Regression

1
Regression factor analyses
2
Regression example - revisited

• Our example
• A financial company wishes to ascertain what the
  drivers of satisfaction are for their service
  They are
• EXPERT"experts"
• Q30A2 "Take the time to understand who you
  are"
• Q30A3 "Communicate clearly, in plain
  language"
• Q30A6 "Go out of their way to tailor
  the best deal"
• Q30A7 "Have the knowledge and authority
  to make"
• Q30A8 "Have a positive, can-do
  approach"
• Q30A11 "Understand your business and
  the market"
• Q30A12 "Are proactive with ideas on how
  to get t"
• Q30A13 "Are prompt and reliable in
  handling any"
• Q30A14 "Treat you with respect and
  listen"
• Q30A15 "Keep in regular contact to keep
  you updated"
• Q32A1 "The competitiveness of their
  fees and rates"
• Q32A2 "Offering a flexible range of
  lending/rep"
• Q32A3 "How easy it is to take out a
  commercial"
• Q32A4 "The features and benefits of
  their comments"
• Q32A5 "Providing a full range of
  commercial product"
• Q32A6 "Being fair and reasonable in
  their lending

3
Lets do a factor analysis

• proc factor data hold.model rotate varimax
  fuzz.3 nfact3
• var expert Q30A2 Q30A3 Q30A6 Q30A7 Q30A8 Q30A11
  Q30A12 Q30A13
• Q30A14 Q30A15
• Q32A1 Q32A2 Q32A3 Q32A4 Q32A5 Q32A6
• run
• 
  Rotated Factor Pattern
• 
  Factor1
  Factor2 Factor3
• EXPERT STAFF - Experts
  in Commercial Finance Ma . .
  0.51465
• Q30A2 Take the time to
  understand who you are . .
  0.72096
• Q30A3 Communicate
  clearly, in plain language 0.58922
  . 0.51987
• Q30A6 Go out of their
  way to tailor the best d . .
  .
• Q30A7 Have the
  knowledge and authority to make 0.67551
  . .
• Q30A8 Have a positive,
  can-do approach to doin 0.70404 .
  .
• Q30A11 Understand your
  business and the market 0.51376 .
  0.66569

4
Lets do a factor analysis

• proc factor data hold.model rotate varimax
  fuzz.5 nfact4
• var expert Q30A2 Q30A3 Q30A6 Q30A7 Q30A8 Q30A11
  Q30A12 Q30A13
• Q30A14 Q30A15
• Q32A1 Q32A2 Q32A3 Q32A4 Q32A5 Q32A6
• run
• 
  Rotated Factor Pattern
• 
  Factor1 Factor2
  Factor3 Factor4
• EXPERT STAFF - Experts in
  Commercial Finance Ma 0.57635 .
  . .
• Q30A2 Take the time to
  understand who you are 0.70602 .
  . .
• Q30A3 Communicate clearly, in
  plain language 0.51025 0.59210
  . .
• Q30A6 Go out of their way to
  tailor the best d 0.53333 .
  . .
• Q30A7 Have the knowledge and
  authority to make . .
  . 0.59786
• Q30A8 Have a positive, can-do
  approach to doin 0.51991 0.59144
  . .
• Q30A11 Understand your
  business and the market 0.67486 .
  . .

5
Lets go for three factors

• Communication
• Products
• Expertise

6
How do we go about regressing these?

• First save the factor output to a file and rename
  
• proc factor data hold.model out hold.model
  outstat hold.modelfac
• rotate varimax fuzz.5 nfact3
• var expert Q30A2 Q30A3 Q30A6 Q30A7 Q30A8 Q30A11
  Q30A12 Q30A13
• Q30A14 Q30A15
• Q32A1 Q32A2 Q32A3 Q32A4 Q32A5 Q32A6
• run
• data hold.model
• set hold.model
• rename
• factor1 comms
• factor2 prod
• factor3 expt
• run
• This just put output for Factor1-3 on the end
  of the file hold.model
• this yields all the stats used in the FA

7
Regressing the factors

• proc reg data hold.model
• model Q24 comms prod expt
• run
• proc reg data hold.model
• model Q24 comms prod expt
• run
• Dependent Variable Q24 Q3a. AMP BANKING OVERALL
  RATING
• 
  Analysis of Variance
• 
  Sum of Mean
• Source
  DF Squares Square F Value
  Pr gt F
• Model
  3 501.84288 167.28096 84.91
  lt.0001
• Error
  296 583.12712 1.97002
• Corrected Total
  299 1084.97000

8
Conclude

• We conclude that
• Note also the orthogonality (linear indepedence
  of the factors)
• 
  Pearson Correlation Coefficients, N 300
• 
  Prob gt r under H0 Rho0
• 
  COMMS PROD EXPT
• 
  COMMS 1.00000 0.00000 0.00000
• 
  1.0000 1.0000
• PROD
  0.00000 1.00000 0.00000
• 
  1.0000 1.0000
• EXPT
  0.00000 0.00000 1.00000
• 
  1.0000 1.0000
• Note also that ususal regression checks should
  apply (not done here - but will need to be
  inspected by you!)

9
Getting to the actual attributes

• This is all very well to recommend more emphasis
  on communication - but just which components do
  we need to look at?
• Easy look at the combination of regresion
  coefficients with the scoring parameters for each
  driver
• COMMS
  1 0.96331 0.08117 11.87
  lt.0001
• PROD
  1 0.56340 0.08117
  6.94 lt.0001
• EXPT
  1 0.65804 0.08117
  8.11 lt.0001
• and Standardized Scoring Coefficients
• 
  Factor1
  Factor2 Factor3
• EXPERT STAFF - Experts in
  Commercial Finance Ma 0.00002
  -0.03013 0.16224
• Q30A2 Take the time to
  understand who you are -0.05261
  -0.10791 0.32007
• Q30A3 Communicate
  clearly, in plain language 0.12441
  -0.07959 0.09350
• Q30A6 Go out of their
  way to tailor the best d 0.01660
  0.04922 0.08251
• Q30A7 Have the knowledge
  and authority to make 0.28300
  0.03159 -0.18644
• Q30A8 Have a positive,
  can-do approach to doin 0.23061
  -0.07805 -0.01169
• Q30A11 Understand your
  business and the market -0.00387
  -0.10390 0.26047
• Q30A12 Are proactive with
  ideas on how to get t -0.09662
  -0.07577 0.32550
• Q30A13 Are prompt and
  reliable in handling any 0.38097
  -0.12283 -0.14483

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Getting to the actual attributes

• The scoring algorithm tells us how much each
  standardised attribute (x-m)/s contributes to
  each factor score
• So one way to see the importance of each
  attribute is looking at the change in modelled
  score as each attribute incerases by a value of 1
  ( ie 1 s)
• The works out to be
• Importance for attribi SibjFij
• Easy to compute in Excel (cut and paste output
  into excel hint use the Text to columns..,
  options in the Data
• Alternatively export hold.modelfac to excel via
  .csv option

11
Getting to the actual attributes
NB compute importance using this type of
code SUMPRODUCT(C6E6,C3E3) where C6E6 is
the attribute say and C3E3 are the betas.
12
Conclusions

• Note how things have changed

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