ISE 525 Design of Experiments Exam #1
Spring Semester 2020 2/20/20

Name: ______________________________________________

1. The data below was collected to investigate a particular system.

Row X1 X2 X3 Y
1 2.7 8.9 9.5 60.1
2 2.3 6.0 8.4 48.3
3 5.6 5.6 2.7 35.1
4 8.1 5.3 3.0 37.0
5 4.1 6.5 2.8 34.6
6 1.9 8.8 5.8 55.5
7 7.6 9.7 2.1 45.6
8 8.2 8.8 2.9 43.1
9 1.8 7.0 3.3 35.9

(30) 1.a) For the model Y = 0 + 2X2 + , find values for 0,2 using
the matrix form of the parameter estimation equation.
Also, calculate the MSE for the model. Note: X2Y = 3003.55

(30) 1.b) For the model Y = 0 + 3X3 + , find values for 0,3 using
the matrix form of the parameter estimation equation.
Also, calculate the MSE for the model. Note: X3Y = 1940.44

(15) 1.c) For the model Y = 0 + 1X1 + , the estimated values of 0,1
are 49.92 and -1.28, respectively. Also, MSE = 85.49.
Based upon your results for MSE in 1.a) and 1.b), which
of the three models would be selected first in the forward
selection procedure? Explain.

2. The data below was obtained for a particular experiment.

Row A B C Y
1 -1 -1 -1 34.5
2 1 -1 -1 33.0
3 -1 1 -1 19.3
4 1 1 -1 16.6
5 -1 -1 1 26.6
6 1 -1 1 28.1
7 -1 1 1 5.5
8 1 1 1 4.4
9 -1 -1 -1 28.7
10 1 -1 -1 27.9
11 -1 1 -1 22.8
12 1 1 -1 19.6
13 -1 -1 1 25.0
14 1 -1 1 20.6
15 -1 1 1 0.6
16 1 1 1 5.6

(25) 2.a) Calculate the sum of squares for the BC interaction.
Given that SSE = 82.58, perform a hypothesis test to determine
whether or not the BC interaction is statistically significant.

(20) 2.b) Write a regression model that predicts the response based upon
the factor B main effect, factor C main effect, and the
BC interaction effect. Note: Y = 318.8

(20) 2.c) In the original experiment, the following design variables and
settings were studied.

Temperature (Factor A): 80, 120
Air Flow Rate (Factor B): 0, 50
Heating Time (Factor C): 17, 22

Use your model from part 2.b) to predict the response when
Temperature = 100, Air Flow Rate = 20, Heating Time = 19.  