An experiment was conducted to determine whether either firing temperature or fu

Question

An experiment was conducted to determine whether either firing temperature or furnace position affects the baked density of a carbon electrode. The data are as follows: (a) Estimate the effects of different factors (i.e., position and temperature) and their standard errors for this design. (b) Construct two-factor interaction plots and comment on the interaction of the factors. (c) Use the t ratio to determine the significance of each effect with alpha = 0.05. (d) Build the regression model for coded variables (i.e., "-1" and "+1"). (e) Perform the residual analysis and model checking.

Explanation / Answer

The means and standard devns of the matrix of variables are

                                      800C                                                       825 C

Posn

1                                         572.7,sd 7.59                   1062, sd 15.12

2                                          532 sd 10.98                       1006    15.58

The two factor plots for temp and position are shown, there are no cross overs

t ratios: at 800 : ( 572.62 - 532)/(10.98/sqrt 3 7.587/sqrt 3) = 20.24 ( wrt posn)

t ratio 825    ( 1062-1006)/( 15.58-15.12)/sqrt3 = 365.2

t ratio posn 1 ( 490.3)sqrt(3)/ 7.53 = 112.7

t ratio posn 2 ( 474/4.6)*sqrt3 =178

These are very large t differences for rowss and columns hence little chance of dependence

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