2007
Lab Stat404
Fall 6
1. The following program will be needed to do this problem: data list list file='c:animals.txt' / id body brain. compute ibody=1/body. compute lbody=lg10(body). compute sbody=sqrt(body). compute ibrain=1/brain. compute lbrain=lg10(brain). compute sbrain=sqrt(brain). examine vars=body/percentiles(20,40,60,80)/plot none/stat none. compute rbody=body. recode rbody(lo thru .248=1)(.2481 thru 1.452=2)(1.4521 thru 4.226=3) (4.2261 thru 71.2=4)(71.2001 thru hi=5). examine vars=brain by rbody / plot boxplot / stat none / nototal. regression vars=body,brain / dep=brain / enter /save=resid(error5) pred(pbrain). examine vars=pbrain/percentiles(20,40,60,80)/plot none/stat none. compute rpbrain=pbrain. recode rpbrain(lo thru 91.244=1)(91.2441 thru 92.407=2) (92.4071 thru 95.088=3)(95.0881 thru 159.818=4)(159.8181 thru hi=5). examine vars=error5 by rpbrain / plot boxplot / stat none / nototal. regression vars=ibody,ibrain/ dep=ibrain / enter /save=resid(error6) pred(pibrain). examine vars=pibrain/percentiles(20,40,60,80)/plot none/stat none. compute rpibrain=pibrain. recode rpibrain(lo thru .1362=1)(.13621 thru .1448=2) (.14481 thru .1623=3)(.16231 thru .2958=4)(.29581 thru hi=5). examine vars=error6 by rpibrain / plot boxplot / stat none / nototal. regression vars=lbody,lbrain/ dep=lbrain / enter /save=resid(error7) pred(plbrain). examine vars=plbrain/percentiles(20,40,60,80)/plot none/stat none. compute rplbrain=plbrain. recode rplbrain(lo thru .4676=1)(.46761 thru 1.0483=2) (1.04831 thru 1.3976=3)(1.39761 thru 2.3156=4)(2.31561 thru hi=5). examine vars=error7 by rplbrain / plot boxplot / stat none / nototal. regression vars=sbody,sbrain/ dep=sbrain / enter /save=resid(error8) pred(psbrain). examine vars=psbrain/percentiles(20,40,60,80)/plot none/stat none. compute rpsbrain=psbrain. recode rpsbrain(lo thru 3.8488=1)(3.84881 thru 4.5702=2) (4.57021 thru 5.4373=3)(5.43731 thru 11.9124=4)(11.91241 thru hi=5). examine vars=error8 by rpsbrain / plot boxplot / stat none / nototal.
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Weisberg (1985, Table 6.6 on pp. 144-5) presents data on brain and body weights for 62 species of mammals. These data are provided (via our class web sites Assignmentspage). The file contains one line of data for each species. (E.g., "Man" is on line 32.) Each line of data contains three numbers: A sequence number (that allows you to identify individual species), body weight in kilograms, and brain weight in grams. Notice that it makes no sense to speak of brain or body weight as causal. (At most, one might expect a positive association between the two.) As it turns out, the variance of each variable increases with the magnitude of the other. a. Obtain a boxplot of the data using SPSS. b. Regress brain weight on body residual brain weight values by Using this diagnostic plot show dependent variable increases as and larger values. weight and obtain a box plot of the the estimated brain weight values. how the conditional variance of the the dependent variable takes larger
c. Perform square root, logarithmic, and inverse transformations on the dependent and independent variables and rerun the regression three times (once with each pair of transformed variables). From each of these regressions obtain a diagnostic plot as in part b. Do the variables' variances appear to increase as a proportion of (i) their means, (ii) their means squared, or (iii) their means to the fourth power? (Differently put, which transformation yields the greatest reduction of heteroscedasticity in the data?) State in words the meanings of the regression coefficient and constant from the regression with the most homoscedastic variances. Be sure to take into account the new meaning your transformation gives to the dependent variable. (Hint: When interpreting the constant, remember that log(1)=0.) d. Weisberg's Table 6.6 lists sequence numbers for identifying the various species. In reference to the regression with the most homoscedastic variances found in part c, the residual values from this regression how indicate much transformed brain weight an animal has above or below what one would estimate given its body weight. Which animals brain weight is farthest above what one would estimate given its body weight (i.e., which is smartest)? Which animals brain weight is farthest below what one would estimate given its body weight (i.e., which is dumbest)? (Hint: Go to the Data Editor in SPSS and select Data, then Sort Cases... Then select sort on the residuals from the appropriate regression model estimated in part c. Which ids end up at the top and bottom rows?)
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2. Using the 1996 General Social Survey of U.S. adults, determine whether people with high SES (socio-economic status) are less likely than people with low SES to watch a lot of television. To do this you must first construct an SES measure. One means of doing this begins by combining distinct SES measures (e.g., income, occupational prestige, and subjective class identification) using principle components analysis. A measure of hours spent watching TV each week is then regressed on this composite measure. Do this using the following program: import file='c:gss96.por'. recode rincome(1=500)(2=2000)(3=3500)(4=4500)(5=5500)(6=6500) (7=7500)(8=9000)(9=12500)(10=17500)(11=22500)(12=35000). factor vars=class,prestg80,rincome/rotate=norotate/save (1 ses). regression vars=ses1,tvhours/dep=tvhours/enter. condescriptive ses1,tvhours. a. The FACTOR routine in SPSS generates principle components when the NOROTATE option is specified. These principle components are standardized (i.e., in this case, SES1 has a mean of zero and a variance equal to one). Yet despite the fact that the independent variable is standardized in the regression of TVHOURS on SES1, the unstandardized regression coefficient in the output from this program does not equal the standardized coefficient. Why is this the case? (Hint: Use algebra to derive one coefficient from the other.) b. What benefit is there in combining CLASS, PRESTG80, and RINCOME into a single measure?
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3. In the U.S. people tend to become more satisfied with their lives as they reach ages in their late 80s and older. Some gerontologists argue that this increase in life satisfaction results as old people learn to accept "what they cannot do" (i.e., their physical limitations resulting from declining health, etc.). Other gerontologists argue that life satisfaction results onl...