Handedness Regression Homework
Download the SPSS Handedness data file from the course website. This is the genuine data set used in the handedness article.
Recall the authors wished to demonstrate a right- and left-handed effect in their data. Specifically, they predicted that extreme right- and left-handed individuals would demonstrate signs of greater developmental instability than individuals who were less extreme in their handedness. They measured hand performance (handperf) using a peg-moving task.
Developmental instability was measured with two variables mpa and atddiff. Minor physical anomalies (mpa) were recorded as well as the difference in their atd-angles between their left and right hands. These two variables were converted to z-scores and then totaled into a single composite variable of “developmental instability (dev_comp)”
1. To test the authors’ prediction, you need to fit the following model to the data:
or,
a.Using a compute statement, create a new variable titled HandSqr (viz., handperf * handperf).
b.Regress dev_comp onto Handperf and HandSqr to test the model above (dev_comp is the DV and Handperf and HandSqrare the IVs). For the record, by entering a squared variable, you are testing a non-linear model; here, one in the shape of a horseshoe. Recall the formula for a parabola? It looks like the regression equation above. Pretty nifty, yes?
c.Is the overall model statistically significant? (Note that your results will be different from Study 1 in the published article due to an unexplained extra case)
d.What proportion of variance in developmental instability is predicted from or explained by the model?
e.What is the value for the y-intercept, even though we don’t really care about it?
f.What are the values for the standardized regression weights? Are they statistically significant? You can compare your results to those in Table 1, but again, they won’t match exactly.
g.If you wanted to compare the magnitudes of regression weights, would you use the standardized or unstandardized weights for this model? Why?
h.Above-and-beyond the linear component, how much variance in developmental instability is explained by the quadratic (curvilinear) component of the model? Hint: remember our discussions of partial and semi-partial correlations?
i.Do the results support the authors’ prediction? Write a brief answer to this question discussing the overall model as well as the magnitudes and signs of the regression weights.
j.Request and examine the Tolerance values. Are they problematic, using a .20 cut-point?
k.Diagnose the model by requesting a scatterplot of the residuals. Do you notice any anomalies?
l.Print everything out and annotate your output.
2.One of the mottos in Observation Oriented Modeling is “aggregation often leads to obfuscation.” Is this the case here? Specifically, is it a good idea to aggregate thempa and atddiff variables into a single “developmental instability” variable? Another way to think of this is to ask, “is atddiffjust another minor physical anomaly?” Let’s examine whether or not the regression models differ if these two variables are treated separately.
a.Compute the bivariate correlation between the ‘mpa’ and ‘atddiff’ variables. Create a scatterplot as well and note any anomalies. By averaging variables, you commit to treating them as essentially “measuring” the same dimension.
b.Regress mpa onto HandPerf and HandSqr to test the curvilinear prediction (mpa is the DV, and HandPerf and HandSqr are the IVs). Was the overall model significant? Was the curvilinear effect significant? Obtain a scatterplot of the residuals and note any anomalies.
c.Regress atddiff onto HandPerf and HandSqr to test the curvilinear prediction (atddiff is the DV and HandPerf and HandSqr are the IVs). Was the overall model significant? Was the curvilinear effect significant? Obtain a scatterplot of the residuals and note any anomalies.
d.Based on the analyses for “a”, “b”, and “c”, would you feel comfortable combining the mpa and atddiff variables if this were your data?