Regression

Term Project-Catapult

Experimental Design

The purpose of this experiment is to determine the settings required to reach an unknown distance, T. The known variables include:

1. Response Variable T = distance

2. Factor 1: relative location of the fulcrum

3. Factor 2: Angle at which the base is set

4. Factor 3: Input material variable

In the final portion of the experiment, each team is allowed five trials to reach an unknown distance, T. Since a 23 Design Matrix results in eight observations, it makes it hard to choose the correct five combinations. Fractional factorial design matrix of 2(3-1) is used to result in four combinations allowed to reach the unknown distance, T. This matrix is shown in Table 1.1.

Table 1.1 Fraction of a Design Matrix for a 23 Design

Four treatments in the 23 matrix were selected by ignoring the effects of ABC. Since all the values of ABC are +, the effects of ABC are unknown in this experiment. This this experiment, ABC will be referred to as the generator. This defining relation is I=+ABC since the intercepts from the regression model are equivalent.

The columns that have identical entries correspond to effects referred to as confounded. The estimate of the A effect is confounded with the BC interaction. The estimate of the B effect is confounded with the AC interaction. The estimate of the C effect is confounded with the AB interaction. These effects cannot be different as change is shown when the same pattern is applied.