Multiple Regression Part 2

Partial correlation

b and β: partial regression coefficients, unique effect of the predictor on DV when other IVs are partialled out.

Imagine three circles slightly overlapping each other. We completely eliminate the influence of one variable from two other variables.

Semipartial or part correlation

correlation between the DV and a partialled predictor variable.

Imagine three circles slightly overlapping each other. We elimate one variable’s effect from the total of anouther, and then test a relationship with an unpartialled variable.

SPSS for partial correlation

Look for: Shown a correlation table, reflected as usual. Then, another correlations table with a control variable off to the side. This is for BOTH VARIABLES.

Interpretation: A partial correlation revealed that age and stress were unrelated/related when negative mood was completely removed (r (DF) = corrval, p = siglvl)

SPSS for semipartial correlation, a regression must be done

Look for: a coefficients table, the constant under unstandard B is the intercept. After sig, there is another section for correlations. These are what is reported.

Interpretation: A semipartial correlation revealed that age and stress were unrelated when negative mood was removed from age (r = -.01, p = .900)

Supressor variables

regression coefficients are different (ooposed direction and/or stronger) then what would be expected based on simple correlations.

When correlation with criterion is 0, it is positve or negaitve classical suppresion depending directly on beta weight

When correlation with criterion is positive, positive is positive cooperative suppression and negaitve is negative net suppression. Opposite for negative correlation with criterion. Be able to identify this in SPSS.

Multivariate outliers

unusual combinations of scores

Classes of diagnostics

distance (outliers in DV), leverage (outliers in IV), and influence (combines dist and leverage)

Cook’s D

a measure of influence, if the value is larger than 1 that is BAD

Residual

measure of distance, smaller value is GOOD

Studentized residual

t test on magnitude of the residuals, significant value is BAD but not ALWAYS a problem

Centered leverage values in SPSS

smaller is GOOD, 0 is perfect, and 1 is chaos

SPSS fo residuals stats

Look for: residual, stud residual, cook’s d, centered leverage value. Look at their means. This is where we determine good or bad.

Tolerance

degree ot which one IV can be predicted by the other IVs, want the value to be high, AT LEAST ABOVE 1, low or near 0 makes a singular covariance matrix, two of those circles on top of each other.

Variance Inflation Factor or VIF

reciprical od tolerance, want to be LOW, want toelrance to be larger than this

SPSS for tolerance and VIF

Look for: at the end of the coefficients table, tolerance and VIF are reported for each variable. Colineraity is the last sentence in this interpretation. Four stats for outliers, 2 for colinearity.

Selection methods

Enter, all subsets, backward elimination, stepwise regression

Enter method

all variables entered simultaneously, default

All subsets regression

examines all possibles subsets of IV, program choses best based on your specs, capitilizes on chance and can be a biased estimate.

Backward elimination

start by including all predictors then removing the ones that contribute the least, can stop when left with only significant predictors, capitilizes on chance.

Stepwise regression

reverse of backward, start with variabel that has hughest correlation with the DV then adds variables that have the highest semipartial, should not be used if you have a theory

SPSS for enter

Look for: a coefficients table, will see every variable

SPSS for backward (ingredient removal)

Look for: shown variables entered/removed table, shows the variables that are significant. Model summary table below shoes R square, model numbers labled. ANOVA shown below this, then shows the coefficients table the same as enter first, and then as many models as needed below. Last model is most updated. Also shows excluded variables.

SPSS for stepwise (empty pot)

Look for: shown variables entered/removed table, shows the variables that are significant. Model summary table below shoes R square, model numbers labled. Same table shows F change and Sig F change, which says if we explained more significant amount of variance by adding predictors. ANOVA shown below this, then shows the coefficients table the same as enter first, and then as many models as needed below. Last model is most updated. Also shows excluded variables.

Missing oberservations

Listwise and pairwise

Listwise deletion

whole case is deleted, is the most common, the drawback is that this can result in a low N

Pariwise deletion

all availible data are used, but can result in an unrepresentative correlation matrix, the data from certain participants specific answers are msising but we keep the whole participant and whatever they did give.