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Regression Analysis & Simulation: Understanding Basics & Notation

Explore regression analysis with simulation and understand basics like assumptions, motivating examples, regression output in Excel, multiple regression, and diagnostics. Learn how to interpret and analyze data effectively.

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Regression Analysis & Simulation: Understanding Basics & Notation

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  1. REGRESSION ANALYSISWITH A SIMULATION SPIN

  2. BASICS & NOTATION Input parameters 1, 2, …, n Values of each denoted X1, X2, Xn For each setting of X1, X2, Xn observe a Y Each set (X1, X2, 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

  3. BASICS • Assumptions • e is independent from sample to sample • e is independent of the X’s • e~N(0, s2) • So we will examine the “noise”

  4. 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

  5. EXPIRATION DEADLINES

  6. DAMAGE SCORE vs EXPIRATION DEADLINE

  7. REGRESSION OUTPUT(Excel) Y= 10.7 + .55 EXP Test for b= 0

  8. REGRESSION LINE } ERROR

  9. SERIAL RESIDUALS

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

  11. MULTIPLE REGRESSION Y=.39 + .81 LAZ + .19 DIST + .54 EXP

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

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