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Instructional Materials. http://. core.ecu.edu/psyc/wuenschk/PP/PP-MultReg.htm. aka. , . http://tinyurl.com/multreg4u. Introducing the General. Linear Models. As noted by the General, the GLM can be used to relate one set of things (. ID: 384681

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## Presentations text content in General Linear Model

General Linear Model

Slide2Instructional Materials

http://

core.ecu.edu/psyc/wuenschk/PP/PP-MultReg.htm

aka

,

http://tinyurl.com/multreg4u

Slide3Introducing the General

Slide4Linear Models

As noted by the General, the GLM can be used to relate one set of things (

Ys

) to another set of things (X).

It can also be used with only one set of things.

Slide5Bivariate Linear Function

Y = a +

bX

+ error

This is probably what you have in mind when thinking of a linear model.

Spatially, it is represented in two-dimensional (Cartesian) space.

Slide6Least Squares Criterion

Linear models produce parameter estimates (intercepts and slopes) such that the sum of squared deviations between Y and predicted Y is minimized.

Slide7Univariate Regression

The mean is a univariate least squares predictor.The prediction model isThe sum of the squared deviations between Y and mean Y is smaller than that for any reference value of Y.

Slide8Fixed and Random Variables

A FIXED variable is one for which you have every possible value of interest in your sample.

Example: Subject sex, female or male.

A RANDOM variable is one where the sample values are randomly obtained from the population of values.

Example: Height of subject.

Slide9Correlation & Regression

If Y is random and X is fixed, the model is a regression model.

If both Y and X are random, the model is a correlation model.

Researchers

generally

think that

Correlation

= compute the

corr

coeff

,

r

Regression = find an equation to predict Y from X

Slide10Assumptions, Bivariate Correlation

Homoscedasticity across Y|X

Normality of Y|X

Normality of Y ignoring X

Homoscedasticity across X|Y

Normality of X|Y

Normality of X ignoring Y

The first three should look familiar,

you make

them with the pooled variances

t

.

Slide11Bivariate Normal

Slide12When Do Assumptions Apply?

Only when employing

t

or

F

.

That is, obtaining a

p

value

or constructing a confidence interval

.

With regression analysis, only the first three assumptions (regarding Y) are made.

Slide13Sources of Error

Y = a +

bX

+ error

Error

in the measurement of X and or Y or in the manipulation of X.

The influence upon Y of variables other than X (extraneous variables), including variables that interact with X.

Any nonlinear influence of X upon Y.

Slide14The Regression Line

r2 < 1 Predicted Y regresses towards mean YIn univariate regression, it regresses all the way to the mean for every case.

Slide15Uses of Correlation/Regression Analysis

Measure the degree of linear association

Correlation

does

imply causation

Necessary but not sufficient

Third variable problems

Reliability

Validity

Independent Samples

t

– point

biserial

r

Y = a + b

Group (Group is 0 or 1)

Slide16Uses of Correlation/Regression Analysis

Contingency tables -- Rows = a + bColumnsMultiple correlation/regression

Slide17Uses of Correlation/Regression Analysis

Analysis of variance (ANOVA)PolitConserv = a + b1 Republican? + b2 Democrat?k = 3, the third group is all others

Slide18Uses of Correlation/Regression Analysis

Canonical correlation/regression(homophobia, homo-aggression) = (psychopathic deviance, masculinity, hypomania, clinical defensiveness)High homonegativity = hypomanic, unusually frank, stereotypically masculine, psychopathically deviant (antisocial)