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Definition
one predictor one criterion. Only two variables
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Term
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Definition
many predictors (IV), one criterion (DV).
Goal of MR: produce a model in the form of a linear equation that identifies the best weighted combination of IVs to optimally predict the DV.
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A weighted combination of predictors (IVs)
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partial regression coefficients
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MR provides
relationships or causality?
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Including variables that are not linked to theory or previous research
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MR is best when each IV is ...
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| strongly correlated with the DV but not with other IVs |
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What problems can be solved using MR?
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Definition
1.Predict one variable from a combined knowledge of several others.
2.Determine which variables are better predictors of the criterion than others
3.How much better we can predict a variable if we add more predictor variables?
4.Determine the relationship of one variable to other variables.
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Formula for Ratio of cases to IVs
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Definition
N ≥ 50 + 8m (where m is the number of Ivs; If 4 IVs, then have at least 82 cases).
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Definition
variables are highly correlated (.90 and above). Collinearity refers to 2 vars; multicollinearity >3 variables.
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Definition
variables are redundant; they are a combination of 2 or more variables
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SMCs (Squared multiple correlations)
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Definition
the variable is the DV and the other variables are IVs
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Definition
If the SMC is 1.0 (tolerance = 0.0) then the variable is perfectly related to others in the set this is undesirable. Tolerance levels of below .10 become problematic.
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Variance Inflation Factor (VIF)
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Definition
refers to the effect other predictor variables have on the variance of a regression coefficient. Large values (above 10.0) indicate a high degree of collinearity or multicollinearity
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Term
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Definition
the difference between the obtained and predicted DV score and is a measure of error
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the variability for one var is the same for all values of another variable. In a plot the bulge of scores is the same width throughout
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Definition
opposite of homoscedasticity
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Definition
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| Residual Plots are used for... |
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Definition
Check for outliers, examine means and standard deviations, check for skewness and kurtosis
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| Significance of Skewness Formula is... |
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Definition
signifance of skewness is conducted by dividing the Skewness score by Std. error of skewness which gives one a z score.
score should preferably be less than 3.29 for normality
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Term
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Definition
signifance of kurtosis is conducted by dividing the kurtosis score by Std. error of kurtosis which gives one a z score.
score should preferably be less than 3.29 for normality
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Term
Casewise Diagnostics in the Regression analyses gives...
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Definition
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Term
In the formula
Ŷ = bo + b1X1 + b2X2 + b3X3…….
Ŷ is?
bo is?
b1 is?
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Definition
Ŷ = predicted value
bo = intercept or value of Ŷ when all Xs are 0
b1 etc = partial regression coefficients
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Beta is standardized or unstandardized?
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Definition
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| B weights are standardized or unstandardized? |
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Definition
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| B weights or Beta tell the relative importance of variables? |
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Definition
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Based on the SPSS output for the standardized coefficients, one would suggest or conclusively state that some variables are more important than other variables in the model?
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Definition
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Definition
variability of the statistic of many samples
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Standard error of the estimate (SEE)
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Definition
the standard error of prediction errors. It tells us the accuracy to expect from our predictions. It gives us an idea of the scatter of the points around the line of regression.
1.96 * SEE = confidence interval using a given predicted score
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Definition
raw correlation from the correlation matrix
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Definition
correlation between 2 vars with one or more other vars partialled out from both IV and DV
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Semi-partial correlation (sr, Part in SPSS)
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Definition
The contribution of the other IVs are taken out only from the IV
They are a gauge of the relative strength of the predictors (IVs). Generally one focuses on the semi-partial correlations, than the partial.
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Term
R = Multiple correlation coefficient
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Definition
It is the correlation between Y and the best linear combination of the predictors (IVs).
We are more interested in R2 because we then know the percentage of accountable variation.
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Term
R2 = multiple correlation or the coefficient of multiple determination.
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Definition
It can be interpreted as the percentage of accountable variation or
the proportion of total variance on the DV that is accounted for by the set of predictors
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Term
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Definition
a less biased estimate of the squared population coefficient than R2
R*2 = 1 - [(1 – R2 ) (N – 1) / N – p – 1)]
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Term
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Definition
conducted to determine the generalizability of the regression model and that the model is not specific to the sample used.
we examined one way to do this- randomly split the sample in half
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Term
Standard Multiple Regression
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Definition
All the IVs are entered into the equation in one single step. Each one is assessed as if it had entered the regression after all the other IVs had entered. Each IV is evaluated in terms of what it adds to prediction of the DV that is different from the predictability given by all the other IVs.
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Term
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Definition
In a MR all vars are entered and then are deleted one at a time if they do not contribute significantly to regression
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Term
Hierarchical (Sequential) Multiple Regression
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Definition
similar to stepwise regression, but the researcher determines the order of entry of the variables. This decision of entry order is be based on theory and or the literature.
This hierarchical procedure is an alternative to comparing betas for purposes of assessing the importance of the IVs.
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Term
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Definition
Standard MR - b
Hierarchical MR - c |
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Term
What is the purpose of the Regression Coefficient?
ie b1, b2, ...
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Definition
| Indicates the change in the estimated value of the DV for a unit of change in one of the IV's, when the other IV's are held constant |
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