# Regression & factor analyses …. Regression example - revisited uOur example: nA financial company wishes to ascertain what the drivers of satisfaction.

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Regression & factor analyses …

Regression example - revisited uOur example: nA 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 nThese were all on a 10 point scale

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 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 Q30A12 Are proactive with ideas on how to get t.. 0.68897 Q30A13 Are prompt and reliable in handling any 0.78677.. Q30A14 Treat you with respect and listen to wha 0.77983.. Q30A15 Keep in regular contact to keep you upda.. 0.79008 Q32A1 The competitiveness of their fees and ra. 0.76013. Q32A2 Offering a flexible range of lending/rep. 0.74967. Q32A3 How easy it is to take out a commercial. 0.67490. Q32A4 The features and benefits of their comme. 0.76336. Q32A5 Providing a full range of commercial and. 0.61487. Q32A6 Being fair and reasonable in their lendi. 0.74213. Values less than 0.5 are not printed.

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 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... Q30A12 Are proactive with ideas on how to get t 0.73501... Q30A13 Are prompt and reliable in handling any. 0.75572.. Q30A14 Treat you with respect and listen to wha. 0.84713.. Q30A15 Keep in regular contact to keep you upda 0.78844... Q32A1 The competitiveness of their fees and ra.. 0.80252. Q32A2 Offering a flexible range of lending/rep.. 0.50843 0.66142 Q32A3 How easy it is to take out a commercial... 0.72790 Q32A4 The features and benefits of their comme.. 0.78841. Q32A5 Providing a full range of commercial and.. 0.59441. Q32A6 Being fair and reasonable in their lendi.. 0.67644. Values less than 0.5 are not printed.

Let’s go for three factors uCommunication: uProducts: uExpertise:

How do we go about regressing these? uFirst 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; 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

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 > F Model 3 501.84288 167.28096 84.91 <.0001 Error 296 583.12712 1.97002 Corrected Total 299 1084.97000 Root MSE 1.40358 R-Square 0.4625 Dependent Mean 7.51000 Adj R-Sq 0.4571 Coeff Var 18.68942 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Intercept Intercept 1 7.51000 0.08104 92.68 <.0001 COMMS 1 0.96331 0.08117 11.87 <.0001 PROD 1 0.56340 0.08117 6.94 <.0001 EXPT 1 0.65804 0.08117 8.11 <.0001

Conclude We conclude that: uNote also the orthogonality (linear indepedence of the factors) Pearson Correlation Coefficients, N = 300 Prob > |r| under H0: Rho=0 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 usual regression checks should apply (not done here - but will need to be inspected by you!)

Getting to the actual attributes uThis is all very well to recommend more emphasis on communication - but just which components do we need to look at? uEasy look at the combination of regression coefficients with the scoring parameters for each driver: COMMS 1 0.96331 0.08117 11.87 <.0001 PROD 1 0.56340 0.08117 6.94 <.0001 EXPT 1 0.65804 0.08117 8.11 <.0001 and Standardized Scoring Coefficients Comms Prod Expt 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 Q30A14 Treat you with respect and listen to wha 0.40169 -0.07319 -0.21807 Q30A15 Keep in regular contact to keep you upda -0.31326 -0.06241 0.52827 Q32A1 The competitiveness of their fees and ra -0.29803 0.30859 0.11545 Q32A2 Offering a flexible range of lending/rep 0.06032 0.28211 -0.21660 Q32A3 How easy it is to take out a commercial 0.15380 0.23604 -0.26978 Q32A4 The features and benefits of their comme -0.20335 0.28074 0.06212 Q32A5 Providing a full range of commercial and 0.06689 0.21454 -0.16961 Q32A6 Being fair and reasonable in their lendi -0.05810 0.26368 -0.06906

Getting to the actual attributes…  The scoring algorithm tells us how much each standardised attribute { (x-  } 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  uThe works out to be Importance for attrib i =  i b j F ij nEasy to compute in Excel (cut and paste output into excel – hint: use the ‘Text to columns’.., options in the ‘Data’ FAlternatively export hold.modelfac to excel via.csv option

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.

Conclusions uNote how things have changed:

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