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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 z-score
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 stand-in 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
(40-4 = 36)
Mean Square
-definition-
Dividing the sum of squares assoiated with each source by the degrees of freedom
F-statistic
-definition-
Dividing the mean square derived for each main and interaction effect, by the mean sqaure associated with the error term