REGRESSION ANALYSIS WITH A SIMULATION SPIN BASICS NOTATION

REGRESSION ANALYSIS WITH A SIMULATION SPIN

BASICS & NOTATION �Input parameters 1, 2, …, n �Values of each denoted X 1, X 2, Xn �For each setting of X 1, X 2, Xn observe a Y �Each set (X 1, X 2, Xn , Y) is one observation �As we vary the X-values, Y changes in a linear (scaled proportional) manner �Some of the X’s don’t matter much, some are key

BASICS � Assumptions • e is independent from sample to sample • e is independent of the X’s • e ~N(0, s 2) � So we will examine the “noise”

MOTIVATING EXAMPLE: Close Air Support �Troops patrol their assigned area �Discover targets for destruction from the air �Call for CAS �May need an aircraft with laser-designation -capable weapons �May have a time deadline �Have a distance from the FARP to the target �Effects measured on 1. . 100 scale

EXPIRATION DEADLINES

DAMAGE SCORE vs EXPIRATION DEADLINE

REGRESSION OUTPUT(Excel) Regression Statistics Multiple R 0. 985 R Square 0. 97 Adjusted R Square Standard Error Observations Y= 10. 7 +. 55 EXP 0. 97 4. 744 100 ANOVA df Regression Residual Total Intercept X Variable 1 1 98 99 SS 71324 2206 73530 Coefficient Standard s Error 10. 74 0. 66 0. 551 0. 01 MS 71324 22. 51 Significanc F e. F 3169 2 E-76 Test for b=0 t Stat P-value Lower 95% Upper 95% 16. 28 1 E-29 9. 43 12. 05 56. 29 2 E-76 0. 532 0. 571

REGRESSION LINE } ERROR

SERIAL RESIDUALS 0. 5 0. 4 0. 3 0. 2 0. 1 0 0 -0. 1 -0. 2 -0. 3 -0. 4 -0. 5 20 40 60 80 100 120

MULTIPLE REGRESSION �Look at all of the independent variables �Builds the complex multidimensional function in n-space

MULTIPLE REGRESSION Regression Statistics Multiple R 0. 999985 R Square 0. 99997 Adjusted R Square 0. 999969 Standard Error 0. 157982 Observations 100 Y=. 39 +. 81 LAZ +. 19 DIST +. 54 EXP ANOVA df Regression SS MS 3 79706. 99 26569 Residual 96 2. 396011 0. 024958 Total 99 79709. 39 Coefficients Standard Error t Stat F 1064529 P-value Significance F 6. 9 E-217 Lower 95% Upper 95% Intercept 0. 392709 0. 041394 9. 487206 1. 88 E-15 0. 310543 0. 474874 X Variable 1 0. 812893 0. 031872 25. 50533 1. 52 E-44 0. 749629 0. 876158 X Variable 2 0. 185655 0. 000587 316. 3272 1. 1 E-146 0. 18449 0. 18682 X Variable 3 0. 535199 0. 000303 1768. 023 2 E-218 0. 534598 0. 5358

REGRESSION DIAGNOSTICS �Residuals that depend on one of the X’s �Residuals that have different variance at different values of an X