Task 1: 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 doesn’t know how to
analyze her data. Can you help her out by conducting a multiple regression to see which variables predict a model’s
salary? How valid is the regression model?
Descriptive Statistics
Mean
Std. Deviation
N
Salary per Day (?
11.3385
16.02644
231
Attractiveness (%)
75.9447
6.77303
231
Number of Years as a Model
4.5854
1.57865
231
Age (Years)
18.0679
2.42190
231
Model Summary
b
Model
R
R Square
Adjusted
R Square
Std. Error
of the
Estimate
Change
Statistics
DurbinWatson
R Square
Change
F Change
df1
df2
Sig. F
Change
1
.429
a
.184
.173
14.57213
.184
17.066
3
227
.000
2.057
a. Predictors: (Constant), beauty, years, age
b. Dependent Variable: salary
ANOVA
a
Model
Sum of
Squares
df
Mean Square
F
Sig.
1
Regression
10871.964
3
3623.988
17.066
.000
b
Residual
48202.790
227
212.347
Total
59074.754
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.
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View Full DocumentWe could use: Adjusted R
2
=1[(2311/23131)(2312/23132)(231+1/231)](10.184)=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 R
2
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
dardize
d
Coeffici
ents
Standar
dized
Coeffici
ents
t
Sig.
95.0%
Confide
nce
Interval
for B
Correlat
ions
Collinearity Statistics
B
Std.
Error
Beta
Lower
Bound
Upper
Bound
Zero
order
Partial
Part
Toleran
ce
VIF
1
(Consta
nt)
60.890
16.497
3.691
.000
93.396
28.384
age
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
a.
Dependent Variable: salary
Collinearity Diagnostics
a
Model
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 Spring '12
 rosnin
 Regression Analysis, Interest, R Square, Collinearity Diagnosticsa

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