Psy 524 Ainsworth S’04 Name:__________________________________________ Exam 1 - Part 1: Short answer questions (write all responses in the blue book) 1. Describe the four levels of measurement (nominal, ordinal, interval and ration). (4 points) 2. What is the difference between univariate and multivariate statistics? (1 point) 3. What is the importance of data screening? (6 points) 4. Discuss the methods of handling missing data? (3 points) 5. What are some problems caused by outliers? (3 points) 6. When is Mahalanobis distance used? (1 point) 7. Describe homoskedasticity. (1 point) 8. Describe multicollinearity/singularity. (1 point) 9. Describe 4 kinds of research questions asked by multiple regression. (10 points) 10. Explain the difference between Pearson, partial and semipartial (part) correlation. (4 points) 11. Describe three types of multiple regression. (6 points) 12. What research questions are answered by canonical correlation? (7 points) 13. List three reasons why canonical correlation is not used more often? (3 points) Psy 524 Ainsworth S’04 Exam 1 - Part 2: Output interpretation Refer to Output 1 for these questions (12 points) 1. Describe the distribution of the variables (V1, V2 and V3 above). Are they normally distributed? Perform the appropriate tests for normality. (5 points). 2. Write the log transformation for “V3”. (2 points). 3. Are there any outliers? If so, which case numbers? (2 points) 4. How much missing data is there? How would you handle it? (2 points). 5. What are the minimum and maximum values of each variable? (1 point). Refer to output 2 for these questions (23 points) 6. What kind of multiple regression is being conducted? (1 point). 7. What variable is being predicted? (1 point). 8. What is “zero-order” correlation? (1 point). 9. Write the prediction equation for model 3. Using this equation, predict a subject’s “exam score” if they scored 13 on “how calm you are”, 10 on “stat confidence”, and he/she studied for 16 hours. (2 points). 10. Interpret the unstandardized regression coefficient for “how calm you are” separately in each of the models (e.g. interpret it in model one, interpret it again for model 2 and again for model 3). (2 points) 11. What is the unique proportion of variance in “exam score” accounted for by “hours of study”? (2 points). 12. Are there any multivariate outliers in the data? Explain you answer. (1 point). 13. Does the data meet the homoskedasticity assumption? Explain. (1 point). 14. Write a short results section (write it in meaningful easy to understand sentences). (12 points). Refer to output 3 for these questions (15 points) 15. How many canonical correlations are significant? (1 point). 16. Draw a diagram for each of the significant canonical correlations. Include all appropriate information in the diagram. (2 points). 17. Write a short results section (write it in meaningful easy to understand sentences). (12 points). Psy 524 Ainsworth S’04 Name:__________________________________________ For part 2 refer to the following set of output Output 1 – Data Screening Explore Ca se Pr oces sing Sum mary Ca ses Va lid N Mi ssing V1 50 0 Pe rcent 10 0.0% V2 48 6 V3 49 3 N To tal 0 Pe rcent .0% 97 .2% 14 98 .6% 7 N 50 0 Pe rcent 10 0.0% 2.8 % 50 0 10 0.0% 1.4 % 50 0 10 0.0% Psy 524 Ainsworth S’04 De scriptiv es V1 Sta tistic 11. 28 Me an 95% Co nfide nce In terva l for Mean Lower B ound Up per B ound 11. 27 11. 00 Va riance 5.5 53 Std . Deviatio n 2.3 56 Min imum 5 Ma ximu m 25 20 3.0 0 Ske wness .32 3 Ku rtosis Me an 95% Co nfide nce In terva l for Mean Lower B ound Up per B ound 5% Trim med Mea n .10 9 1.7 48 .21 8 143 .98 3.4 13 137 .27 150 .69 139 .94 Me dian 144 .00 Va riance 566 0.49 0 Std . Deviatio n 75. 236 Min imum 4 Ma ximu m 480 Ra nge 476 Inte rqua rtile Rang e V3 11. 49 Me dian Inte rqua rtile Rang e V2 11. 07 5% Trim med Mea n Ra nge Std . Erro r .10 5 115 .00 Ske wness .87 9 .11 1 Ku rtosis .94 3 .22 1 270 .40 4.1 34 Me an 95% Co nfide nce In terva l for Mean Lower B ound Up per B ound 262 .28 278 .52 5% Trim med Mea n 272 .68 Me dian 292 .00 Va riance Std . Deviatio n 842 5.83 8 91. 792 Min imum -12 Ma ximu m 501 Ra nge Inte rqua rtile Rang e 513 120 .00 Ske wness -.39 1 .11 0 Ku rtosis -.10 2 .22 0 Psy 524 Ainsworth S’04 Ex treme Val ues V1 Hig hest Lo west V2 Hig hest Lo west V3 Hig hest Lo west 1 Ca se Nu mbe r 5 Va lue 2 38 17 3 45 17 4 15 1 17 5 25 9 1 45 5 5 2 20 5 3 47 3 6 4 18 4 6 5 38 7 1 33 8 48 0 2 28 7 40 0 3 38 40 0 4 32 0 36 1 5 17 1 20 4 2 56 16 3 38 0 16 4 14 2 16 5 12 6 16 1 20 50 1 2 15 0 46 8 3 44 46 8 4 21 2 45 3 5 17 6 1 10 -12 2 45 -12 3 39 9 -12 4 37 6 33 5 9 a. On ly a p artia l list of cases with th e valu e 16 are sho wn in the table of u pper extre mes. b. On ly a p artia l list of cases with th e valu e 6 are sho wn in the table of lo wer e xtrem es. c. On ly a p artia l list of cases with th e valu e 36 1 are sho wn in the table of u pper extre mes. d. On ly a p artia l list of cases with th e valu e 45 3 are sho wn in the table of u pper extre mes. e. On ly a p artia l list of cases with th e valu e 33 are sho wn in the table of lo wer e xtrem es. 25 .a .b .c .d .e Psy 524 Ainsworth S’04 V1 Histogram 300 200 Frequency 100 Std. Dev = 2.36 Mean = 11.3 N = 500.00 0 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 V1 V2 Histogram 200 Frequency 100 Std. Dev = 75.24 Mean = 144.0 N = 486.00 0 0.0 100.0 50.0 200.0 150.0 300.0 250.0 400.0 350.0 500.0 450.0 V2 V3 Histogram 140 120 100 80 Frequency 60 40 Std. Dev = 91.79 20 Mean = 270.4 N = 493.00 0 0.0 100.0 50.0 V3 200.0 150.0 300.0 250.0 400.0 350.0 500.0 450.0 Psy 524 Ainsworth S’04 Output 2 Regression De scriptiv e Stati stics 52 4 exa m 1 score Me an Std . De viatio n 70 .04 8.9 90 N 12 0 ho w cal m yo u are 11 .11 2.1 14 12 0 sta t con fiden ce 13 .99 2.2 13 12 0 ho urs st udied 21 .37 2.9 30 12 0 Correlations Pe arson Corre latio n 524 exa m 1 score Sig . (1-t ailed ) N 524 exa m 1 score how calm you are sta t conf idenc e hou rs stu died 1.0 00 .34 1 .41 7 .76 1 how calm you are .34 1 1.0 00 .04 5 sta t conf idenc e .41 7 .04 5 1.0 00 .31 0 hou rs stu died .76 1 .33 8 .31 0 1.0 00 524 exa m 1 score . .00 0 .00 0 .00 0 how calm you are .00 0 . .31 2 .00 0 sta t conf idenc e .00 0 .31 2 . .00 0 hou rs stu died .00 0 .00 0 .00 0 . 524 exa m 1 score 120 120 120 120 how calm you are 120 120 120 120 sta t conf idenc e 120 120 120 120 hou rs stu died 120 120 120 120 .33 8 Va riabl es Entere d/Rem ov e db Va riable s Re move d Mo del 1 Va riable s En tered ho w cal m yo u are a Me thod . En ter 2 sta t con fiden ce a . En ter 3 ho urs st udied a . En ter a. All requ ested vari ables ente red. b. De pend ent V ariab le: 5 24 e xam 1 sco re Model S ummaryd Mo del 1 R .34 1 a R S quare Ad justed R S quare .11 6 .10 9 Std . Erro r of the Estim ate R S quare Ch ange 8.4 86 .11 6 Ch ange Stati stics F Chang e 15 .547 df1 1 df2 11 8 Sig . F Chang e .00 0 2 .52 7 b .27 8 .26 6 7.7 04 .16 2 26 .169 1 11 7 .00 0 3 .79 1 c .62 5 .61 5 5.5 75 .34 7 10 7.435 1 11 6 .00 0 a. Pre dicto rs: (Consta nt), h ow calm you a re b. Pre dicto rs: (Consta nt), h ow calm you a re, sta t con fiden ce c. Pre dicto rs: (Consta nt), h ow calm you a re, sta t con fiden ce, h ours studi ed d. De pend ent V ariab le: 5 24 exam 1 score Psy 524 Ainsworth S’04 ANOVA d Mo del 1 2 3 Re gression Su m of Squa res 11 19.55 8 df 1 Me an S quare 11 19.55 8 72 .010 Re sidua l 84 97.23 3 11 8 To tal 96 16.79 2 11 9 Re gression 26 72.73 6 2 13 36.36 8 Re sidua l 69 44.05 5 11 7 59 .351 To tal 96 16.79 2 11 9 Re gression 60 11.66 8 3 20 03.88 9 Re sidua l 36 05.12 4 11 6 31 .079 To tal 96 16.79 2 11 9 F 15 .547 Sig . .00 0 a 22 .516 .00 0 b 64 .478 .00 0 c a. Pre dicto rs: (Consta nt), h ow c alm you a re b. Pre dicto rs: (Consta nt), h ow c alm you a re, st at co nfide nce c. Pre dicto rs: (Consta nt), h ow c alm you a re, st at co nfide nce, hours stud ied d. De pend ent V ariab le: 5 24 ex am 1 score Coeffi cientsa Model 1 Unstandardized Coeffic ient s B St d. Error (Constant) 53.921 how calm you are 3 4.161 Sig. .000 3.943 .000 5.575 .000 1.451 .368 5.725 how calm you are 1.374 .334 .323 4.108 stat confidence 1.634 .319 .402 5.116 (Constant) 9.888 4.656 2.124 .036 how calm you are .463 .258 .109 1.798 stat confidence .843 .243 .207 3.462 2.023 .195 .659 10.365 hours s tudied .341 t 12.958 31.917 (Constant) 2 St andardiz ed Coeffic ient s Beta Correlations Zero-order Partial Part Collinearity St atist ics Tolerance VIF .341 .341 .341 1.000 1.000 .000 .341 .355 .323 .998 1.002 .000 .417 .428 .402 .998 1.002 .075 .341 .165 .102 .882 1.134 .001 .417 .306 .197 .900 1.111 .000 .761 .693 .589 .799 1.252 a. Dependent Variable: 524 ex am 1 sc ore Collinea rity Diagnostic sa Va riance Pro portio ns Mo del 1 Dim ensi on 1 2 Eig enva lue Co nditio n Ind ex 1.9 83 1.0 00 .01 7 (Co nstan t) how calm you are sta t conf idenc e hou rs stu died .01 .01 10. 649 .99 .99 3 4 2 1 2.9 61 1.0 00 .00 .00 .00 2 .02 9 10. 167 .01 .71 .33 3 .01 0 17. 322 .99 .29 .66 4 3 1 3.9 50 1.0 00 .00 .00 .00 .00 2 .02 9 11. 724 .01 .66 .28 .00 3 .01 2 17. 829 .04 .31 .57 .60 4 .00 9 21. 332 .95 .04 .15 .40 a. De pend ent V ariab le: 52 4 exa m 1 score Psy 524 Ainsworth S’04 Re sidua ls Statisti cs a Min imum 51. 26 Ma ximu m 88. 18 -2.6 42 2.5 51 .00 0 1.0 00 120 .51 3 1.8 41 .97 5 .29 4 120 Ad justed Pred icted Valu e 50. 97 88. 04 70. 03 7.1 19 120 Re sidua l -15 .21 14. 94 .00 5.5 04 120 Std . Residual -2.7 29 2.6 81 .00 0 .98 7 120 Stu d. Re sidua l -2.7 49 2.7 71 .00 1 1.0 05 120 De leted Resid ual -15 .44 15. 97 .02 5.7 04 120 Stu d. De leted Residual -2.8 31 2.8 55 .00 2 1.0 15 120 Ma hal. Distan ce .01 8 11. 983 2.9 75 2.4 46 120 Co ok's Distan ce .00 0 .13 1 .00 9 .01 9 120 Ce ntere d Lev erage Val ue .00 0 .10 1 .02 5 .02 1 120 Pre dicte d Va lue Std . Pre dicte d Val ue Sta ndard Erro r of Pre dicte d Va lue Me an Std . Dev iatio n 70. 04 7.1 08 a. De pend ent V ariab le: 52 4 ex am 1 score Charts Scatterplot Dependent Variable: 524 exam 1 score 3 2 1 0 -1 -2 -3 -3 -2 -1 0 1 Regression Standardized Predicted Value 2 3 N 120 Psy 524 Ainsworth S’04 Output 3 Canonical Correlation Run MATRIX procedure: Correlations for Set-1 PHYHEAL MENHEAL PHYHEAL 1.0000 .5056 MENHEAL .5056 1.0000 Correlations for Set-2 ESTEEM CONTROL ESTEEM 1.0000 .3467 CONTROL .3467 1.0000 Correlations Between Set-1 and Set-2 ESTEEM CONTROL PHYHEAL .0839 .1120 MENHEAL .1991 .2859 Canonical Correlations 1 .307 2 .007 Test that remaining correlations are zero: _ 1 2 Wilk's .905 1.000 Chi-SQ 45.251 .021 DF 4.000 1.000 Sig. .000 .886 Standardized Canonical Coefficients for Set-1 1 2 PHYHEAL .142 -1.150 MENHEAL -1.064 .459 Raw Canonical Coefficients for Set-1 1 2 PHYHEAL .059 -.480 MENHEAL -.257 .111 Standardized Canonical Coefficients for Set-2 1 2 ESTEEM -.370 -1.000 CONTROL -.810 .694 Raw Canonical Coefficients for Set-2 Psy 524 Ainsworth S’04 ESTEEM CONTROL 1 -.094 -.637 2 -.253 .546 Canonical Loadings for Set-1 1 2 PHYHEAL -.396 -.918 MENHEAL -.992 -.123 Cross Loadings for Set-1 1 2 PHYHEAL -.122 -.006 MENHEAL -.305 -.001 Canonical Loadings for Set-2 1 2 ESTEEM -.651 -.759 CONTROL -.938 .347 Cross Loadings for Set-2 1 2 ESTEEM -.200 -.005 CONTROL -.288 .002 Redundancy Analysis: Proportion of Variance of Set-1 Explained by Its Own Can. Var. Prop Var CV1-1 .571 CV1-2 .429 Proportion of Variance of Set-1 Explained by Opposite Can.Var. Prop Var CV2-1 .054 CV2-2 .000 Proportion of Variance of Set-2 Explained by Its Own Can. Var. Prop Var CV2-1 .651 CV2-2 .349 Proportion of Variance of Set-2 Explained by Opposite Can. Var. Prop Var CV1-1 .062 CV1-2 .000 ------ END MATRIX ----- Psy 524 Ainsworth S’04 Appendix Table 1: Common Transformations in SPSS Condition of Variable SPSS Compute Language Moderate Positive Skewness NEWX=SQRT(X) Substantial Positive Skewness NEWX=LG10(X) Variable includes 0 NEWX=LG10(X + C) Severe Pos Skewness, L Shaped NEWX=1/(X) Variable includes 0 NEWX=1/(X + C) Moderate Negative Skewness NEWX=SQRT(K - X) Substantial Negative Skewness NEWX=LG10(K - X) Severe Neg Skewness, J Shaped NEWX=1/(K - X) C = constant added to each score so that the smallest score is 1. K = constant from which each score is subtracted so that the smallest score is 1; usually equal to the largest score + 1. Table 2: Chi Square Values df 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 P = 0.05 3.84 5.99 7.82 9.49 11.07 12.59 14.07 15.51 16.92 18.31 19.68 21.03 22.36 23.69 25.00 P = 0.01 P = 0.001 6.64 10.83 9.21 13.82 11.35 16.27 13.28 18.47 15.09 20.52 16.81 22.46 18.48 24.32 20.09 26.13 21.67 27.88 23.21 29.59 24.73 31.26 26.22 32.91 27.69 34.53 29.14 36.12 30.58 37.70