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42 Cards in this Set
- Front
- Back
Multiple Correlation
-definition- |
Extends the bivariate Pearson correlation (r) to analytic circumstances involving 3+
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Multiple Correlation is also known as...
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Multiple R
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Mutliple Correlation allows us to...
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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 |
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Multiple correlation has the capacity to help select what?
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Select the "best" set of predictors available
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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
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The value of multiple R is interpreted as...
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An indication of the strength/magnitude of the relationship
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Multiple R values signify
1) Close to 0 2) +1 or -1 |
1) Less consequential relationships
2) Strong, influential relationships |
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Coefficient of Mulitple determination R₂
-definition- |
Provides a measuire of explained variance
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Multiple R₂tells us...
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The proportion of variance in the criterion variable, expressed as %, that can be predicted, accounted for, and explained
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The R value can never exceed...
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1.00
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Examples of R and R₂
1) R = 0.80 2) R₂ = 0.64 |
1) Strong correlation
2) Accounts for about 64% in variation |
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R and R₂ considered biased estimators, but what can be done to offset it?
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1) # of predictor variables should be kept small
2)R₂ should be adjusted downward |
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Adjusted R₂
-definition- |
When R₂ is adjusted downward to refelct the actual number of cases and predictor variables included in the analysis
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4 Basic assumptions to meet BEFORE Mutliple correlation analysis
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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 |
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Homoscedasticity
-definition- |
Equal scatter or consistent variance across a predictor variable
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Collinerity
-definition- |
Predictor variables should not correlate highly with one another
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Multicollinearity
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When 2+ predictors take up a good deal of the same explanatory space making findings inaccurate
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Mutliple Regression
-definiton- |
Multivariate counterpart of the regression procedure involving a single predictor
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Multiple Regression allows us to predict the value of what?
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Predict the value of a criterion/dependent variable when we know the values of two or more predictor variables
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b Coefficient is also known as what?
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Slope or Partial Slope
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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
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Beta weights is also known as...
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Beta coefficients or Partial regression Coefficients
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Beta coefficients
-definition- |
Allows for the decription of the amount of variation in the criterion variable that's associated with each predictor variable
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Beta coefficients are determined by...
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Converting scores to their respective z-score
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2 Critical Decisions when conducting a multiple regression analysis:
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1) Which predictor variables to include
2) Specifiying the order in which these items will be entered |
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Hierarchial Inclusion Method
-definition- |
Draw on their knowledge of the problem
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Stepwise Inclusion Method
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Order in which th epredictor variables are entreed into the analysis is determined on statistical grounds.
Variable with highest correlate is entered 1st |
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Dicotomous variable
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Offers only 2 response options
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Binary Variable
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Dichotomous variable in which 0 is used to signfiy none of something and 1 the presence of something
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Dummy Variable
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New stand-in variable that is mutually exclusive, a stnadardized unit, and 0 is meaningful
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Factor
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Independent or predictor variable
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In describing ANOVAs you refer to...
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The number of factors involved
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The purpose of a 2way ANOVA is...
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To test the signficance of differences occuring among group means
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Main Effect
-definition- |
When you focus on the impact of only 1 factor
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Interaction Effect
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Focuses on the combined effect of the 2 independent variables
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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
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Grand Mean
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Overall group mean
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Error
-definition- |
Variance associated with individual differences occuring among subjects within the 4 groups defined by these independent variables
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Degress of Freedom for Error
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Number of cases incolced minus the number of groups associated with the independent variables of factors
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E.G. of degrees of freedom for error
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2 x 2 Design with 40 Cases
DofF for E = 36 (40-4 = 36) |
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Mean Square
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Dividing the sum of squares assoiated with each source by the degrees of freedom
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F-statistic
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Dividing the mean square derived for each main and interaction effect, by the mean sqaure associated with the error term
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