. A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value. We use these values to compare how close other data values are to them. To construct a box plot, use a horizontal or vertical number line and a rectangular box. The...
Quantifying and Rejecting Outliers: The Grubbs Test01:02

Quantifying and Rejecting Outliers: The Grubbs Test

Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This number is...

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Related Experiment Video

Updated: May 8, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Quantifying heteroscedasticity in linear models using quantile locally weighted scatterplot smoothing intervals.

Martina Sladekova1, Andy P Field1

  • 1School of Psychology, University of Sussex.

Psychological Methods
|May 7, 2026
PubMed
Summary
This summary is machine-generated.

A new Quantile Locally Weighted Scatterplot Smoothing Interval (QLI) measure quantifies heteroscedasticity in ordinary least squares (OLS) models. This method provides reliable estimates for models with 60+ cases, aiding OLS analysis performance evaluation.

Related Experiment Videos

Last Updated: May 8, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • Psychometrics
  • Statistical modeling
  • Data analysis

Background:

  • Ordinary least squares (OLS) estimation assumes homoscedasticity (constant error variance).
  • Heteroscedasticity (non-constant error variance) violates this assumption, impacting OLS model reliability.
  • Existing methods for continuous predictors lack interpretable quantification of heteroscedasticity.

Purpose of the Study:

  • To develop and evaluate a novel measure for quantifying heteroscedasticity in OLS models.
  • To provide benchmark values for the new measure under various heteroscedasticity patterns.
  • To assess the measure's utility in understanding OLS performance issues.

Main Methods:

  • Development of the Quantile Locally Weighted Scatterplot Smoothing Interval (QLI) measure.
  • Estimation of changes in QLI width as a function of predictors or fitted values.
  • Simulation study evaluating OLS models with varying heteroscedasticity and sample sizes.

Main Results:

  • The QLI method consistently estimated trends across different variance patterns for models with 60 or more cases.
  • Benchmark values were established for QLI estimates related to false-positive rates, power, and confidence interval coverage.
  • QLI-generated estimates demonstrated relevance to OLS linear model performance.

Conclusions:

  • The QLI measure offers a reliable and interpretable way to quantify heteroscedasticity for continuous predictors.
  • This method aids in diagnosing and understanding the impact of heteroscedasticity on OLS analyses.
  • The study provides practical guidance for applying and interpreting QLI estimates in psychological research.