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“
Q24 ="Q3a. AMP BANKING OVERALL RATING“ NB: this is the response
These were all on a 10 point scale

3. Let’s do a factor analysis
proc factor data = hold.model rotate =varimax fuzz=.3 nfact=3;
var expert Q30A2 Q30A3 Q30A6 Q30A7 Q30A8 Q30A11 Q30A12 Q30A13
Q30A14 Q30A15
Q32A1 Q32A2 Q32A3 Q32A4 Q32A5 Q32A6;
run;
Rotated Factor Pattern
Factor Factor Factor3
EXPERT STAFF - Experts in Commercial Finance Ma
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 d
Q30A7 Have the knowledge and authority to make
Q30A8 Have a positive, can-do approach to doin
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 to wha
Q30A15 Keep in regular contact to keep you upda
Q32A1 The competitiveness of their fees and ra
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 comme
Q32A5 Providing a full range of commercial and
Q32A6 Being fair and reasonable in their lendi
Values less than 0.5 are not printed.

4. Let’s do a factor analysis
proc factor data = hold.model rotate =varimax fuzz=.5 nfact=4;
var expert Q30A2 Q30A3 Q30A6 Q30A7 Q30A8 Q30A11 Q30A12 Q30A13
Q30A14 Q30A15
Q32A1 Q32A2 Q32A3 Q32A4 Q32A5 Q32A6;
run;
Rotated Factor Pattern
Factor Factor Factor Factor4
EXPERT STAFF - Experts in Commercial Finance Ma
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 d
Q30A7 Have the knowledge and authority to make
Q30A8 Have a positive, can-do approach to doin
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 to wha
Q30A15 Keep in regular contact to keep you upda
Q32A1 The competitiveness of their fees and ra
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 comme
Q32A5 Providing a full range of commercial and
Q32A6 Being fair and reasonable in their lendi
Values less than 0.5 are not printed.

5. Let’s 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 nfact=3;
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;
* 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;
Dependent Variable: Q24 Q3a. AMP BANKING OVERALL RATING
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model <.0001
Error
Corrected Total
Root MSE R-Square
Dependent Mean Adj R-Sq
Coeff Var
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept <.0001
COMMS <.0001
PROD <.0001
EXPT <.0001

8. Conclude We conclude that:
Note also the orthogonality (linear indepedence of the factors)
Pearson Correlation Coefficients, N = 300
Prob > |r| under H0: Rho=0
COMMS PROD EXPT
COMMS
PROD
EXPT
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 <.0001
PROD <.0001
EXPT <.0001
and Standardized Scoring Coefficients
Factor Factor Factor3
EXPERT STAFF - Experts in Commercial Finance Ma
Q30A Take the time to understand who you are
Q30A Communicate clearly, in plain language
Q30A Go out of their way to tailor the best d
Q30A Have the knowledge and authority to make
Q30A Have a positive, can-do approach to doin
Q30A Understand your business and the market
Q30A Are proactive with ideas on how to get t
Q30A Are prompt and reliable in handling any
Q30A Treat you with respect and listen to wha
Q30A Keep in regular contact to keep you upda
Q32A The competitiveness of their fees and ra
Q32A Offering a flexible range of lending/rep
Q32A How easy it is to take out a commercial
Q32A The features and benefits of their comme
Q32A Providing a full range of commercial and
Q32A Being fair and reasonable in their lendi

10. 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(C6:E6,C$3:E$3) where C6:E6 is the
attribute say and C$3:E$3 are the beta’s.

12. Conclusions
Note how things have changed: