Variables and Effect

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.