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Regression & factor analyses …. 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"
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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
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 • Communication: • Products: • Expertise:
How do we go about regressing these? • First save the factor output to a file and rename : procfactordata = hold.model out =hold.model* outstat =hold.modelfac** rotate =varimax fuzz=.5nfact=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 procregdata =hold.model; model Q24 = comms prod expt; run; procregdata =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: • Note 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 • 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 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-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
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 • Note how things have changed:
