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42 Cards in this Set
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Multiple Correlation
definition 
Extends the bivariate Pearson correlation (r) to analytic circumstances involving 3+


Multiple Correlation is also known as...

Multiple R


Mutliple Correlation allows us to...

1) tell how much variation is ovserved w/in a selected criterion
2) And associated with the variation in socres noted within a given set of 2+ predictors 

Multiple correlation has the capacity to help select what?

Select the "best" set of predictors available


Coefficient of Mutliple Correlation R
definition 
A measure of correlation between 2+ predictor variables that have been optimally weighted to yield the highest possible correlation


The value of multiple R is interpreted as...

An indication of the strength/magnitude of the relationship


Multiple R values signify
1) Close to 0 2) +1 or 1 
1) Less consequential relationships
2) Strong, influential relationships 

Coefficient of Mulitple determination R₂
definition 
Provides a measuire of explained variance


Multiple R₂tells us...

The proportion of variance in the criterion variable, expressed as %, that can be predicted, accounted for, and explained


The R value can never exceed...

1.00


Examples of R and R₂
1) R = 0.80 2) R₂ = 0.64 
1) Strong correlation
2) Accounts for about 64% in variation 

R and R₂ considered biased estimators, but what can be done to offset it?

1) # of predictor variables should be kept small
2)R₂ should be adjusted downward 

Adjusted R₂
definition 
When R₂ is adjusted downward to refelct the actual number of cases and predictor variables included in the analysis


4 Basic assumptions to meet BEFORE Mutliple correlation analysis

1) Interval/Ratio are required
2)Relationships between the criterion variable and the predictors shoudl be reasonably linear 3) Data must be homoscedastic 4) Predictor variable should not correlate highly with another 

Homoscedasticity
definition 
Equal scatter or consistent variance across a predictor variable


Collinerity
definition 
Predictor variables should not correlate highly with one another


Multicollinearity
definiton 
When 2+ predictors take up a good deal of the same explanatory space making findings inaccurate


Mutliple Regression
definiton 
Multivariate counterpart of the regression procedure involving a single predictor


Multiple Regression allows us to predict the value of what?

Predict the value of a criterion/dependent variable when we know the values of two or more predictor variables


b Coefficient is also known as what?

Slope or Partial Slope


b Coefficient
definition 
Computed for each predictor in the regression equation tells us how much of the criterion variable variation is accounted for by that predictor alone


Beta weights is also known as...

Beta coefficients or Partial regression Coefficients


Beta coefficients
definition 
Allows for the decription of the amount of variation in the criterion variable that's associated with each predictor variable


Beta coefficients are determined by...

Converting scores to their respective zscore


2 Critical Decisions when conducting a multiple regression analysis:

1) Which predictor variables to include
2) Specifiying the order in which these items will be entered 

Hierarchial Inclusion Method
definition 
Draw on their knowledge of the problem


Stepwise Inclusion Method
definition 
Order in which th epredictor variables are entreed into the analysis is determined on statistical grounds.
Variable with highest correlate is entered 1st 

Dicotomous variable
definition 
Offers only 2 response options


Binary Variable
definition 
Dichotomous variable in which 0 is used to signfiy none of something and 1 the presence of something


Dummy Variable
definition 
New standin variable that is mutually exclusive, a stnadardized unit, and 0 is meaningful


Factor
defintion 
Independent or predictor variable


In describing ANOVAs you refer to...

The number of factors involved


The purpose of a 2way ANOVA is...

To test the signficance of differences occuring among group means


Main Effect
definition 
When you focus on the impact of only 1 factor


Interaction Effect
defintition 
Focuses on the combined effect of the 2 independent variables


Sum of Squares
definition 
Tells us how much variation was observed in the depression scores obtained overall, the main effects, interaction, and residual error effect


Grand Mean
definition 
Overall group mean


Error
definition 
Variance associated with individual differences occuring among subjects within the 4 groups defined by these independent variables


Degress of Freedom for Error
definition 
Number of cases incolced minus the number of groups associated with the independent variables of factors


E.G. of degrees of freedom for error

2 x 2 Design with 40 Cases
DofF for E = 36 (404 = 36) 

Mean Square
definition 
Dividing the sum of squares assoiated with each source by the degrees of freedom


Fstatistic
definition 
Dividing the mean square derived for each main and interaction effect, by the mean sqaure associated with the error term
