How well do a combination of anxiety and weight predict systolic blood pressure (SBP)? Also, how much variance in blood pressure is uniquely explained by each of these two predictor variables?

1. As preliminary data screening, generate a histogram of scores on each of the three variables in the data table and do a bivariate scatter plot for each pair of variables. Do you see evidence of violations of assumptions? For example, do any variables have non normal distribution shapes? Are any pairs of variables related in a way that is not linear? Are there bivariate outliers?
2. Run a regression analysis to predict SBP from weight and anxiety. Make sure that you request the part and partial correlation statistics, and a graph of the standardized residuals (ZRESID) against the standardized predicted values (ZPRED).
3. Write up a results section. What can you conclude about the predictive usefulness of these two variables, individually and combined?
4. Does examination of the plot of standardized residuals indicate any serious violation of assumptions? Explain.
5. Why is the b coefficient associated with the variable weight so much smaller than the b coefficient associated with the variable anxiety (even though weight accounted for a larger unique share of the variance in SBP)?
6. Set up a table to summarize the results of your regression analysis.
7. Draw a diagram to show how the total variance of SBP is partitioned into variance that is uniquely explained by each predictor, variance that can be explained by either predictor, and variance than cannot be explained; also fill in the numerical values that represent the proportions of variance in this case.
8. Were the predictors highly correlated with each other? Did they compete to explain the same variance? How do you know?
9. Ideally, how many cases do you need to do a regression analysis with two predictor variables?

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