homoscedasticity
(noun)
A property of a set of random variables where each variable has the same finite variance.
Examples of homoscedasticity in the following topics:
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Homogeneity and Heterogeneity
- By drawing vertical strips on a scatter plot and analyzing the spread of the resulting new data sets, we are able to judge degree of homoscedasticity.
- When various vertical strips drawn on a scatter plot, and their corresponding data sets, show a similar pattern of spread, the plot can be said to be homoscedastic.
- In technical terms, a data set is homoscedastic if all random variables in the sequence have the same finite variance.
- A residual plot displaying homoscedasticity should appear to resemble a horizontal football.
- The assumption of homoscedasticity simplifies mathematical and computational treatment; however, serious violations in homoscedasticity may result in overestimating the goodness of fit.
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Checking the Model and Assumptions
- Constant variance (aka homoscedasticity).
- In order to determine for heterogeneous error variance, or when a pattern of residuals violates model assumptions of homoscedasticity (error is equally variable around the 'best-fitting line' for all points of x), it is prudent to look for a "fanning effect" between residual error and predicted values.
- Paraphrase the assumptions made by multiple regression models of linearity, homoscedasticity, normality, multicollinearity and sample size.
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Model Assumptions
- Constant variance (aka homoscedasticity).
- In order to determine for heterogeneous error variance, or when a pattern of residuals violates model assumptions of homoscedasticity (error is equally variable around the 'best-fitting line' for all points of $x$), it is prudent to look for a "fanning effect" between residual error and predicted values.
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Comparing Nested Models
- Homoscedasticity.
- The assumption of homoscedasticity, also known as homogeneity of variance, assumes equality of population variances.
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Least-Squares Regression
- It is considered optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated.
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ANOVA Assumptions
- Both these analyses require homoscedasticity, as an assumption for the normal model analysis and as a consequence of randomization and additivity for the randomization-based analysis.
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Two-Way ANOVA
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The F-Test
- However, when any of these tests are conducted to test the underlying assumption of homoscedasticity (i.e., homogeneity of variance), as a preliminary step to testing for mean effects, there is an increase in the experiment-wise type I error rate.
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Regression Analysis for Forecast Improvement
- The variance of the error is constant across observations (homoscedasticity).
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Further Discussion of ANOVA
- Residuals are examined or analyzed to confirm homoscedasticity and gross normality.