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

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

Data/Models (t=3, bullet type, n i =9 layers per bullet type)

Model 1 – Individual Intercepts/Slopes

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

Model 1 – Matrix Formulation

Model 2 – Matrix Formulation

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.

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?

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

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

Bartlett’s Test of Equal Variances MSE