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