QUESTION
PART ONE
A researcher is interested in quantifying the relationship between the salary of a Board Member in a
company and other factors such as the size of the Board (including Executives and Nonexecutives), the
number of committees that the Board members are involved, Type of industry, and the level of success of
the company. To this end, he has compiled an Excel file (Data 2A_Assignment 2_S3 2019 LSBF.xls) that
contains 75 members of boards from public companies listed on ASX. The variables included are as follows:
SALARY Salary in $A
EXECUTIVES Number of EXECUTIVE board members
NONEXECUTIVES Number of NONEXECUTIVE board members
COMMITTEE Number of COMMITTEEs that board member is involved
TYPE TYPE of industry (1= Mining, 2 = Energy 3 = Financial Services, 4 =
Manufacturing, 5 = Utilities)
SUCCESS Level of SUCCESS (1= the worst, 5=the best)
Note that TYPE and SUCCESS are two categorical variables and four dummy variables for each of these
categorical variables are included in the data file. TYPE 1 and SUCCESS 1 are considered as the base level.
Use SPSS to conduct the regression analysis and inform the agent with regards to the results of the analysis. In
interpreting the SPSS results, you may have to answer the following questions.
(1) Using Ordinary Least Square (OLS) method estimate the regression model. The below is the
estimating model to help with model estimation (hint: use the estimated coefficients to write the regression
equation using the following model).
SALARY = β0 + β1 EXECUTIVES + β2 NONEXECUTIVES + β3 COMMITTES + β4 T2 +
β5 T3 + β6 T4 + β7 T5 + β8 S2 + β9 S3 + β10 S4 + β11 S5 + ε
(2) What are the a priori signs of the coefficients based on your experience or theories and are they the
same as the signs of the estimated coefficients from the model in the SPSS output? If you find that
the signs are not as you expected, you may need further explanations as to why this is the case.
(3) Interpret the meanings of slopes of this model and check whether these coefficients are significant.
(4) Use the adjusted R2 and CV to evaluate the goodness of fit of the model.
(5) Using ANOVA statistics check also whether the model is significant.
(6) Is there any evidence that the regression might have problems associated with multicollinearity, heteroskedasticity or nonnormality of the regression residuals?
(7) Using the regression model estimated, predict the SALARY of a board member in a company with 4
Executives, 2 Nonexecutives, 5 Committees, Industry Type of 3, and a Success level of 4.
PART TWO
A large number of decisions involved in the consumer lending business require the application of models
that are based on personal characteristics including marital status, age, income and other factors. The file
Data 2B_Assignment2_S3 2019 LSBF.xls has been compiled with 150 observations from a random
sample of borrowers who are in fulltime or parttime employment.
The bank of Victoria’s lending manager wants to develop a credit risk model that distinguishes between
populations of good and bad borrowers. The good borrower pays principal and interest on time. The bad
borrower may default a part or the full payment of principal and interest. The survey that is used to compile
the data file dealt with whether respondents are good or bad borrowers and their attitudes towards the bank
loan. The following variables are included:
Borrower 1 if the borrower is a good borrower, 0 otherwise
Age age in years
Income borrower’s annual earnings in $K
Marital 1 if the person is married, 0 otherwise
Profession 1 if the borrower is in fulltime employment, 0 otherwise
Gender 1 = male, 0 = female
Borrowers are also asked their responses to six statements concerning the loan. The statements and the
variable names are:
Cheaper “It is cheaper to borrow from the bank of Victoria than to borrow from the other
banks.”
Mode “I am willing to apply for online borrowing mode if available.”
Useful “Online applications are useful to people who surf the Internet frequently.”
Informative “I gain a lot of information from reading the PDS (Product Disclosure Statement)
of the loan.”
Payment “I borrow from the bank that charges application fee of not more than $100.”
Current “Consumer loan supports my daily life.”
The responses to the attitudinal questions are coded as follows:
1 = strongly disagree
2 = disagree
3 = no view either way
4 = agree
5 = strongly agree
Use SPSS to perform a discriminant analysis in which the dependent variable is BORROWER and the
independent variables are AGE, INCOME, MARITAL, PROFESSION, and GENDER.
(8) Hold out the last 50 observations from the analysis.
(9) Generate means, univariate ANOVAs, unstandardised function coefficients, withingroups
correlations and a summary table.
(10) Estimate the discriminant function and analyse all tables in your report.
(11) Using the discriminant function estimated in your analysis, determine whether the person with the
following characteristics is likely to be a good borrower or otherwise:
A 45 years old married male in parttime employment and earns an annual income of $55,000.
PART THREE
Use SPSS to perform a factor analysis of the six attitudinal variables and analyse all tables in your report.
(12) Produce univariate descriptive statistics and correlation coefficients. Use principal components to
extract the factors and varimax to rotate the factors. Also produce a scree plot and identify the factors.
(13) Save the factors and use them in a discriminant analysis together with the independent variables
AGE, INCOME, MARITAL, PROFESSION, and GENDER.
(14) Does using the factors improve the discriminant analysis?, Explain why?
Presentation: General guidelines
1. Your assignment must be presented on Microsoft Word. Copy and paste all SPSS output to this
MS Word document. Make sure the document is a single sided print.
2. You are required to write the report to suit the academic standards.
3. Attach an assignment declaration with your name and ID numbers clearly written.
4. All tables and figures should contain a title that clearly explains the content.
5. SPSS tables, once copied to word file should be formatted to suite the presentation of report.
6. Interpretations should be precise and you are required to use the plain language
7. Assignments without interpretations will attract low marks.
8. An electronic copy of the assignment should be submitted to the drop box in VUC Space of the
unit.
9. Download the similarity report and attach the report to the hard copy of your assignment.
10. Submit the hard copy of the assignment personally to your tutor for marking. This must be securely
stapled in the top left hand corner.
(Data 2A_Assignment 2_S3 2019 LSBF.xls)(Excel File)
Salary  EXECUTIVES  NONEXECUTIVES  COMMITTEE  T2  T3  T4  T5  S2  S3  S4  S5 
367000  2  1  2  1  0  0  0  1  0  0  0 
368000  3  1  3  1  0  0  0  1  0  0  0 
368000  3  1  3  1  0  0  0  1  0  0  0 
369000  2  1  3  1  0  0  0  0  1  0  0 
372000  4  2  5  1  0  0  0  1  0  0  0 
375000  2  1  3  0  1  0  0  0  0  1  0 
376000  2  1  2  1  0  0  0  0  1  0  0 
376900  3  1  3  1  0  0  0  0  1  0  0 
377000  2  3  5  1  0  0  0  0  1  0  0 
378000  2  1  2  0  1  0  0  1  0  0  0 
379000  3  2  3  1  0  0  0  0  1  0  0 
380000  3  1  2  1  0  0  0  0  1  0  0 
380000  3  1  2  1  0  0  0  0  1  0  0 
381000  2  1  3  0  1  0  0  0  1  0  0 
382000  3  1  3  1  0  0  0  0  1  0  0 
383000  3  1  3  1  0  0  0  0  1  0  0 
384000  3  1  3  1  0  0  0  1  0  0  0 
384000  3  1  3  1  0  0  0  0  1  0  0 
386250  4  2  3  0  0  0  0  0  0  1  0 
387000  3  2  2  0  1  0  0  0  1  0  0 
389500  3  2  2  0  1  0  0  1  0  0  0 
390400  4  2  4  1  0  0  0  0  0  1  0 
390500  3  1  3  0  1  0  0  0  1  0  0 
391000  3  2  3  0  1  0  0  0  1  0  0 
391500  4  2  3  0  1  0  0  0  0  0  0 
391500  4  2  3  0  1  0  0  0  0  0  0 
392500  3  1  4  0  0  0  1  0  1  0  0 
393500  3  2  3  1  0  0  0  0  1  0  0 
393500  4  2  2  1  0  0  0  0  1  0  0 
394000  3  1  3  0  0  0  0  1  0  0  0 
395500  3  2  2  0  1  0  0  0  1  0  0 
396000  3  2  3  1  0  0  0  0  0  1  0 
396000  3  2  3  1  0  0  0  0  1  0  0 
397900  3  2  3  0  1  0  0  0  0  1  0 
398000  3  2  3  0  1  0  0  0  0  1  0 
398000  3  2  4  1  0  0  0  0  0  1  0 
398000  3  2  3  0  1  0  0  0  0  1  0 
399000  4  2  4  1  0  0  0  0  1  0  0 
399000  4  2  4  0  1  0  0  1  0  0  0 
399000  3  2  3  0  1  0  0  0  1  0  0 
402000  4  2  3  0  1  0  0  0  1  0  0 
402000  3  1  3  1  0  0  0  0  1  0  0 
402000  4  2  3  0  0  0  1  0  1  0  0 
402000  3  1  3  0  1  0  0  0  0  1  0 
403000  3  2  3  0  1  0  0  0  1  0  0 
403000  3  1  2  0  1  0  0  1  0  0  0 
403500  3  2  5  0  1  0  0  1  0  0  0 
403500  3  2  5  0  0  0  1  0  1  0  0 
405000  3  2  5  0  1  0  0  0  1  0  0 
405000  3  1  3  0  0  0  1  0  0  1  0 
408000  3  2  3  1  0  0  0  0  0  1  0 
412000  4  2  4  0  1  0  0  1  0  0  0 
412500  3  2  4  0  1  0  0  0  0  1  0 
414900  5  2  3  1  0  0  0  1  0  0  0 
415500  4  2  3  0  1  0  0  0  0  1  0 
420500  3  2  4  0  0  1  0  0  0  0  1 
422000  3  3  4  1  0  0  0  1  0  0  0 
425500  4  2  3  0  1  0  0  0  1  0  0 
427000  3  2  4  1  0  0  0  0  0  1  0 
428000  3  2  4  0  0  1  0  0  0  1  0 
429900  4  2  3  0  1  0  0  0  0  1  0 
430350  3  2  4  0  1  0  0  0  1  0  0 
432350  3  2  4  0  1  0  0  0  0  1  0 
433000  3  2  4  0  1  0  0  0  1  0  0 
434500  3  2  3  0  0  1  0  0  1  0  0 
435500  3  3  3  0  1  0  0  0  1  0  0 
435500  3  3  3  0  0  1  0  0  1  0  0 
436500  3  2  4  0  0  1  0  0  0  1  0 
436500  3  2  4  0  0  1  0  0  1  0  0 
437400  4  2  4  0  1  0  0  0  1  0  0 
437400  4  2  4  0  0  1  0  0  1  0  0 
437500  3  2  4  0  0  1  0  0  0  1  0 
439500  4  2  4  0  1  0  0  0  0  1  0 
444000  4  2  5  0  0  1  0  0  1  0  0 
445000  3  2  3  0  0  1  0  0  1  0  0 
(Data 2B_Assignment2_S3 2019 LSBF.xls)(Excel File)
BORROWER  Age  Income  Marital  Profession  Gender  Informative  Current  Cheaper  Mode  Payment  Useful 
1  37  56  1  0  0  2  1  1  1  2  3 
0  24  42  0  1  1  2  2  1  5  4  5 
1  33  51  1  0  1  2  1  2  4  4  4 
0  30  40  0  1  0  1  2  1  4  4  5 
1  38  48  1  0  0  2  1  5  4  5  5 
1  32  52  1  0  1  1  2  1  4  3  4 
0  25  43  0  0  1  1  1  1  4  4  4 
1  32  62  1  0  0  2  2  5  5  3  5 
1  35  51  0  1  1  5  4  5  2  2  3 
1  38  48  0  0  1  3  2  2  3  3  4 
1  33  54  1  1  0  3  2  2  3  2  3 
1  42  50  1  0  1  2  1  3  3  3  3 
1  33  61  1  1  1  2  2  4  4  4  4 
0  31  42  0  1  0  1  2  4  4  4  4 
1  34  49  1  0  1  1  1  3  3  3  3 
0  24  54  1  1  1  1  1  2  4  2  4 
1  46  51  0  1  1  5  4  2  4  2  5 
0  30  48  0  1  0  1  2  3  5  3  5 
1  37  55  1  0  1  3  3  1  5  1  5 
1  44  65  0  0  0  5  5  2  2  2  2 
0  28  52  1  0  0  1  1  1  5  1  5 
1  30  77  1  0  1  4  4  2  3  2  3 
1  28  49  1  0  0  1  1  2  3  2  3 
1  35  57  0  0  1  5  4  4  3  4  4 
0  31  36  1  0  0  2  3  2  5  2  5 
1  43  57  0  1  1  1  5  4  5  4  5 
1  42  49  1  1  1  5  3  3  4  3  5 
0  25  51  1  0  1  2  3  5  5  5  5 
0  30  33  1  1  1  5  4  4  4  4  4 
1  32  59  1  0  1  4  3  2  4  2  5 
0  30  38  0  0  1  3  3  3  5  3  5 
1  38  45  1  0  0  2  1  3  3  3  2 
1  39  54  0  0  0  2  3  3  5  3  5 
0  25  42  1  0  1  4  3  3  3  3  1 
1  41  49  0  1  1  2  2  4  3  4  3 
1  39  44  0  0  1  3  3  4  1  4  1 
0  26  61  1  0  1  2  2  4  5  4  4 
0  22  53  0  0  1  1  1  4  3  4  3 
1  36  54  1  0  1  5  3  3  2  3  1 
1  45  60  0  0  1  4  5  5  4  5  4 
0  28  59  1  0  1  1  1  1  5  1  5 
1  30  55  1  0  1  3  3  5  4  5  4 
0  38  54  0  0  1  2  2  4  5  4  5 
1  39  56  1  0  1  2  2  2  4  2  4 
0  30  48  0  0  0  1  2  1  5  1  5 
0  33  36  1  0  0  1  1  3  4  3  5 
1  39  51  0  0  1  5  4  2  4  2  4 
0  38  57  0  1  1  1  1  5  5  5  5 
0  28  44  1  0  0  2  2  4  2  4  1 
1  40  44  0  0  0  4  4  5  5  5  1 
0  35  52  0  0  1  2  2  2  4  2  4 
0  32  54  1  0  1  1  1  4  5  4  5 
1  45  70  0  0  1  2  3  1  5  1  5 
1  31  44  1  0  0  2  2  3  1  3  2 
1  42  51  0  1  0  3  3  1  1  1  1 
1  38  50  1  0  1  5  5  3  5  3  5 
1  40  50  1  1  1  2  2  5  1  5  1 
1  33  44  1  1  1  2  3  5  3  5  3 
1  33  52  0  0  1  2  2  1  5  1  5 
0  40  36  1  0  1  2  2  1  5  2  5 
0  37  50  1  0  1  5  4  3  5  3  5 
0  33  59  0  0  1  2  2  3  4  3  4 
0  37  51  0  0  1  3  3  2  4  3  4 
1  38  53  1  0  1  2  2  4  3  3  4 
0  32  39  1  0  1  1  2  5  1  3  2 
1  44  50  0  0  0  3  3  3  4  4  4 
0  38  41  1  0  0  1  1  5  4  3  4 
0  33  48  0  0  0  4  4  2  4  3  4 
0  30  42  0  1  1  3  3  1  5  3  5 
1  35  40  1  0  1  1  2  1  3  3  5 
1  29  48  1  0  1  1  2  3  1  3  1 
0  33  56  0  0  1  2  1  5  4  3  4 
0  33  47  1  0  1  2  1  4  1  3  5 
0  38  37  1  0  0  1  1  4  3  3  3 
0  28  48  0  0  0  1  2  5  5  3  5 
1  31  61  1  0  1  1  2  5  3  2  3 
0  29  41  1  0  1  2  1  3  5  3  5 
0  30  58  0  0  1  1  2  5  4  3  5 
1  31  58  1  0  1  2  2  3  4  3  4 
0  34  40  0  0  0  2  2  2  4  4  5 
1  33  38  1  1  1  2  2  1  3  3  3 
0  28  57  1  0  1  5  3  3  4  3  4 
0  28  54  0  0  0  3  3  3  4  3  5 
0  30  44  1  0  1  5  1  1  1  3  5 
1  36  47  0  1  0  3  2  3  1  3  2 
0  37  42  1  0  1  3  3  1  4  3  4 
0  35  48  0  0  1  2  2  2  3  3  3 
1  43  56  0  1  1  3  3  4  2  3  5 
0  40  34  1  0  0  1  1  1  5  2  5 
1  35  48  1  0  1  4  4  2  4  3  4 
1  38  51  0  0  1  4  5  3  1  3  2 
0  36  47  0  0  1  5  2  3  2  3  2 
1  30  51  1  0  1  4  4  5  3  3  3 
1  28  54  1  0  1  1  2  4  1  3  1 
1  35  52  1  0  1  1  1  1  3  5  3 
0  31  45  0  0  1  4  4  4  5  3  4 
1  40  52  1  0  1  2  3  1  2  3  2 
0  31  53  1  0  1  1  2  5  4  3  4 
1  31  46  1  0  0  3  3  2  2  3  1 
0  23  49  0  1  1  1  2  4  3  3  4 
0  35  38  1  0  0  2  1  1  1  4  2 
1  25  44  0  0  1  3  2  1  5  3  4 
1  36  55  1  0  1  2  1  2  4  3  4 
0  31  47  0  1  0  1  2  1  4  3  4 
0  40  45  1  0  0  2  1  5  4  3  4 
1  35  51  1  0  1  1  2  1  4  2  4 
0  28  48  0  0  1  1  1  1  4  3  4 
1  34  62  1  0  0  3  2  5  5  3  4 
1  39  51  0  1  1  5  4  5  2  3  2 
0  35  48  0  0  1  3  2  2  3  3  3 
1  33  54  1  0  0  3  2  2  3  3  3 
1  42  50  1  0  1  2  1  3  3  3  3 
1  33  61  1  0  1  2  2  4  3  3  3 
0  31  46  1  0  1  1  2  4  3  3  3 
1  34  49  1  0  1  2  1  3  3  3  3 
0  24  54  0  1  0  1  1  2  4  3  4 
1  46  51  1  0  1  5  4  2  4  3  5 
0  30  48  1  1  0  1  2  3  5  4  4 
1  37  55  1  0  1  3  3  1  4  3  5 
1  44  65  0  0  1  5  5  2  2  3  2 
0  28  52  1  0  1  2  1  1  5  3  5 
1  30  77  1  0  1  4  4  2  3  2  3 
0  28  49  1  0  0  2  1  2  3  3  3 
1  35  57  0  0  1  5  4  4  3  3  4 
0  31  36  1  0  0  2  3  2  5  3  4 
1  43  57  0  1  1  1  5  4  5  3  5 
0  42  49  0  1  0  4  3  3  4  3  4 
1  25  51  0  0  0  2  3  5  5  3  5 
0  30  33  0  1  1  5  4  4  4  3  5 
1  32  59  1  0  1  4  3  2  4  3  5 
0  30  38  0  0  1  3  3  3  5  5  5 
1  38  45  1  0  0  2  1  3  3  3  2 
1  39  54  0  0  0  2  3  3  5  4  5 
0  25  42  1  0  1  4  3  3  3  2  3 
1  41  49  0  1  1  2  2  4  3  3  3 
1  39  44  0  0  1  3  3  4  1  3  1 
0  26  61  1  0  1  2  2  4  5  3  4 
0  22  53  0  0  1  1  1  4  3  3  3 
1  36  54  1  0  1  5  3  3  2  3  1 
1  45  60  0  0  1  4  5  5  4  3  4 
1  28  59  1  0  1  1  1  1  5  3  5 
1  30  55  1  0  1  3  3  5  4  3  4 
0  38  54  0  0  1  2  2  4  5  3  4 
1  39  56  1  0  1  2  2  2  4  2  4 
0  30  48  1  0  0  1  2  1  5  3  5 
0  33  36  1  0  0  1  1  3  4  3  5 
1  39  51  1  0  1  5  4  2  4  3  4 
0  38  57  0  1  1  1  1  5  5  3  5 
1  28  44  1  0  0  2  2  4  2  3  2 
1  40  44  1  0  0  4  4  5  5  3  5 
ANSWER
Part ONE
(1)
The following is the result of the regression:
Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 

B 
Std. Error 
Beta 

1  (Constant) 
312574.128 
17208.492 
18.164 
.000 

Executives 
9339.975 
2731.768 
.258 
3.419 
.001 

NONEXECUTIVES 
9154.166 
3345.334 
.228 
2.736 
.008 

COMMITTEE 
2705.949 
2137.446 
.100 
1.266 
.210 

T2 
1011.466 
9520.493 
.022 
.106 
.916 

T3 
15139.793 
9488.188 
.347 
1.596 
.116 

T4 
40065.857 
10439.446 
.631 
3.838 
.000 

T5 
9352.708 
11428.170 
.097 
.818 
.416 

S2 
18391.783 
10018.505 
.332 
1.836 
.071 

S3 
23575.602 
9687.212 
.546 
2.434 
.018 

S4 
27631.944 
9813.240 
.566 
2.816 
.006 

S5 
10707.963 
16558.871 
.057 
.647 
.520 

a. Dependent Variable: Salary 
The following is the final equation:
SALARY = 312574.128 + 9339.975 EXECUTIVES + 9154.166 NONEXECUTIVES + 2705.949 COMMITTEE + 1011.466 T2 + 15139.793 T3 + 40065.857 T4 + 9352.708 T5 + 18391.783 S2 + 23575.602 S3 + 27631.944 S4 + 10707.963 S5
(2)
My experience and theory says that the a priori signs of all the coefficients should be positive and same is the case. The following is the rationale for expecting the signs to be positive:
(Constant) : there should be a base level positive salary which the board member receives
EXECUTIVES: A larger pool of executive members in the board generally indicates a larger company and thus higher salaries
NONEXECUTIVES: A larger pool of nonexecutive members in the board generally indicates a larger company and thus higher salaries
COMMITTEE: More committees means more responsibilities, a more important role and added salaries for being part of the committees
T2T5: All the other industries should have more salary than mining
S2S5: A better success should directly translate to a higher salary
(3)
The slope of EXECUTIVES, NONEXECUTIVES and COMMITTEE represents the incremental increase in salary over the base salary that a board member gains as the value of these variables increases. On the contrary T2T5 and S2S5 are categorical dummy variables and hence only one in each group is equal to one at max. Their slopes represent the increment in salary over the base values when one has a specific success level or type of industry.
Coefficients^{a} 

Model 
Sig. 

Executives 
.001 

NONEXECUTIVES 
.008 

COMMITTEE 
.210 

T2 
.916 

T3 
.116 

T4 
.000 

T5 
.416 

S2 
.071 

S3 
.018 

S4 
.006 

S5 
.520 

a. Dependent Variable: Salary 
At a confidence level of 95% EXECUTIVES, NONEXECUTIVES, T4, S3 and S4 have significant coefficients.
(4)
Model Summary 

Model 
R 
R Square 
Adjusted R Square 
Std. Error of the Estimate 
1 
.843^{a} 
.711 
.660 
12663.78909 
a. Predictors: (Constant), S5, T5, Executives, S4, T3, COMMITTEE, S2, T4, NONEXECUTIVES, T2, S3 
The adjusted R^{2} value for the model is 0.660. It means that 66% of variation in the salary of the board members can be explained by the variables that have been used un the model. The value is fairly high and we can say that the model is a good fit.
(5)
The following is the ANOVA output for the model
ANOVA^{b} 

Model 
Sum of Squares 
df 
Mean Square 
F 
Sig. 

1  Regression 
2.485E10 
11 
2.259E9 
14.085 
.000^{a} 
Residual 
1.010E10 
63 
1.604E8 

Total 
3.495E10 
74 

a. Predictors: (Constant), S5, T5, Executives, S4, T3, COMMITTEE, S2, T4, NONEXECUTIVES, T2, S3  
b. Dependent Variable: Salary 
We can see that the significance level is 0 and the F statistic is 14.085 which is lower than the critical F value. Thus, the model is significant.
(6)
The r squared value of the model is 0.711 whereas the adjusted r square is 0.66. Thus, there is evidence that the model is having problems with multicollinearity of the variables however the difference is low. The regression does not seem to have problems with heteroskedasticity or nonnormality of the regression residuals.
(7)
The predicted salary is as follows:
Salary = 312574.128 + 9339.975*4 + 9154.166*2+ 2705.949*5 + 15139.793 + 27631.944
= 424543.842
Part B
(8)
The following is the output of the discriminant analysis after holding out the last 50 records:
Discriminant
Analysis Case Processing Summary 

Unweighted Cases 
N 
Percent 

Valid 
100 
100.0 

Excluded  Missing or outofrange group codes 
0 
.0 
At least one missing discriminating variable 
0 
.0 

Both missing or outofrange group codes and at least one missing discriminating variable 
0 
.0 

Total 
0 
.0 

Total 
100 
100.0 
Group Statistics 

BORROWER 
Mean 
Std. Deviation 
Valid N (listwise) 

Unweighted 
Weighted 

0  AGE 
31.2128 
4.64822 
47 
47.000 
INCOME 
46.9149 
7.45954 
47 
47.000 

MARITAL 
.4894 
.50529 
47 
47.000 

PROFESSION 
.1915 
.39773 
47 
47.000 

GENDER 
.6809 
.47119 
47 
47.000 

1  AGE 
36.3962 
4.84109 
53 
53.000 
INCOME 
52.4340 
6.90738 
53 
53.000 

MARITAL 
.6415 
.48415 
53 
53.000 

PROFESSION 
.2453 
.43437 
53 
53.000 

GENDER 
.7358 
.44510 
53 
53.000 

Total  AGE 
33.9600 
5.39532 
100 
100.000 
INCOME 
49.8400 
7.65377 
100 
100.000 

MARITAL 
.5700 
.49757 
100 
100.000 

PROFESSION 
.2200 
.41633 
100 
100.000 

GENDER 
.7100 
.45605 
100 
100.000 
Tests of Equality of Group Means 

Wilks’ Lambda 
F 
df1 
df2 
Sig. 

AGE 
.768 
29.645 
1 
98 
.000 
INCOME 
.869 
14.752 
1 
98 
.000 
MARITAL 
.976 
2.361 
1 
98 
.128 
PROFESSION 
.996 
.413 
1 
98 
.522 
GENDER 
.996 
.360 
1 
98 
.550 
Pooled WithinGroups Matrices 

AGE 
INCOME 
MARITAL 
PROFESSION 
GENDER 

Correlation  AGE 
1.000 
.078 
.297 
.031 
.072 
INCOME 
.078 
1.000 
.138 
.132 
.233 

MARITAL 
.297 
.138 
1.000 
.235 
.060 

PROFESSION 
.031 
.132 
.235 
1.000 
.016 

GENDER 
.072 
.233 
.060 
.016 
1.000 
Analysis 1
Standardized Canonical Discriminant Function Coefficients 

Function 

1 

AGE 
.870 
INCOME 
.662 
MARITAL 
.603 
PROFESSION 
.281 
GENDER 
.060 
Structure Matrix 

Function 

1 

AGE 
.652 
INCOME 
.460 
MARITAL 
.184 
PROFESSION 
.077 
GENDER 
.072 
Pooled withingroups correlations between discriminating variables and standardized canonical discriminant functions
Variables ordered by absolute size of correlation within function. 
Canonical Discriminant Function Coefficients 

Function 

1 

AGE 
.183 
INCOME 
.092 
MARITAL 
1.220 
PROFESSION 
.672 
GENDER 
.132 
(Constant) 
11.570 
Unstandardized coefficients 
Functions at Group Centroids 

BORROWER 
Function 
1 

0 
.887 
1 
.786 
Unstandardized canonical discriminant functions evaluated at group means 
Classification Statistics
Classification Processing Summary 

Processed 
100 

Excluded  Missing or outofrange group codes 
0 
At least one missing discriminating variable 
0 

Used in Output 
100 
Prior Probabilities for Groups 

BORROWER 
Prior 
Cases Used in Analysis 

Unweighted 
Weighted 

0 
.470 
47 
47.000 
1 
.530 
53 
53.000 
Total 
1.000 
100 
100.000 
Classification Results^{a} 

BORROWER 
Predicted Group Membership 
Total 

0 
1 

Original  Count  0 
33 
14 
47 
1 
12 
41 
53 

%  0 
70.2 
29.8 
100.0 

1 
22.6 
77.4 
100.0 

a. 74.0% of original grouped cases correctly classified. 
Summary of Canonical Discriminant Functions
Eigenvalues 

Function 
Eigenvalue 
% of Variance 
Cumulative % 
Canonical Correlation 
1 
.712^{a} 
100.0 
100.0 
.645 
a. First 1 canonical discriminant functions were used in the analysis. 
Wilks’ Lambda 

Test of Function(s) 
Wilks’ Lambda 
Chisquare 
df 
Sig. 
1 
.584 
51.327 
5 
.000 
(9)
Means, univariate ANOVAs, unstandardized function coefficients, withingroups correlations and a summary table has been generated and displayed above.
(10)
The discrimination function is as follows:
Function = 11.570 + .183 AGE + .092 INCOME + 1.220 MARITAL + . 672 PROFESSION – .132 GENDER
The following is the analysis of all the tables:
 The group statistics shows the mean and standard deviation of the variables in each of the groups
 Test of equality means shows that only Age and Income are significant discriminants for classifying a borrower
 Pooled within group matrix shows the within group correlation of the variables
 We have a high eigen value and a good correlation showing that 64.5% of the results are properly explained by our discriminants
 Wilks’ Lambda shows that we have a significant equation in the discriminant analysis just performed.
 Standardised canonical discriminant function coefficients shows that Age and Income are leading to the maximum change in the final decision.
 The Structure matrix supports our notion from the canonical discriminant function as Age leads to 65.2% of total variation in the results and Income causes 46% of the total variation.
 Then we have the unstandardized coefficients which actually forms our discriminant equation.
 The centroids of the groups is what we compare the result of the discriminant equation with.
 The classification results show that 29.8% of the borrowers predicted as bad are actually good and similarly we predict the good borrowers incorrectly about 22.6% of times.
(11)
The value of the discriminant function for the given data is as follows:
Function = 11.570 + .183*45 + .092*55 + 1.220 – .132 = 2.813
The person is likely to be good borrower
Part C
(12)
The following are the outputs:
Descriptive Statistics 

Mean 
Std. Deviation 
Analysis N 

Informative 
2.4500 
1.35121 
100 
Current 
2.3900 
1.11821 
100 
Cheaper 
2.9400 
1.39856 
100 
Mode 
3.5400 
1.29817 
100 
Payment 
3.0600 
.99311 
100 
Useful 
3.7500 
1.30558 
100 
Correlation Matrix 

Informative 
Current 
Cheaper 
Mode 
Payment 
Useful 

Correlation  Informative 
1.000 
.705 
.018 
.123 
.043 
.125 

Current 
.705 
1.000 
.086 
.041 
.015 
.085 

Cheaper 
.018 
.086 
1.000 
.071 
.534 
.141 

Mode 
.123 
.041 
.071 
1.000 
.018 
.736 

Payment 
.043 
.015 
.534 
.018 
1.000 
.105 

Useful 
.125 
.085 
.141 
.736 
.105 
1.000 

Communalities 

Initial 
Extraction 

Informative 
1.000 
.855 

Current 
1.000 
.867 

Cheaper 
1.000 
.767 

Mode 
1.000 
.880 

Payment 
1.000 
.768 

Useful 
1.000 
.864 

Extraction Method: Principal Component Analysis.  
Total Variance Explained 

Component 
Initial Eigenvalues 
Extraction Sums of Squared Loadings 
Rotation Sums of Squared Loadings 

Total 
% of Variance 
Cumulative % 
Total 
% of Variance 
Cumulative % 
Total 
% of Variance 
Cumulative % 

1 
1.926 
32.097 
32.097 
1.926 
32.097 
32.097 
1.745 
29.080 
29.080 

2 
1.629 
27.144 
59.241 
1.629 
27.144 
59.241 
1.710 
28.492 
57.572 

3 
1.446 
24.094 
83.335 
1.446 
24.094 
83.335 
1.546 
25.763 
83.335 

4 
.467 
7.786 
91.121 

5 
.324 
5.392 
96.513 

6 
.209 
3.487 
100.000 

Extraction Method: Principal Component Analysis. 
Component Matrix^{a} 

Component 

1 
2 
3 

Informative 
.566 
.725 
.097 
Current 
.511 
.726 
.280 
Cheaper 
.386 
.404 
.674 
Mode 
.705 
.342 
.516 
Payment 
.306 
.438 
.694 
Useful 
.777 
.323 
.394 
Extraction Method: Principal Component Analysis.  
a. 3 components extracted. 
Rotated Component Matrix^{a} 

Component 

1 
2 
3 

Informative 
.110 
.916 
.060 
Current 
.031 
.928 
.068 
Cheaper 
.074 
.038 
.872 
Mode 
.938 
.002 
.008 
Payment 
.016 
.029 
.875 
Useful 
.920 
.080 
.107 
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization. 

a. Rotation converged in 4 iterations. 
Component Transformation Matrix 

Component 
1 
2 
3 
1 
.756 
.550 
.354 
2 
.367 
.805 
.467 
3 
.542 
.223 
.810 
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization. 
Three factors have been identified and have been saved. The following are the analysis of the tables:
 Descriptive Statistics gives us an overview of the attitude variables
 The correlation matrix gives us the correlation of the variables. We can see that current is highly correlated with Informative and mode is correlated with Useful.
 Communalities table gives us the final extraction values for different variables
 The total variance explained table gives us the amount of variance each new factor is explaining
 We are using the scree plot to determine the number of variables to choose. We decide to keep 3 variables
 The component matrix shows the contribution of each variable in the 3 factors
 The rotated component matrix rotated the factors to be perpendicular to each other.
 The component transfer matrix can be multiplied to variables to get the factors.
(13)
The following is the output of the discriminant analysis conducted with the factors:
Discriminant
Analysis Case Processing Summary 

Unweighted Cases 
N 
Percent 

Valid 
100 
100.0 

Excluded  Missing or outofrange group codes 
0 
.0 
At least one missing discriminating variable 
0 
.0 

Both missing or outofrange group codes and at least one missing discriminating variable 
0 
.0 

Total 
0 
.0 

Total 
100 
100.0 
Group Statistics 

BORROW 
Mean 
Std. Deviation 
Valid N (listwise) 

Unweighted 
Weighted 

0  REGR factor score 1 for analysis 1 
.3833560 
.80887912 
47 
47.000 
REGR factor score 2 for analysis 1 
2.8151511E1 
.89411798 
47 
47.000 

REGR factor score 3 for analysis 1 
.0374858 
.93041676 
47 
47.000 

AGE 
3.1212766E1 
4.64821691 
47 
47.000 

INCOME 
4.6914894E1 
7.45954244 
47 
47.000 

MARITAL 
.4893617 
.50529115 
47 
47.000 

PROFESSION 
.1914894 
.39772712 
47 
47.000 

GENDER 
.6808511 
.47118643 
47 
47.000 

1  REGR factor score 1 for analysis 1 
3.3995724E1 
1.03654756 
53 
53.000 
REGR factor score 2 for analysis 1 
.2496455 
1.03028695 
53 
53.000 

REGR factor score 3 for analysis 1 
3.3242105E2 
1.06567352 
53 
53.000 

AGE 
3.6396226E1 
4.84108865 
53 
53.000 

INCOME 
5.2433962E1 
6.90738021 
53 
53.000 

MARITAL 
.6415094 
.48414634 
53 
53.000 

PROFESSION 
.2452830 
.43437224 
53 
53.000 

GENDER 
.7358491 
.44509910 
53 
53.000 

Total  REGR factor score 1 for analysis 1 
7.1054274E17 
1.00000000 
100 
100.000 
REGR factor score 2 for analysis 1 
1.5987212E16 
1.00000000 
100 
100.000 

REGR factor score 3 for analysis 1 
3.1086245E17 
1.00000000 
100 
100.000 

AGE 
3.3960000E1 
5.39532158 
100 
100.000 

INCOME 
4.9840000E1 
7.65377044 
100 
100.000 

MARITAL 
.5700000 
.49756985 
100 
100.000 

PROFESSION 
.2200000 
.41633320 
100 
100.000 

GENDER 
.7100000 
.45604802 
100 
100.000 
Tests of Equality of Group Means 

Wilks’ Lambda 
F 
df1 
df2 
Sig. 

REGR factor score 1 for analysis 1 
.868 
14.857 
1 
98 
.000 
REGR factor score 2 for analysis 1 
.929 
7.489 
1 
98 
.007 
REGR factor score 3 for analysis 1 
.999 
.124 
1 
98 
.726 
AGE 
.768 
29.645 
1 
98 
.000 
INCOME 
.869 
14.752 
1 
98 
.000 
MARITAL 
.976 
2.361 
1 
98 
.128 
PROFESSION 
.996 
.413 
1 
98 
.522 
GENDER 
.996 
.360 
1 
98 
.550 
Pooled WithinGroups Matrices 

REGR factor score 1 for analysis 1 
REGR factor score 2 for analysis 1 
REGR factor score 3 for analysis 1 
AGE 
INCOME 
MARITAL 
PROFESSION 
GENDER 

Correlation  REGR factor score 1 for analysis 1 
1.000 
.108 
.014 
.138 
.194 
.101 
.022 
.068 

REGR factor score 2 for analysis 1 
.108 
1.000 
.010 
.231 
.080 
.272 
.020 
.165 

REGR factor score 3 for analysis 1 
.014 
.010 
1.000 
.031 
.007 
.048 
.114 
.097 

AGE 
.138 
.231 
.031 
1.000 
.078 
.297 
.031 
.072 

INCOME 
.194 
.080 
.007 
.078 
1.000 
.138 
.132 
.233 

MARITAL 
.101 
.272 
.048 
.297 
.138 
1.000 
.235 
.060 

PROFESSION 
.022 
.020 
.114 
.031 
.132 
.235 
1.000 
.016 

GENDER 
.068 
.165 
.097 
.072 
.233 
.060 
.016 
1.000 
Analysis 1
Standardized Canonical Discriminant Function Coefficients 

Function 

1 

REGR factor score 1 for analysis 1 
.574 
REGR factor score 2 for analysis 1 
.256 
REGR factor score 3 for analysis 1 
.013 
AGE 
.741 
INCOME 
.645 
MARITAL 
.534 
PROFESSION 
.260 
GENDER 
.077 
Structure Matrix 

Function 

1 

AGE 
.525 
REGR factor score 1 for analysis 1 
.372 
INCOME 
.370 
REGR factor score 2 for analysis 1 
.264 
MARITAL 
.148 
PROFESSION 
.062 
GENDER 
.058 
REGR factor score 3 for analysis 1 
.034 
Pooled withingroups correlations between discriminating variables and standardized canonical discriminant functions
Variables ordered by absolute size of correlation within function. 
Canonical Discriminant Function Coefficients 

Function 

1 

REGR factor score 1 for analysis 1 
.613 
REGR factor score 2 for analysis 1 
.264 
REGR factor score 3 for analysis 1 
.013 
AGE 
.156 
INCOME 
.090 
MARITAL 
1.080 
PROFESSION 
.623 
GENDER 
.169 
(Constant) 
10.410 
Unstandardized coefficients 
Functions at Group Centroids 

BORROW 
Function 
1 

0 
1.101 
1 
.976 
Unstandardized canonical discriminant functions evaluated at group means 
Classification Statistics
Classification Processing Summary 

Processed 
100 

Excluded  Missing or outofrange group codes 
0 
At least one missing discriminating variable 
0 

Used in Output 
100 
Prior Probabilities for Groups 

BORROW 
Prior 
Cases Used in Analysis 

Unweighted 
Weighted 

0 
.470 
47 
47.000 
1 
.530 
53 
53.000 
Total 
1.000 
100 
100.000 
Classification Results^{a} 

BORROW 
Predicted Group Membership 
Total 

0 
1 

Original  Count  0 
39 
8 
47 
1 
7 
46 
53 

%  0 
83.0 
17.0 
100.0 

1 
13.2 
86.8 
100.0 

a. 85.0% of original grouped cases correctly classified. 
Summary of Canonical Discriminant Functions
Eigenvalues 

Function 
Eigenvalue 
% of Variance 
Cumulative % 
Canonical Correlation 
1 
1.097^{a} 
100.0 
100.0 
.723 
a. First 1 canonical discriminant functions were used in the analysis. 
Wilks’ Lambda 

Test of Function(s) 
Wilks’ Lambda 
Chisquare 
df 
Sig. 
1 
.477 
69.598 
8 
.000 
(14)
We can see that the correlation in the eigenvalues table has increased from 66% to 72% percent which suggests that there is an increase in the amount of variation that is now explained. Also, the false positive and false negative rate has decreased to 17% and 13.2% respectively. Thus, the discriminant analysis has definitely increased. One reason can be attributed to the fact that the attitude of the person does affect his/her ability to payback their debt.
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