PSY 555 Homework 17

Chapter 15: #6,8,16,21

15.6.

15.8.     The regression coefficient of a variable indicates the slope of the best fit line for the data.  If a variable is collinear with other predictors, then the slope will be changed dramatically based on the other predictors that are used in the model (because their values will change from sample to sample and the one variable’s observation points will covary with the other predictor’s observations and the best fit line describing the one variable’s data will change and so will the slope).  If a variable is largely unrelated with the other predictors, we would expect that the regression coefficient (slope) of that variable would be relatively stable because only the random error from its observations will influence its slope (rather than also having the other variables’ random error influence its points and thus the model (and thus its slope as well).  In this case, the inclusion of other variables in the model and thus their error would not significantly alter the one variable and its parameter estimates.  Thus, the stability of any regression coefficient of a variable across different samples of data is partly a function of how that variable relates with other predictors.

15.16(a). The values of R for the successive steps are .6215, .7748, and .8181 (in successive order).

15.16(b).

15.21.    Within the context of a multiple-regression equation, we cannot look at one variable alone. The slope for one variable is only the slope for that variable when all other variables are held constant.  The percentage of mothers not seeking care until the third trimester is correlated with a number of other variables.

1.        Observations can fall within normal ranges on each individual variable and still be outliers on a bivariate distribution.  This is because an observation may not be normal when paired with the observation on another variable (it may be unusual to have that combination), e.g., it would not be unusual to find someone who is 6’2 (height) or to find someone who weighs 100 pounds.  However, it would be unusual for these two things to be found in the same person.  Thus, an observation may be normal on one variable’s distribution and an outlier in a plot of two variables.

2.        Semi-partial and partial correlations are terms used with multiple linear regression.  Semipartial correlation refers to the amount of variation that a model explains that is accounted for out of the total variation by a single predictor.  Partial correlation refers to the amount of unexplained variation that is accounted for by including a particular predictor in the model.

3(a).     Partial correlation=

The first predictor accounts for only 2.67% of the variation of the criterion (), which indicates it is not likely to be a significant predictor of the criterion.  The second variable accounts for 73% of the variation in the criterion (), which indicates it likely is a significant predictor of the criterion.

3(b).     Partial=

partial=

The first variable accounts for 84.4% ()of the variation of the criterion, indicating it is likely to be a significant predictor in the regression model.  The second variable accounts for only 7% ()of the variation in the criterion, indicating it is not likely to be a significant predictor in the regression model.

4.        The three classes of diagnostic statistics are distance, leverage, and influence. Distance statistics measure the distance between a point and the regression line (e.g., residual) and they allow for the identification of outliers.  Leverage statistics are those that measure the degree to which a point in unusual with respect to the predictor variable (e.g., SD) and allows for the determination of outliers.  Influence statistics determine the amount of influence a point or potential outlier has on a regression line (by taking the distance and leverage of a point into this determination as well).

5.        Unexplained variation=.218

1-.218=.782explained variation (of the model)

1-unexplained variation with just  in the model=1-.542=.458

partial correlation=

partial correlation=

Collinearity=.340-.240=.1