1. Experiments with Bullet Proof Panels and Various Bullet Types
R.A. Prosser, S.H. Cohen, and R.A. Segars (2000). "Heat as a Factor of Cloth Ballistic Panels by 0.22 Caliber Projectiles," Textile Research Journal, Vol. 70: pp

2. Data Description
Response: V50 – The velocity at which approximately half of a set of projectiles penetrate a fabric panel (m/sec)
Predictors:
Number of layers in the panel (2,6,13,19,25,30,35,40)
Bullet Type (Rounded, Sharp, FSP)
Transformation of Response: Y* = (V50/100)2
Two Models:
Model 1: 3 Dummy Variables for Bullet Type, No Intercept
Model 2: 2 Dummy Variables for Bullet Type, Intercept

3. Data/Models (t=3, bullet type, ni=9 layers per bullet type)

4. Model 1 – Individual Intercepts/Slopes

5. Model 2 – Dummy Coding (Sharp (j=2), FSP (j=3))

6. Model 1 – Matrix Formulation

7. Model 2 – Matrix Formulation

8. Equations Relating Y to #Layers by Bullet Type
Note: Both models give the same lines (ignore rounding for Sharp). Same lines would be obtained if Baseline Category had been Sharp or FSP.

9. Tests of Hypotheses
Equal Slopes: Allowing for Differences in Bullet Type Intercepts, is the “Layer Effect” the same for each Bullet Type?
Equal Intercepts (Only Makes sense if all slopes are equal): Controlling for # of Layers, are the Bullet Type Effects all Equal?
Equal Variances: Do the error terms of the t = 3 regressions have the same variance?

10. Testing Equality of Slopes
Complete Models (Both 1 and 2)
Reduced Models (Both 1 and 2)
Conclude Slopes are not all equal
Model 2
Model 2

12. Testing Equality of Intercepts – Assuming Equal Slopes
Note: Does not apply to this problem, just providing formulas.

13. Bartlett’s Test of Equal Variances
MSE