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What does the homoscedasticity of errors mean?
Homoskedastic (also spelled “homoscedastic”) refers to a condition in which the variance of the residual, or error term, in a regression model is constant. That is, the error term does not vary much as the value of the predictor variable changes.
What is independence of error?
Checking the Independence of Errors Assumption. The “I” in the LINE mnemonic stands for Independence of Errors. This means that the distribution of errors is random and not influenced by or correlated to the errors in prior observations. The opposite is independence is called autocorrelation.
What is the homoscedasticity assumption?
The assumption of equal variances (i.e. assumption of homoscedasticity) assumes that different samples have the same variance, even if they came from different populations. Running a test without checking for equal variances can have a significant impact on your results and may even invalidate them completely.
How does Heteroskedasticity affect standard errors?
Heteroscedasticity does not cause ordinary least squares coefficient estimates to be biased, although it can cause ordinary least squares estimates of the variance (and, thus, standard errors) of the coefficients to be biased, possibly above or below the true of population variance.
What is independence of errors in regression?
Independence of Errors If your points are following a clear pattern, it might indicate that the errors are influencing each other. The errors are the deviations of an observed value from the true function value. The following image shows two linear regression lines; on the left, the points are scattered randomly.
How do you find the error of Independence?
Check this assumption by examining a scatterplot of x and y. Independence of errors: There is not a relationship between the residuals and the variable; in other words, is independent of errors. Check this assumption by examining a scatterplot of “residuals versus fits”; the correlation should be approximately 0.
Why do we need to assume homoscedasticity of errors?
Homoscedasticity of errors (or, equal variance around the line). Because we are fitting a linear model, we assume that the relationship really is linear, and that the errors, or residuals, are simply random fluctuations around the true line.
How does homoscedasticity affect the amount of spread?
Under the assumption of homoscedasticity, the amount of spread is unaffected by the passage of time (i.e., it remains constant over time). However, under the assumption of heteroscedasticity, the amount of spread is affected by the passage of time – for example, the amount of spread can increase over time.
Can the errors be independent in linear regression?
In linear regression I often see homoscedasticity and independence of errors listed as assumptions (for example on wikipedia ). But I would think that independence of errors would imply homoscedasticity. Look at this error plot example: Could the errors be independent?
Which is a violation of independence in a regression model?
Violations of independence are potentially very serious in time series regression models: serial correlation in the errors (i.e., correlation between consecutive errors or errors separated by some other number of periods) means that there is room for improvement in the model,…