Candidate Number
976C8
THE UNIVERSITY OF SUSSEX
MRes/MSc Examination January 2017 (A1)
LINEAR MODELS IN STATISTICS
OPEN BOOK EXAM
SAMPLE PAPER
Assessment Period:
DO NOT TURN OVER UNTIL INSTRUCTED TO BY
THE CHIEF INVIGILATOR
INSTRUCTIONS
This exam is an OPEN BOOK EXAM. You may bring books, papers, notes, etc. into
the exam, and a calculator, but no other electronic devices.
Please write your answers in this booklet and if necessary request a continuation
booklet if you run out of space. At the end of the examination the question paper and
any answer books/answer sheets, used or unused, will be collected from you before
you leave the examination room
Time allowed: 2 hours
Answer TWO questions only. Question 1 is compulsory. Answer EITHER
question 2 OR question 3
Question 1 carries 40% of the marks so be sure to allocate your time appropriately.
(40% of 2 hours is 48 minutes)
For each question you are given the details of a study and the output from an SPSS
analysis of the data from the study to interpret.
Please note: The only approved calculators for use in University
examinations are the Casio fx82, fx83, fx85, fx115, fx570 and fx991 (all with
any suffix). Students are not permitted to take instruction notes or booklets
relating to their calculator into an examination.
Please indicate below which questions you answered.
Q1 (COMPULSORY)
Q2
Q3
976C8
Linear Models in Statistics – Sample Paper
Question 1:
A researcher randomly selects 20 couples and compares the time the husbands and
wives spend watching TV. Interpret the output presented below
Paired Samples Statistics
Mean
Pair
1
Hours per week
female spends
watching TV
Hours per week male
spends watching TV
N
Std.
Std. Error
Deviation
Mean
17.4000
20
9.70838
2.17086
19.7500
20
9.72720
2.17507
Paired Samples Correlations
N
Correlation
Sig.
Pair 1 Hours per week
female spends
watching TV &
Hours per week
male spends
watching TV
20
.955
.000
Output continued overleaf...
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976C8
Linear Models in Statistics – Sample Paper
Paired Samples Test
Mean
Pair 1
Hours per week
female spends
watching TV Hours per week
male spends
watching TV
-2.35000
Paired Differences
95% Confidence
Interval of the
Std.
Difference
Std.
Error
Deviation Mean
Lower
Upper
2.90689
.65000
t
-3.71047 -.98953
df
-3.615
Sig. (2tailed)
19
.002
The researcher is also interested in the effect of age on TV viewing, particularly in males,
and so divides the 20 males into a younger group of 10 and an older group of 10.
Group Statistics
Hours per week
male spends
watching TV
young vs old
males
Young
N
Old
Mean
Std. Deviation
Std. Error
Mean
10
17.3000
9.03143
2.85599
10
22.2000
10.23936
3.23797
Independent Samples Test
Levene's Test
for Equality of
Variances
F
Hours per
week male
spends
watching TV
Equal
variances
assumed
Equal
variances
not assumed
.211
Sig.
.651
t-test for Equality of Means
t
df
Sig. (2tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-1.135
18
.271
-4.90000
4.31754
-13.97081
4.17081
-1.135
17.724
.272
-4.90000
4.31754
-13.98095
4.18095
Answer overleaf…
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976C8
Linear Models in Statistics – Sample Paper
Answer for question 1:
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976C8
Linear Models in Statistics – Sample Paper
Answer for question 1 (continued):
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976C8
Linear Models in Statistics – Sample Paper
Question 2
A psychology teacher was interested is whether exam performance by her students
was affected by the number of hours they spend revising, their anxiety levels before
the exam, and their A-level grades on entry to university. Interpret the output below
and the calculate the predicted exam score for a student who revised for 30 hours,
had an anxiety score of 45, and 26 A-level points.
Descriptive Statistics
Std.
Mean
Deviation
exam score
hours spent
revising
anxiety
A-level entry
points
Pearson
Correlation
Sig. (1-tailed)
N
exam score
hours spent
revising
anxiety
A-level entry
points
exam score
hours spent
revising
anxiety
A-level entry
points
exam score
hours spent
revising
anxiety
A-level entry
points
N
61.0000
10.96406
20
39.1500
9.07440
20
49.3000
18.91004
20
23.2000
3.20526
20
Correlations
exam
hours spent
A-level entry
score
revising
anxiety
points
1.000
.821
-.118
.872
.821
1.000
-.340
.732
-.118
-.340
1.000
-.244
.872
.732
-.244
1.000
.
.000
.310
.000
.000
.
.072
.000
.310
.072
.
.150
.000
.000
.150
.
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
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976C8
Linear Models in Statistics – Sample Paper
Model Summaryb
Std. Error of
R
Adjusted R
the
Model
R
Square
Square
Estimate
a
1
.927
.860
.834
4.46756
a. Predictors: (Constant), A-level entry points, anxiety,
hours spent revising
b. Dependent Variable: exam score
ANOVAa
Model
1
Regression
Residual
Total
Sum of
Squares
1964.654
319.346
2284.000
df
3
16
19
Mean Square
654.885
19.959
F
32.811
Sig.
.000b
a. Dependent Variable: exam score
b. Predictors: (Constant), A-level entry points, anxiety, hours spent revising
Coefficientsa
Model
1
(Constant)
hours spent
revising
anxiety
A-level
entry points
Unstandardized Standardized
Coefficients
Coefficients
Std.
B
Error
Beta
t
-11.823
8.806
-1.343
95.0% Confidence
Collinearity
Interval for B
Statistics
Lower
Upper
Sig.
Bound
Bound Tolerance
VIF
.198
-30.490
6.845
.551
.171
.456
3.226
.005
.189
.913
.437
2.288
.104
.058
.179
1.796
.091
-.019
.226
.885
1.130
1.989
.469
.581
4.239
.001
.994
2.984
.464
2.153
a. Dependent Variable: exam score
Output continued overleaf...
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976C8
Linear Models in Statistics – Sample Paper
Collinearity Diagnosticsa
Model
1
Dimension
1
2
3
4
Eigenvalue Condition Index
3.849
1.000
.129
5.454
.016
15.410
.005
26.701
(Constant)
.00
.00
.38
.62
Variance Proportions
hours spent
revising
anxiety
.00
.01
.04
.59
.56
.39
.40
.02
A-level entry
points
.00
.00
.02
.98
a. Dependent Variable: exam score
Residuals Statisticsa
Predicted Value
Residual
Std. Predicted
Value
Std. Residual
Minimum
42.7247
-8.49329
Maximum
76.7360
6.65373
Mean
Std. Deviation
61.0000
10.16872
.00000
4.09972
N
-1.797
1.547
.000
1.000
20
-1.901
1.489
.000
.918
20
20
20
a. Dependent Variable: exam score
Output continued overleaf...
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976C8
Linear Models in Statistics – Sample Paper
Answer overleaf…
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976C8
Linear Models in Statistics – Sample Paper
Answer for question 2:
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976C8
Linear Models in Statistics – Sample Paper
Answer for question 2 (continued):
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Linear Models in Statistics – Sample Paper
976C8
Question 3
A researcher investigated two methods for teaching female and male secondary
school students good study behaviours. In the first condition (called “traditional”)
students attended lectures and were given handouts. In the second (“audiovisual”)
condition specially developed audio-visual presentations were used. The study also
included a control condition in which students received no special training on how to
study. Four measures were taken of study behaviour at the end of the study: quality
of the study environment, study habits, note-taking ability and ability to summarise.
On all measures higher scores are better. Interpret the following output.
Between-Subjects Factors
Value Label
N
group
0
CONTROL
GROUP
sex
Box's Test of
Equality of
Covariance
Matricesa
40
1
TRADITIONAL
34
2
AUDIO-VISUAL
36
0
FEMALE
56
1
MALE
54
Box's M
F
59.949
1.079
df1
50
df2
19035.849
Sig.
.325
Tests the null hypothesis that
the observed covariance
matrices of the dependent
variables are equal across
groups.
a. Design: Intercept + group +
sex + group * sex
Output continued overleaf
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976C8
Linear Models in Statistics – Sample Paper
Descriptive Statistics
Study environment post
group
CONTROL GROUP
TRADITIONAL
AUDIO-VISUAL
Total
Study habits - post
CONTROL GROUP
TRADITIONAL
AUDIO-VISUAL
Total
Note taking - post
CONTROL GROUP
TRADITIONAL
AUDIO-VISUAL
Total
Summarising - post
CONTROL GROUP
TRADITIONAL
AUDIO-VISUAL
Total
sex
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
FEMALE
MALE
Total
Mean
8.75
8.75
8.75
8.28
7.25
7.79
7.83
8.44
8.14
8.30
8.20
8.25
8.25
7.95
8.10
8.22
7.13
7.71
7.17
7.22
7.19
7.89
7.46
7.68
17.25
18.40
17.83
18.00
16.56
17.32
17.72
15.61
16.67
17.64
16.93
17.29
18.65
19.15
18.90
20.50
17.69
19.18
17.78
17.61
17.69
18.96
18.20
18.59
Std. Deviation
1.860
1.803
1.808
1.841
1.770
1.855
1.724
2.229
1.988
1.818
2.013
1.908
1.251
1.761
1.516
1.353
1.455
1.488
1.295
2.157
1.754
1.371
1.830
1.619
2.593
2.521
2.591
3.430
2.804
3.188
1.965
4.286
3.456
2.693
3.441
3.090
3.558
3.150
3.327
4.515
4.408
4.622
3.703
4.340
3.977
4.023
3.954
3.989
N
20
20
40
18
16
34
18
18
36
56
54
110
20
20
40
18
16
34
18
18
36
56
54
110
20
20
40
18
16
34
18
18
36
56
54
110
20
20
40
18
16
34
18
18
36
56
54
110
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976C8
Linear Models in Statistics – Sample Paper
Multivariate Testsa
Effect
Intercept
group
sex
group * sex
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Value
.979
.021
45.584
45.584
.150
.856
.162
.097
.033
.967
.034
.034
.135
.869
.147
.108
F
1150.992b
1150.992b
1150.992b
1150.992b
2.061
2.044b
2.026
2.465c
.863b
.863b
.863b
.863b
1.847
1.843b
1.839
2.760c
Hypothesis df
4.000
4.000
4.000
4.000
8.000
8.000
8.000
4.000
4.000
4.000
4.000
4.000
8.000
8.000
8.000
4.000
Error df
101.000
101.000
101.000
101.000
204.000
202.000
200.000
102.000
101.000
101.000
101.000
101.000
204.000
202.000
200.000
102.000
Sig.
.000
.000
.000
.000
.041
.043
.045
.050
.489
.489
.489
.489
.070
.071
.072
.032
a. Design: Intercept + group + sex + group * sex
b. Exact statistic
c. The statistic is an upper bound on F that yields a lower bound on the significance level.
Levene's Test of Equality of Error Variancesa
F
Study environment
- post
Study habits - post
Note taking - post
Summarising post
df1
df2
Sig.
.304
5
104
.909
1.720
1.963
5
5
104
104
.137
.090
.760
5
104
.581
Tests the null hypothesis that the error variance of the dependent variable is
equal across groups.
a. Design: Intercept + group + sex + group * sex
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976C8
Linear Models in Statistics – Sample Paper
Output continued overleaf
Tests of Between-Subjects Effects
Source
Corrected Model
Intercept
group
sex
group * sex
Error
Total
Corrected Total
Dependent Variable
Study environment post
Study habits - post
Note taking - post
Summarising - post
Study environment post
Study habits - post
Note taking - post
Summarising - post
Study environment post
Study habits - post
Note taking - post
Summarising - post
Study environment post
Study habits - post
Note taking - post
Summarising - post
Study environment post
Study habits - post
Note taking - post
Summarising - post
Study environment post
Study habits - post
Note taking - post
Summarising - post
Study environment post
Study habits - post
Note taking - post
Summarising - post
Study environment post
Study habits - post
Note taking - post
Summarising - post
Type III Sum of
Squares
df
Mean Square
F
Sig.
29.817a
5
5.963
1.690
.144
26.691b
96.315c
114.165d
5
5
5
5.338
19.263
22.833
2.142
2.121
1.465
.066
.069
.207
7385.431
1
7385.431
2092.558
.000
6410.510
32572.373
37685.165
1
1
1
6410.510
32572.373
37685.165
2572.394
3587.052
2418.658
.000
.000
.000
18.449
2
9.224
2.614
.078
15.538
25.423
41.245
2
2
2
7.769
12.711
20.622
3.117
1.400
1.324
.048
.251
.271
.527
1
.527
.149
.700
5.469
17.478
18.672
1
1
1
5.469
17.478
18.672
2.194
1.925
1.198
.142
.168
.276
11.935
2
5.967
1.691
.189
6.062
56.746
54.718
2
2
2
3.031
28.373
27.359
1.216
3.125
1.756
.301
.048
.178
367.056
104
3.529
259.172
944.376
1620.426
104
104
104
2.492
9.081
15.581
7892.000
110
6777.000
33928.000
39753.000
110
110
110
396.873
109
285.864
1040.691
1734.591
109
109
109
a. R Squared = .075 (Adjusted R Squared = .031)
b. R Squared = .093 (Adjusted R Squared = .050)
c. R Squared = .093 (Adjusted R Squared = .049)
d. R Squared = .066 (Adjusted R Squared = .021)
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976C8
Linear Models in Statistics – Sample Paper
Eigenvalues
Function
1
2
Eigenvalue % of Variance Cumulative %
.096a
60.3
60.3
.063a
39.7
100.0
Canonical
Correlation
.296
.244
a. First 2 canonical discriminant functions were used in the analysis.
Standardized Canonical
Discriminant Function
Coefficients
Functions at Group Centroids
Function
1
Study environment
- post
Study habits - post
Note taking - post
Summarising post
Function
2
1.209
-.081
-.023
.120
.832
.303
-1.070
.098
group
CONTROL
GROUP
TRADITIONAL
AUDIO-VISUAL
1
2
.250
.258
-.452
.150
.050
-.334
Unstandardized canonical discriminant functions
evaluated at group means
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976C8
Linear Models in Statistics – Sample Paper
Answer for question 3:
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976C8
Linear Models in Statistics – Sample Paper
Answer for question 3 (continued):
End of paper
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