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.
RowX1X2X3 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 1-1-133.0 3-1 1-119.3 4 1 1-116.6 5-1-1 126.6 6 1-1 128.1 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 1-119.6 13 -1 -1 1 25.0 14 1-1 120.6 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.