Given the following sums of the measured data for a 2 replic

Given the following sums of the measured data for a 2 replicate (n=2) 2³ factorial experiment:

a) Place the above data in their appropriate locations in a table

b) Calculate the main and interaction effects.

c) Calculate the confidence intervals for the main and interaction effects and determine which effects are significant. (alpha = 0.05)

d) Write down the regression model for the above experiment. What is the value predicted by this model for S = 1800 rpm, F = 40 N and T = 100 ^oC?

Comment

T=30\"C T 30 °C T= 100 \"C Tz 100 °C S 900 rpm S 1800 rpm 26 29 29 35 32

ANSWER OF PART(b)

using the yates algorithm the main and different interaction effects are

2.In the yield column enter the total yields for each treatment combination.

3.Fill in as many columns headed by Roman numerals as there are factors in the experiment in the following way.

a.Add successive pairs in the previous column. (1st +2nd), (3rd + 4th) etc

b.Subtract successive pairs in the previous column (2nd - 1st), (4th - 3rd) etc

4.To obtain entries in column II repeat steps 3a and 3b on the entries of column I.

5.To obtain entries in column III repeat steps 3a and 3b on the entries of column II

6.Continue in this way until as many columns have been filled as factors.

7.Square the effect total (entry in last column).

8.Divide the result by the number of observations r2^k (here replication r=2 , number of factor k=3 i.e. T,F,S)

ANSWER OF PART (c)

since the replicated data is not available therefore difficult to calculate error sum of squre for further calculation.

ANSWER OF PART (d)

The regression model for the above data is

Response= 12.405+0.0643T*+0.117F*+0.0067S* (* significant at 5%)

value predicted by this model for S = 1800 rpm, F = 40 N and T = 100 ^oC

is given by 12.405+0.0643x100+0.117x40+0.0067x1800=35.07

ANSWER OF PART (a)