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Topic: Homoscedasticity

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	Regression Review:
		Homoscedasticity is an assumption that we make when using a regression line to make predictions.
		Homoscedasticity simply says that errors of prediction are random around each x value (the variability in y is constant around each x value).
		To make an evaluation of the assumption of homoscedasticity, you must have several x,y pairs in your data set where the x’s are the same and y’s are different.
	www.unm.edu /~marni1/regressionreview.htm (587 words)

	The Homogeniety of Error Variance Assumption (Site not responding. Last check: 2007-10-20)
		This assumption is different from, but often confused with, the assumption of homoscedasticity (that residual scores are similarly distributed across various points of the X scale).
		Aguinis and Pierce (1998a) deftly clarified that the homoscedasticity assumption applies to all regression models, whereas the heterogeneity of error variance assumption applies only to MMR models where one variable in the interaction term (e.g., group membership) is polychotomous.
		The better known homoscedasticity assumption is assessed (usually via an inspection of a scatterplot of residuals on the predicted values as above) while the heterogeneity of error variance assumption is ignored (Aguinis and Pierce, 1998a).
	members.aol.com /imsap/homogeneity.html (475 words)

	S501 HW8 SOLUTIONS
		c Homoscedasticity means equal variances in the three labs, or, in more practical terms, equal variability or scatter in the measurements from the labs.
		Plots of Residuals vs. Fitted Values: both plots are consistent with homoscedasticity: in the one-way plot there is only a slight difference in vertical spreads and one point that looks like an outlier (but a boxplot shows that it is not an outlier).
		The plots of residuals vs. fitted values are consistent with homoscedasticity; likewise the normal probability plots are consistent with normality.
	www.math.umass.edu /~joeh/s501/hw8solns.htm (807 words)

	DSS - Introduction to Regression
		The assumption of homoscedasticity is that the residuals are approximately equal for all predicted DV scores.
		Data are homoscedastic if the residuals plot is the same width for all values of the predicted DV.
		In fact, this residuals plot shows data that meet the assumptions of homoscedasticity, linearity, and normality (because the residual plot is rectangular, with a concentration of points along the center):
	dss.princeton.edu /online_help/analysis/regression_intro.htm (3860 words)

	Quiz #9 STAT 535 (Site not responding. Last check: 2007-10-20)
		[ B ] Homoscedasticity is used to indicate unequal sample sizes.
		[ E ] Homoscedasticity is used to indicate identical distributions.
		[ F ] Homoscedasticity is used to indicate nonidentical distributions.
	mason.gmu.edu /~csutton/quiz9f03535.html (157 words)

	Multiple Regression and Correlation Summary
		Homoscedasticity, homogeneity of variance of residuals around predicted values - scatterplots
		If samples are not random, validity of inferences about populations sampled is brought into question.
		Homoscedasticity (Problem exists if ratio of largest to smallest SD > 3:1 - reduces statistical power - transform troublesome variables)
	www.uth.tmc.edu /uth_orgs/educ_dev/HI5353/MULTRG.htm (393 words)

	[No title]
		Use the F-table to establish the critical values for F and test for homoscedasticity.
		White argues that the (2 test assumes that: -the errors are homoscedastic -the errors are independent of the regressors -the linear specification model is correct.
		VAR(ei) = k = s2 homoscedasticity The errors are distributed independently from (not correlated with) the explanatory variables.
	www.faculty.fairfield.edu /rakelly/Ec380/CH08-Heteroscedasticity.doc (2757 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		The normality of error assumption can be evaluated by obtaining a histogram, box-and-whisker plot, and/or normal probability plot of the residuals.
		The homoscedasticity assumption can be evaluated by plotting the residuals on the vertical axis and the X variable on the horizontal axis.
		The independence of errors assumption can be evaluated by plotting the residuals on the vertical axis and the time order variable on the horizontal axis.
	www.econ.uiuc.edu /ECON173/lecture12_ans.doc (167 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		%.%.%.ÓR ¦¦@ Ð;ÐººÓ =%.X%.}2ÞP:X ¦Ð;@ êDÐïÞIÂºº%'¨;(Chapter 8 Heteroscedasticity Overview This chapter begins with a general discussion of homoscedasticity and heteroscedasticity: the meanings of the terms, the reasons why the distribution of a disturbance term may be subject to heteroscedasticity, and the consequences of the problem for OLS estimators.
		However the observations for the regular schools appear to be homoscedastic and this accounts for the fact that we did not (quite) reject the null hypothesis of homoscedasticity for the combined sample.
		Thus in both cases the null hypothesis of homoscedasticity is rejected, but the problem appears to much less severe for the logarithmic specification.
	www.oup.co.uk /doc/college/dougherty2/guide/ch08.doc (3054 words)

	Correcting the standard errors of regression slopes for heteroscedasticity
		When one tests for the significance of regression slopes in simple or multiple regression, the accuracy of the test depends heavily on that assumption.
		Therefore SE(b) will be affected primarily by the majority of cases near the mean of X, while the actual random fluctuations in b will be determined by the minority of cases at the far left and right.
		That is why the assumption of homoscedasticity is so crucial: the data points affecting SE(b) and the data points affecting b must be assumed to have the same degree of random variability.
	comp9.psych.cornell.edu /Darlington/heterosc.htm (1664 words)

	Speed of Light Analysis
		This may satisfy condition 2 (homoscedasticity) but for the c data a poor fit.
		If the variance of e, is proportional to T (exp 2), where T is measured in years prior, the variance of e/T is constant and a regression line will be homoscedastic.
		The regression model in this paper ought to be given priority over previously published regression lines since it is the only one which is weighted, homoscedastic and non-autocorrelated.
	www.ldolphin.org /cdkalan.html (6200 words)

	[No title]
		Under EMBED Equation.3 (homoscedasticity) EMBED Equation.3 in large sample : asymptotic test Reject null of homoscedasticity if it is significant.
		Since the data are cross-sectional involving a heterogeneity of countries, a priori one would expect heteroscedasticity in the error variance.
		Under EMBED Equation.3 of homoscedasticity EMBED Equation.3 Solutions to heteroscedasticity problem Heteroscedasticity does not destroy the unbiasedness and consistency properties of OLS estimators, but they are no longer efficient.
	www.personal.kent.edu /~mqi/econ1/EconI8.doc (1341 words)

	Reciprocal Transformation Example
		Preceding task required.05 seconds CPU time;.30 seconds elapsed.
		TRDEP Residuals Statistics: Min Max Mean Std Dev N PRED.1233.1364.1275.0037 27 RESID -.0415.0354.0000.0222 27 ZPRED -1.1477 2.3915.0000 1.0000 27 ZRESID -1.8300 1.5631.0000.9806 27 Total Cases = 27 11 Jan 98 CHATTERJI & PRICE PAGE 49 - VIOLATION OF HOMOSCEDASTICITY Page 10 19:44:15 sigma.oac.ucla.edu IBM RS/6000 IBM AIX 3.2.
		Preceding task required.01 seconds CPU time;.06 seconds elapsed.
	www.gseis.ucla.edu /courses/ed230bc1/examples/reciptrans.html (684 words)

	Cjatterji & Price Page 49 - Violation of Homoscedasticity
		Cjatterji and Price Page 49 - Violation of Homoscedasticity
		Click here to download as SPSS syntax file)
		Data List will read 1 records from the command file
	www.gseis.ucla.edu /courses/ed230b/examples/spss7.htm (48 words)

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