This document presents the results of a study analyzing factors that affect mortgage approval times. A multiple linear regression model was developed to predict approval times based on credit history, mortgage size, region, and their interactions. The model found some factors had significant effects on approval times individually and through interactions. The document recommends further studies using additional variables and a larger sample size to identify stronger interactions affecting approval times.

1. CASE STUDY 2
Mortgage Approval Time Study
Sherry Manning
Dr. Eliette Barrios
Business Statistics
MAT 510
11/21/2019

2. MODEL EQUATION AND INTERPRETATION
Ŷ =𝛽0 + 𝛽1 𝑋1 + 𝛽2x2 + 𝛽3 𝑋3 + 𝛽4X1X2 + 𝛽5 𝑋1 𝑋3 + 𝛽6X2X3+𝛽7X1X2X3
Factors’ Interactions
Y-intercept
Using the model complete the interpretation and importance
Y = 141.35 + 24.78X1 + 19.082X2 + 9.933X3 + 16.764X1X2 + -0.335X1X3 + 1.386X2X3 + -1.837X1X2X3

3. Approval Times
Run Credit History (X1) Mortgage Size (X2) Region (X3) X1X2 X1X3 X2X3 X1X2X3 Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Average Standard Deviation
1 Good <$500,000 Western + + + - 59 50 64 62 47 56.4 7.503332593
2 Fair <$500,000 Western - - + + 81 58 69 65 74 69.4 8.734987121
3 Good >$500,000 Western - + - + 38 52 58 60 65 54.6 10.38267788
4 Fair >$500,000 Western + - - - 146 159 133 143 129 142 11.78982612
5 Good <$500,000 Eastern + - - + 28 26 38 41 21 30.8 8.408329204
6 Fair <$500,000 Eastern - + - - 42 53 40 50 64 49.8 9.602083107
7 Good >$500,000 Eastern - - + - 49 31 49 42 38 41.8 7.661592524
8 Fair >$500,000 Eastern + + + + 106 115 126 118 138 120.6 12.07476708
Sum+ 381.8 359 243 349.8 281.4 288.2 275.4
Sum- 183.6 206.4 322.4 215.6 284 277.2 290
Avg+ 95.45 89.75 60.75 87.45 70.35 72.05 68.85
Avg- 45.9 51.6 80.6 53.9 71 69.3 72.5
Effect 49.55 38.15 19.85 33.55 -0.65 2.75 -3.65
Design of Experiments uses a multifactorial approach employing statistical methodologies to both design and analyze an
experimental process says Singleton, Gilman, Rollit, Zhang, Parker, & Love, (2019).

4. Regression Coefficients
b0= 141.35
b1= 24.775
b2= 19.075
b3= 9.925
b4= 16.775
b5= -0.325
b6= 1.375
b7= -1.825
The Regression Coefficient is the constant b in the regression equation.

5. INTERACTIONS GRAPHS AND INTERPRETATION
Credit History Low High
Good (-) 30.8 56.4
Fair(+) 49.8 142
0
100
200
Low High
AxisTitle
Credit History
High Low Chart
Good (-) Fair(+)

6. Interactions graphs and interpretation
Mortgage Size Low High
<$500,000 30.8 69.4
>$500,000 41.8 142
Mortgage Size Low High
<$500,000 30.8 69.4
>$500,000 41.8 142
30.8
69.441.8
142
0
100
200
300
Low High
Mortgage
<$500,000 >$500,000

7. Interactions graphs and interpretation
Region Low High
Western 54.6 142
Eastern 30.8 120.6
0
100
200
300
Low High
Region
Western Eastern

8. ANALYSIS OF THE SAMPLE SIZE
 Objective – Agreement must be obtained to ensure success.
 Output variables Identify the output or measure the process performance.
 Identify the levels of input to be studied.
 Verify the available resources for the size of the experiment.
Time – the amount of time for the number of tests performed and when the results are needed.
Funds – How much money to spend depends on the amount spent on personnel and the
experimentation. No more than 20% should be spent on the first experiment.
.

9. VARIABLES OF INTEREST TO MEASURE
AND STUDY
 Annual Salary
 Marital Status
 Criminal Background Check
 Debt to Earnings Ratio

10. ANALYSIS OF THE SAMPLE SIZE
 Replication - replicating some or all of the experiment is important as it
increases the sensitivity of the experiment. By doing so assists us in
detecting smaller differences.
 Randomization – Running a test in an experiment in a random order. This
guards against any unknown changes that may have occurred during the
conduct of the experiment.
 The planning t the results f the test. Will the data be collected electronically or manually.
Researched by Hoerl and Snee (2012).

11. INTERACTIONS BETWEEN DOE WITH 3
FACTOR EXPERIMENT
Factorial experiments enable us to identify interactions and is a three-factor experiment. The three possible
two factor interactions are (x1x2, x1x3, x2x3) and one three factor interaction (x1x2x3). Although they are rarely
important in real applications, a three factor interaction would mean that the interaction of x1 and x2 is
dependent on the level of x3 .
Researched by Hoerl and Snee (2012).

12. RECOMMENDATIONS AND
CONCLUSION OF THE DOE
 Use the annual salary, marital status, background checks and debt to earnings ratio instead of
just the credit check, region and mortgage size.
 Use other sample times for the approval rate because the interaction effect charts have mild
interaction instead of strong interaction.
 Use different sample numbers because the effect numbers, which are the difference between
the avg(+) minus the avg(-), are below 20 and some are negative numbers.

13. REFERENCES
Singleton, C., Gilman, J., Rollit, J., Zhang, K., Parker, D. A., & Love, J. (2019). A design of experiments approach for the rapid
formulation of a chemically defined medium for metabolic profiling of industrially important microbes.
PLoS ONE, 14(6), 1–18. https://doi.org/10.1371/journal.pone.0218208
Hoerl, R., Snee, Ron. (2012) Statistical Thinking, Improving Business Performance. Hoboken, New Jersey: John Wiley & Sons, Inc.