Residual Plots SPSS

8/10/2019 Residual Plots SPSS

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Producing and Interpreting Residuals Plots in SPSS

In a linear regression analysis it is assumed that the distribution of residuals,)( YY , is, in the population, normal at every level of predicted Y and constant in

variance across levels of predicted Y. I shall illustrate how to check that assumption.Although I shall use a bivariate regression, the same techniue would work for amultiple regression.

!tart by downloading Residual-Skew.datand Residual-Hetero.datfrom my!tat"ata pageand A#$%A&.sav from my !'!! data page. ach line of data has fourscores *, Y, *+, and Y+. he delimiter is a blank space.

-reate new variable !/0Y+ this way ransform, -ompute,

$1.

2irst some descriptive statistics on the variables

Descriptive Statistics

+33 &4 56 67.89 9.978 :.38; .&5+ .&4& .;6+

+33 ++ 55 69.44 9.765 :.349 .&5+ :.+66 .;6+

+33 & &66 68.47 +5.&+; &.364 .&5+ &.3;7 .;6+

+33 ; &4; 67.6; +5.676 .967 .&5+ &.+83 .;6+

+33 &.5; &+.55 4.458& &.95+99 .&5& .&5+ :.&94 .;6+

+33

*

Y

*+Y+

Y+0!/

%alid # (listwise)

!tatistic !tatistic !tatistic !tatistic !tatistic !tatistic !td. rror !tatistic !td. rror

#


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+


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Model Summaryb

.683a .+3; .&99 7.7&8


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!'!! has saved the residuals, unstandardiCed (/!0&) and standardiCed(E/0&) to the data file

AnalyCe, =plore E/0& to get a better picture of the standardiCed residuals.

he plots look fine. As you can see, the skewness and kurtosis of the residuals is aboutwhat you would e=pect if they came from a normal distribution

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Descriptives

.3333333

:+.8867&

+.488&7

8.+3999

:.356

:.+46


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#otice that the residuals plots shows the residuals not to be normally distributed > theyare pulled out (skewed) towards the top of the plot. =plore also shows trouble

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Descriptives

.3333333

:&.75656

;.4&;99

8.6775;

&.;63;9

.73;

.948


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Model Summaryb

.689a .+&& .+35 &.585;7


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e are done with the /esidual:!kew data set now. /ead into !'!! theA#$%A&.sav data file. -onduct a linear regression analysis to predict illness from doseof drug. !ave the standardiCed residuals and obtain the same plots that we producedabove.

Model Summaryb

.&&3a .3&+ .33+ &+.&&;


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#ow predict Illness from a combination of "ose and "ose0!. Ask for the usualplots and save residuals and predicted scores.

Model Summary(b


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@et us have a look at the regression line. e saved the predicted scores('/0&), so we can plot their means against dose of the drug

-lick Fraphs, @ine, !imple, "efine.

!elect @ine /epresents $ther statistic and scoot '/0& into the variable bo=.!coot "ose into the -ategory A=is bo=. $1.

&&


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ow, that is certainly no straight line. hat we have done here is a polynomialregression, fitting the data with a uadratic line. A uadratic line can have one bend init.

@et us get a scatter plot with the data and the uadratic regression line. -lickFraph, !catter, !imple !catter, "efine. !coot Illness into the Y:a=is bo= and "ose intothe *:a=is bo=. $1. "ouble:click the graph to open the graph editor and selectlements, 2it line at total. !'!! will draw a nearly flat, straight line. In the 'ropertiesbo= change 2it


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e are done with the A#$%A.sav data for now. Gring into !'!! the /esidual:?/$.dat data. ach case has two scores, * and Y. he delimiter is a blank space.-onduct a regression analysis predicting Y from *. -reate residuals plots and save thestandardiCed residuals as we have been doing with each analysis.

&;


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As you can see, the residuals plot shows clear evidence of heteroscedasticity. Inthis case, the error in predicted Y increases as the value of predicted Y increases. Ihave been told that transforming one the variables sometimes reducesheteroscedasticity, but in my e=perience it often does not help.

/eturn to uenschHs !'!! @essons 'age

-opyright +335, 1arl @. uensch : All rights reserved.

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Residual Plots SPSS

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