1: Task A fashion student was interested in factors that predicted the salaries of catwalk models. She collected data from
231 models. For each model she asked them their salary per day on days when they were working (salary), their age (age),
how many years they had worked as a model (years), and then got a panel of experts from modeling agencies to rate the
attractiveness of each model as a percentage with 100% being perfectly attractive(beauty). The data are in the file
Supermodel.sav. Unfortunately, this fashion student bought some substandard statistics text and so doesnt know how to
analyze her data. Can you help her out by conducting a multiple regression to see which variables predict a models
salary? How valid is the regression model?
Descriptive Statistics
Salary per Day (?
Attractiveness (%)
Number of Years as a Model
Age (Years)
Mean
11.3385
75.9447
4.5854
18.0679
Std. Deviation
16.02644
6.77303
1.57865
2.42190
N
231
231
231
231
Model Summaryb
Model
R
R Square
Adjusted
Std. Error
Change
R Square
of the
Durbin-Watson
Statistics
Estimate
R Square
F Change
df1
df2
Sig. F
Change
1
.429a
.184
.173
14.57213
.184
Change
17.066
3
227
.000
a. Predictors: (Constant), beauty, years, age
b. Dependent Variable: salary
ANOVAa
Model
Sum of
df
Mean Square
F
Sig.
Squares
Regression
3
3623.988
Residual
48202.790
227
59074.754
17.066
.000b
212.347
Total
1
10871.964
230
a. Dependent Variable: salary
b. Predictors: (Constant), beauty, years, age
Adjusted states the shrinkage from the unadjusted value(0.184) pointing the model could not occur well.
2.057
We could use: Adjusted R2 =1-[(231-1/231-3-1)(231-2/231-3-2)(231+1/231)](1-0.184)=0.159
This is meaning these results are indicative that the model may not cross generalize well. The population used
was 231 models and three predictors were observed which is suitable in observing medium to large effects. The
18.4% of the variance in salary per day, it is a suitable fit of the all data F (3227)=17.07,p<0.0001). The R2
The tolerance is below 0.2 which also indicates a serious problem in the collinearity of the model. This
indicates that the age and years are almost identical meaning they measure almost the same thing.
The reasoning for this is because as you age skin becomes wrinkled therefore making it harder to impress others
in photo shoots due to large amounts of applied makeup. This is an indicator that the assumption may be
unreliable for this model.
Model
Unstan Standar
t
Sig.
95.0%
Correlat
ions
dardize
dized
Confide
d
Coeffici
nce
Coeffici
ents
Collinearity Statistics
Interval
ents
B
for B
Std.
Beta
Lower
(Consta
Bound
Partial
Part
Toleran
order
VIF
ce
-60.890
16.497
6.234
1.411
.942
4.418
.000
3.454
9.015
.397
.281
.265
.079
12.653
years
-5.561
2.122
-.548
-2.621
.009
-9.743
-1.380
.337
-.171
-.157
.082
12.157
beauty
-.196
.152
-.083
-1.289
.199
-.497
.104
.068
-.085
-.077
.867
1.153
nt)
1
a.
age
-3.691
Zero-
Bound
Error
Upper
.000 -93.396 -28.384
Dependent Variable: salary
Collinearity Diagnosticsa
Model
Dimension
Eigenvalue
Condition
Index
Variance Proportions
(Constant)
age
years
beauty
1
1.000
.00
.00
.00
.00
2
.070
7.479
.01
.00
.08
.02
3
.004
30.758
.30
.02
.01
.94
4
1
3.925
.001
63.344
.69
.98
.91
.04
a. Dependent Variable: salary
Case
Number
Std.
Residual
Casewise Diagnosticsa
Salary per
Predicted
Day (?
5
4.603
116
3.422
135
4.672
dimension0
155
3.257
191
3.153
198
3.510
a. Dependent Variable: Salary per Day (?
Value
95.34
64.79
89.98
74.86
50.66
71.32
Residual
28.2647
67.07340
14.9259
49.86537
21.8946
68.08541
27.4025
47.45824
4.7164
45.93938
20.1729
51.14779
We could find clearly that the salary per day is predicted by the age of the model and it shows the positive relationship between
them. Also, we could find that there is a negative relationship between years spending on model and theirs salary.
Salary = 0+1age2experience+2attractivene
=-60.89+(6.23 age) - (5.56experience) (0.02 attractivenes
Task 2: Using the Glastonbury data from this chapter (with the dummy coding in GlastonburyDummy.
sav), which you shouldve already analyzed, comment on whether you think the model is reliable and
generalizable.
Model Summaryb
Model
R
R Square Adjusted R Std. Error
Change
Square
Statistics
of the
Durbin-Watson
Estimate
R Square
F Change
df1
df2
Sig. F
Change
1
a
.276
.076
.053
a. Predictors: (Constant), Indie_Kid, Crusty, Metaller
b. Dependent Variable: change
.68818
.076
Change
3.270
3
119
.024
1.893
ANOVAa
Model
Sum of
Df
Mean Square
F
Sig.
Squares
Regression
3
1.549
Residual
56.358
119
61.004
.024b
.474
Total
1
4.646
3.270
122
a. Dependent Variable: change
b. Predictors: (Constant), Indie_Kid, Crusty, Metaller
Coefficientsa
Model
Unstand Standar
ardized
T
Sig.
dized
Confide
Coefficie Coefficie
nts
95.0% Correlati
Collinearity Statistics
ons
nce
nts
Interval
for B
B
Std.
Beta
Lower
(Consta
nt)
1
Crusty
Metaller
Indie_Ki
d
-.554
.090
-.412
.167
.028
-.410
Zero-
Bound
Error
Upper
Bound
Partial
Part
Toleranc
order
VIF
e
-6.134
.000
-.733
-.375
-.232
-2.464
.015
-.742
-.081
-.203
-.220
-.217
.879
1.138
.160
.017
.177
.860
-.289
.346
.112
.016
.016
.874
1.144
.205
-.185
-2.001
.048
-.816
-.004
-.147
-.180
-.176
.909
1.100
a. Dependent Variable: change
Collinearity Diagnosticsa
Model
Dimension
Eigenvalue
Condition
Index
Variance Proportions
(Constant)
Crusty
Metaller
Indie_Kid
1
1
1.727
1.000
.14
.08
.08
.05
2
1.000
1.314
.00
.07
.36
.30
3
1.000
1.314
.00
.38
.04
.33
4
.273
2.515
.86
.48
.52
.32
a. Dependent Variable: change
Casewise Diagnosticsa
Case Number
Std. Residual
change
Predicted Value
Residual
31
-2.302
-2.55
-.9658
-1.58417
153
2.317
1.04
-.5543
1.59431
202
-2.653
-2.38
-.5543
-1.82569
346
-2.479
-2.26
-.5543
-1.70569
479
2.215
.97
-.5543
1.52431
a. Dependent Variable: change
Normality of the histogram and the normal P-P Plot indicate that there is a normal distribution in the histogram and
normal (straight) line from the dashed line in the P-P Plot. In the histogram the assumption of normality has been met.
With the P-P Plot, the dashed line does not deviate from the straight line, hence assuming normality.
Homoscedasticity mean that the residual levels at each level of the predictor(s) should have the same variance. When they
are unequal, they are said to be heteroscedasticity. The scatterplot of ZPred vs. ZResid does show that the height of each
predictor is the same, indicating that they have the same variance. This tells us that the model used is realistic, hence
proving homoscedasticity.
Task 3:
A study was carried out to explore the relationship between Aggression and several potential predicting factors
in children 666 that had an older sibling. Variables measured were Parenting Style (high score bad parenting
practices), Computer Games (high score more time spent playing computer games), Television (high score more
time spent watching television), Diet (high score the child has a good diet low in E-numbers), and
Sibling Aggression (high score more aggression seen in their older sibling). Past research indicated that
parenting style and sibling aggression were good predictors of the level of aggression in the younger child. All
other variables were treated in an exploratory fashion. The data are in the file Child Aggression.sav. Analyse
them with multiple regression.
: A study was carried out to explore the relationship between Aggression and several
potential predicting factors in 666 children that had an older sibling. Variables measured
were Parenting Style (high score = bad parenting practices), Computer Games (high
score = more time spent playing computer games), Television (high score = more time spent
watching television), Diet (high score = the child has a good diet low in E-numbers), and
Sibling Aggression (high score = more aggression seen in their older sibling). Past research
indicated that parenting style and sibling aggression were good predictors of the level of
Aggression in the younger child. All other variables were treated in an exploratory fashion.
The data are in the file Child Aggression.sav. Analyse them with multiple regression.
Based on this subject, we know that parenting style and sibling aggression were good predictors of the level of
aggression in the younger child. So we separate these two variables from others to conduct this analysis. I select
AnalyzeRegressionLinear to enter parenting style and sibling aggression in the first step (forced entry) and
the remaining variables in a second step (stepwise) to get the output shown below:
Model Summaryd
Model
Std.
Adjusted
R
Error of
Change
R
R
the
Statistic
Square
Square
Estimate
s
R
Square
F
Sig. F
1
.231a
.053
Change Change
.050
.31125
.053
df1
18.644
df2
Change
2
663
.000
dimensio 2
n0
.264b
.070
.066
.30875
.017
11.787
1
662
.001
3
.286c
.082
.076
.30697
.012
8.682
1
661
.003
a. Predictors: (Constant), Sibling Aggression, Parenting Style
b. Predictors: (Constant), Sibling Aggression, Parenting Style, Use of Computer Games.
Durbin-Watson
c. Predictors: (Constant), Sibling Aggression, Parenting Style, Use of Computer Games., Good Diet
d. Dependent Variable: Aggression
1.911
Coefficientsa
Model
95.0%
Unstandard Standardiz
ized
Confidence
ed
Interval for
Coefficients Coefficients
t
B
Collinearity Statistics
Lower
-.479
Bound
.632
Bound
-.029
Tolerance
.018
Std. Error
-.006
Beta
.012
.062
.012
.194
5.057
.000
.038
.086
.970
.093
.038
Sig.
.096
2.491
.013
.020
.167
.970
-.007
.012
-.574
.566
-.030
.017
Parenting
.054
.012
.170
4.385
.000
.030
.079
.937
Style
Sibling
.068
.038
.070
1.793
.073
-.006
.142
.933
Aggression
Use
of
.126
.037
.134
3.433
.001
.054
.197
.918
Games.
(Constant)
-.006
.012
-.497
.619
-.029
.017
Parenting
.062
.013
.194
4.925
.000
.037
.087
.897
Style
Sibling
.086
.038
.088
2.258
.024
.011
.161
.908
Aggression
Use
of
1
B
(Constant)
Upper
.143
.037
.153
3.891
.000
.071
.216
.893
-.112
.038
-.118
-2.947
.003
-.186
-.037
.870
Parenting
Style
Sibling
2
Aggression
(Constant)
VIF
Computer
3
Computer
Games.
Good Diet
a. Dependent Variable: Aggression
Excluded Variablesd
Model
1
Beta In
t
Sig.
Collinearity Statistics
.049a
1.091
.276
Tolerance
.042
VIF
.704
.134a
3.433
.001
.132
.918
1.090
.918
-.092a
Time spent
Minimum Tolerance
1.421
.704
-2.313
.021
-.090
.894
1.119
.894
.044b
.986
.324
.038
.703
1.423
.703
-.114
.870
1.150
.870
.028
.697
1.436
.669
watching
television.
Use
of
Computer
Games.
Good Diet
2
Time spent
watching
Partial
television.
Good Diet
3
Correlation
-2.947
.003
-.118b
Time spent
.032c
.715
.475
watching
television.
a. Predictors in the Model: (Constant), Sibling Aggression, Parenting Style
b. Predictors in the Model: (Constant), Sibling Aggression, Parenting Style, Use of Computer Games.
c. Predictors in the Model: (Constant), Sibling Aggression, Parenting Style, Use of Computer Games., Good Diet
d. Dependent Variable: Aggression
Residuals Statisticsa
Minimum
-.4630
Maximum
.3279
-1.15286
1.18037
.00000
.30605
666
Std. Predicted
-5.011
3.643
.000
1.000
666
Value
Std. Residual
-3.756
3.845
.000
.997
666
Predicted
Value
Residual
a. Dependent Variable: Aggression
Mean
Std. Deviation
-.0050
.09139
N
666
Casewise Diagnosticsa
Case
Number
Std.
Aggression
-3.067
Value
-.93
157
3.845
1.13
-.0529
1.18037
169
3.182
.85
-.1251
.97673
200
3.026
.75
-.1805
.92899
221
3.205
1.14
.1543
.98372
270
-3.018
-.73
.1936
-.92649
439
-3.092
-.85
.1041
-.94922
440
-3.290
-.95
.0624
-1.00982
463
-3.756
-1.15
.0055
-1.15286
482
3.476
1.07
.0025
1.06707
505
-3.223
-1.12
-.1284
-.98938
539
dimension0
Residual
45
Predicted
3.416
1.18
.1300
1.04877
a. Dependent Variable: Aggression
Residual
.0106
-.94162
We could analysis from the graphs above.
Sibling aggression ( =0.088, b=0.086, t=2.26 and p<0.05). It is a significantly predicted aggression. The
represents when the time of spending playing computer games increases, the aggression increases too. This is a
positive relationship between them.
Parenting style ( b=0.062, =0.088, t=2.26 and p<0.05). It is a significantly predicted aggression. The
represents when the sibling aggression increases, the aggression increases too. This is a positive relationship
between them.
Computer games ( b=0.143, =0.037, t=3.89 and p<0.001). It is a significantly predicted aggression. The
represent that the time of spending playing computer games increases, the aggression increase too. This is a
positive relationship between them.
E-number (b=0.112,t=2.95, =0.118 and p<0.01.). It is a significantly predicted aggression. The
represent that when the diet changes, the aggression decreases. This is a negative relationship between them.
There is only one factor could not to predict aggression. This is
Television (t=0.72, b=0.032 and p> .05). It is not a significantly predict aggression.
By the analysis above, we could find that the actually parenting style is the most substantive predictor of
aggression. And the computer games factor, good diet and sibling aggression are behind it. The scatterplot of
ZPRED and ZRESID do not point the random pattern. There is no independence of errors assumption. And the
residuals could be uncorrelated in this model. The output of the statistic states that the errors are reasonably
independent.
In conclusion, by the errors, we could find there is no violations of the assumptions.