State the Cell Means Model for two-factor studies with equal sample sizes and its important features. [10 marks]

b) The response time in milliseconds was determined for three different types of circuits in an electronic calculator. The results are recorded here. Circuit Type Response 1 19 22 20 18 25 2

20

21

33

27

40 3 16 15 18 26 17

i) Using = 0.01, test the hypothesis that the three circuit types have the same response time. [8 marks]

ii) Analyze the residuals from this experiment. [8 marks]

iii) Find a 95% confidence interval on the response time for circuit three. [3 marks]

QUESTION TWO [41 marks]

A study was performed on wear of a bearing Y and its relationship to X1 oil viscosity and X2 load. The following data were obtained. Y X1 X2 293 1.6 851

230

15.5

816 172 22.0 1058

91

43.0

1201 113 33.0 1357

125

40.0

1115

a) Fit a multiple linear regression model to these data. [12 marks]

b) Estimate 2 and the standard errors of the regression coefficients. [8 marks]

c) Use the model to predict wear when X1 = 25 and X2 = 1000. [1 mark]

d) Fit a multiple linear regression model with an interaction term to these data. [8 marks]

e) Estimate 2 and se ( ) for this new model. How did these quantities change? Does this tell you anything about the value of adding the interaction term to the model? [10 marks]

f ) Use the model in d) to predict when X1 = 25 and X2 = 1000. Compare this prediction with the predicted value from part b) above. [2 marks]