# Regression and factor analysis assignment help

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## Regression and Factor Analysis

Please use the data attached to tackle the case of "Customer Satisfaction at Harver & Boecker".  Please answer the following questions:
1. Using regression analysis, locate those variables that best explain the customers' overall satisfaction.  Evaluate the model fit and assess the impact of each variable on the criterion variable.  Remember to use collinearity diagnostics.
1. Determine the factors that characterize the respondents by means of a factor analysis.  Consider the following issues:
(a) Are FA assumptions met? (b) How many factors should be extracted? (c) Try to find suitable labels for the extracted factors. (d) Evaluate the solution's goodness-of-fit.
1. Use the factor scores and regress the customers' overall satisfaction (overall) on these.

Solution

proc import datafile=”c:\myfiles\Accounts.xls”

out=sasuser.accounts

sheet=”Prices”;

getnames=no;

run;

proc print data=sasuser.accounts(obs=10);

run;

proc import datafile=”C:/Users/Mohamed/Desktop/data.xls”

DBMS=excel

out=Work.data ;

run;

proc print data=sasuser.accounts(obs=10);

run;

PROC IMPORT DATAFILE= “C:\Users\Mohamed\Desktop\data.xlsx”

OUT= WORK.data

DBMS=XLS

REPLACE;

SHEET=”Sheet1″;

GETNAMES=YES;

RUN;

libname assign ‘C:\Users\Mohamed\Desktop\sas’;

PROC IMPORT DATAFILE= “C:\Users\Mohamed\Desktop\data.xls”

OUT= assign.data

dbms=xls

REPLACE;

GETNAMES=YES;

Sheet=”Sheet1″;

RUN;

ods graphics on;

procreg;

model overall = s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12;

run;

ods graphics off;

ods graphics on;

procreg;

model overall = s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 / tolvifcollin;

run;

ods graphics off;

ods graphics on;

proc factor data=Assign.Data

priors=smcmsa residual

rotate=promax reorder

outstat=fact_all

plots=(scree initloadingspreloadings loadings);

var s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 ;

run;

ods graphics off;

data fact2(type=factor);

setfact_all;

if _TYPE_ in(‘PATTERN’ ‘FCORR’) then delete;

if _TYPE_=’UNROTATE’ then _TYPE_=’PATTERN’;

ods graphics on;

proc factor data=Assign.Data

priors=smcmsa residual

rotate=promax reorder

outstat=fact_all

score=fact

plots=(scree initloadingspreloadings loadings);

var s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 ;

run;

ods graphics off;

proc factor data=Assign.Data score outstat=fact;

var s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 ;

run;

proc score data=Assign.Data score=fact out=scores;

var s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 ;

run;

ods graphics on;

procreg data=Scores;

model overall = Factor1 Factor2 factor3;

run;

ods graphics off;

Haver&Boecker is one of the world’s leading providers of filling and screening systems. The company operates a number of facilities in Germany, as well as production plants in the UK, Belgium, USA, Canada, and Brazil. It is a recognized specialist in the fields of weighing, filling, and material handling technology.

Haver&Boecker designs, produces, and markets systems and plants for filling and processing loose bulk materials of every type and, thus, solely operates in industrial markets. The company’s relationships with its customers are usually long-term oriented, and complex.

Since the company’s philosophy is to assist customers and business partners in solving technical problems and innovating new solutions, their products are often customized to the buyers’ needs. Therefore, the customer is no longer a passive buyer, but an active partner. Given this background, the customer’s satisfaction plays an important role in establishing, developing, and maintaining successful customer relationships.

Very early on, the company’s management realized the importance of customer satisfaction and decided to commission a market research project to identify marketing activities that can positively contribute to the business’s overall success. Based on a thorough literature review as well as interviews with experts, the company developed a short survey to explore their customers’ satisfaction with specific performance features and their overall satisfaction. All items were measured on 7-point scales with higher scores denoting higher levels of satisfaction. A standardized survey was mailed to customers in 12 countries worldwide, which yielded 281 fully completed questionnaires. The following items (names in parentheses) were listed in the survey:

• Reliability of the machines and systems (s1)
• Life-time of the machines and systems (s2)
• Functionality and user-friendliness operation of the machines and systems (s3)
• Appearance of the machines and systems (s4)
• Accuracy of the machines and systems (s5)
• Timely availability of the after-sales service (s6)
• Local availability of the after-sales service (s7)
• Fast processing of complaints (s8)
• Composition of quotations (s9)
• Transparency of quotations (s10)
• Fixed product prize for the machines and systems (s11)
• Cost/performance ratio of the machines and systems (s12)
• Overall, how satisfied are you with the supplier (overall)?
1. Using regression analysis, let us locate those variables that best explain the customers' overall satisfaction. The following tables represent the regression outputs from SAS:
SAS command:
 odsgraphicson; procreg; model overall = s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12; run; odsgraphicsoff;
 The SAS System
The REG Procedure Model: MODEL1 Dependent Variable: OVERALL overall
 Number of Observations Read 281 Number of Observations Used 281
 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model 12 198.91066 16.57589 15.69 <.0001 Error 268 283.07510 1.05625 Corrected Total 280 481.98577
 Root MSE 1.02774 R-Square 0.4127 Dependent Mean 5.00712 Adj R-Sq 0.3864 CoeffVar 20.5256
 Parameter Estimates Variable Label DF Parameter Estimate Standard Error t Value Pr > |t| Intercept Intercept 1 2.68730 0.22756 11.81 <.0001 S1 s1 1 0.17898 0.05198 3.44 0.0007 S2 s2 1 0.03091 0.04280 0.72 0.4709 S3 s3 1 0.05274 0.05177 1.02 0.3092 S4 s4 1 0.06009 0.05042 1.19 0.2344 S5 s5 1 0.02594 0.04602 0.56 0.5735 S6 s6 1 -0.00967 0.04832 -0.20 0.8416 S7 s7 1 -0.02486 0.04157 -0.60 0.5504 S8 s8 1 0.06262 0.04669 1.34 0.1810 S9 s9 1 0.06358 0.04729 1.34 0.1799 S10 s10 1 0.01909 0.04504 0.42 0.6720 S11 s11 1 -0.11662 0.04563 -2.56 0.0112 S12 s12 1 0.16684 0.04634 3.60 0.0004
From the regression coefficient table above, we notice that the variables s1,s11 and s12 are significantly associated with our dependent variable overallsince the p-values associated to the t-test are less than the 5% significance level (p-value<0.005) The coefficient of determination R-Square is of 0.4127 meaning that 41.27% of Overall (s12, how satisfied are you with the supplier (overall)?) variability is explained by the regression model Collinearity diagnostics The following table represent the calculations of VIF SAS command:
 odsgraphicson; procreg; model overall = s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12   / tolvifcollin; run; odsgraphicsoff;
 Parameter Estimates Variable Label DF Parameter Estimate Standard Error t Value Pr > |t| Tolerance Variance Inflation Intercept Intercept 1 2.68730 0.22756 11.81 <.0001 . 0 S1 s1 1 0.17898 0.05198 3.44 0.0007 0.36902 2.70989 S2 s2 1 0.03091 0.04280 0.72 0.4709 0.41655 2.40068 S3 s3 1 0.05274 0.05177 1.02 0.3092 0.44269 2.25890 S4 s4 1 0.06009 0.05042 1.19 0.2344 0.43494 2.29917 S5 s5 1 0.02594 0.04602 0.56 0.5735 0.51240 1.95160 S6 s6 1 -0.00967 0.04832 -0.20 0.8416 0.39505 2.53133 S7 s7 1 -0.02486 0.04157 -0.60 0.5504 0.52572 1.90214 S8 s8 1 0.06262 0.04669 1.34 0.1810 0.38187 2.61872 S9 s9 1 0.06358 0.04729 1.34 0.1799 0.36659 2.72783 S10 s10 1 0.01909 0.04504 0.42 0.6720 0.38487 2.59826 S11 s11 1 -0.11662 0.04563 -2.56 0.0112 0.50294 1.98829 S12 s12 1 0.16684 0.04634 3.60 0.0004 0.41761 2.39456
From the table above, the variance inflation coefficients are all smaller than 10 and hence we can securely confirm that we don’t have a multicollinearity problem in our regression model
1. Let us determine the factors that characterize the respondents by performing a factor analysis:
1. Before performing a factor analysis, it is recommended to check the FA assumptions
2. The following results were obtained using SAS:
SAS command:
 odsgraphicson; procfactordata=Assign.Data priors=smcmsa residual rotate=promaxreorder outstat=fact_all plots=(screeinitloadingspreloadings loadings); var s1  s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 ; run; odsgraphicsoff;
 Eigenvalues of the Reduced Correlation Matrix: Total = 6.84974007 Average = 0.57081167 Eigenvalue Difference Proportion Cumulative 1 4.99825280 3.87778870 0.7297 0.7297 2 1.12046410 0.32833702 0.1636 0.8933 3 0.79212708 0.29569712 0.1156 1.0089 4 0.49642996 0.21084773 0.0725 1.0814 5 0.28558224 0.32084982 0.0417 1.1231 6 -.03526758 0.02317729 -0.0051 1.1179 7 -.05844487 0.03761719 -0.0085 1.1094 8 -.09606207 0.01664101 -0.0140 1.0954 9 -.11270307 0.03596681 -0.0165 1.0789 10 -.14866989 0.03274139 -0.0217 1.0572 11 -.18141127 0.02914608 -0.0265 1.0307 12 -.21055735 -0.0307 1.0000
3 factors will be retained by the PROPORTION criterion.

As we can notice, the first three largest positive eigenvalues of the reduced correlation matrix account for 100.89% of the common variance.The scree and variance explained plots clearly support the conclusion that three common factors are present.

1. The following tables represent the quartimax rotation from type=factor
 The SAS System
The FACTOR Procedure Rotation Method: Quartimax
 Orthogonal Transformation Matrix 1 2 3 1 0.95280 0.23208 0.19575 2 -0.29862 0.83273 0.46626 3 -0.05480 -0.50270 0.86272
 Rotated Factor Pattern Factor1 Factor2 Factor3 S3 s3 0.76878 0.01891 0.01975 S1 s1 0.76676 0.08647 -0.17922 S6 s6 0.74527 -0.01233 0.20478 S2 s2 0.73721 -0.02689 -0.20578 S4 s4 0.72969 0.16241 -0.06462 S8 s8 0.69994 0.06638 0.26004 S5 s5 0.64419 0.15131 0.00818 S7 s7 0.59822 -0.14136 0.31048 S9 s9 0.31265 0.75647 0.13789 S10 s10 0.35498 0.73627 0.10118 S11 s11 0.27322 0.17054 0.65092 S12 s12 0.51801 0.14334 0.53542
 Variance Explained by Each Factor Factor1 Factor2 Factor3 4.6398200 1.2463468 1.0246772
 Final Communality Estimates: Total = 6.910844 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 0.62751549 0.58655527 0.59176624 0.56300275 0.43794391 0.59751792 0.47425167 0.56194856 0.68900934 0.67834519 0.52742980 0.57555786
From the rotated factor pattern, we can suggest labels for the factors extracted
• Factor1 : general characteristics of the machine and systems (variables s1, s2, s3, s4, s5, s6, s7 and s8)
• Factor2 : composition and transparency of quotations (variables s9 and s10)
• Factor3 : cost and prize of the machines and systems (variables s11,s12)
1. Goodness of fit
The FACTOR Procedure Initial Factor Method: Principal Factors
 Partial Correlations Controlling all other Variables S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S1 s1 1.00000 0.53364 0.08440 0.21083 -0.06904 0.02151 -0.05023 0.12656 0.04780 0.03591 -0.17162 0.19072 S2 s2 0.53364 1.00000 0.21205 0.02173 0.03700 0.08820 0.01627 0.00369 -0.12243 0.06437 -0.00185 -0.05719 S3 s3 0.08440 0.21205 1.00000 0.16996 0.21912 0.12463 0.04091 0.06178 0.01031 -0.04926 0.01954 0.09331 S4 s4 0.21083 0.02173 0.16996 1.00000 0.39920 0.02519 0.00325 0.02253 -0.03544 0.11584 -0.05966 0.09087 S5 s5 -0.06904 0.03700 0.21912 0.39920 1.00000 0.09408 0.08136 -0.07459 0.13282 -0.03575 -0.01364 0.03805 S6 s6 0.02151 0.08820 0.12463 0.02519 0.09408 1.00000 0.25105 0.40322 -0.04941 0.07276 0.00267 0.01977 S7 s7 -0.05023 0.01627 0.04091 0.00325 0.08136 0.25105 1.00000 0.32910 -0.14730 0.01204 0.07300 0.06058 S8 s8 0.12656 0.00369 0.06178 0.02253 -0.07459 0.40322 0.32910 1.00000 0.28431 -0.12448 0.03698 0.01487 S9 s9 0.04780 -0.12243 0.01031 -0.03544 0.13282 -0.04941 -0.14730 0.28431 1.00000 0.70788 0.13231 -0.09990 S10 s10 0.03591 0.06437 -0.04926 0.11584 -0.03575 0.07276 0.01204 -0.12448 0.70788 1.00000 -0.01613 0.12426 S11 s11 -0.17162 -0.00185 0.01954 -0.05966 -0.01364 0.00267 0.07300 0.03698 0.13231 -0.01613 1.00000 0.62577 S12 s12 0.19072 -0.05719 0.09331 0.09087 0.03805 0.01977 0.06058 0.01487 -0.09990 0.12426 0.62577 1.00000
 Kaiser's Measure of Sampling Adequacy: Overall MSA = 0.83846511 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 0.84308697 0.84677623 0.93908778 0.90005427 0.88364757 0.90375303 0.88854400 0.85856369 0.66694994 0.72117052 0.69422859 0.79622332
The data are appropriate for the common factor model, because the partial correlations (controlling all other variables) should are small compared to the original correlations
1. Let us use the factor scores and regress the customers' overall satisfaction (overall) on these. First we need to extract the first three factors then run a regression analysis.
SAS commands:
 procscoredata=Assign.Datascore=fact out=scores; var s1  s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 ; run; odsgraphicson; procregdata=Scores; model overall = Factor1 Factor2 factor3; run; odsgraphicsoff;
Results:
 The SAS System
The REG Procedure Model: MODEL1 Dependent Variable: OVERALL overall
 Number of Observations Read 281 Number of Observations Used 281
 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model 3 175.32101 58.44034 52.79 <.0001 Error 277 306.66476 1.10709 Corrected Total 280 481.98577

 Root MSE 1.05218 R-Square 0.3637 Dependent Mean 5.00712 Adj R-Sq 0.3569 CoeffVar 21.0138
 Parameter Estimates Variable Label DF Parameter Estimate Standard Error t Value Pr > |t| Intercept Intercept 1 5.00712 0.06277 79.77 <.0001 Factor1 1 0.76425 0.06288 12.15 <.0001 Factor2 1 -0.05840 0.06288 -0.93 0.3539 Factor3 1 -0.19663 0.06288 -3.13 0.0020
From the regression table we see that Factor1 and Factor3 are significantly associated with our dependent variable since their p-values associated to the t-test are less than 0.005 (5% significance level) but factor2 is not significant at the 5% significance level. The Coefficient of determination is of 0.3637 meaning that 36.37% is explained by the model.