# Regression: ANOVA

An experiment was conducted to investigate the effect of four treatments, A, B, C and D on the yield of penicillin in a manufacturing process. It was necessary to use a different blend for each application if the four treatments. The results of the yields for this randomised block experiment are given in the table below.

Construct an ANOVA table to analysis these data to determine whether the treatment affect the yield.

Blend A B C D

1 89 88 97 94

2 84 77 92 79

3 81 87 87 85

4 87 92 89 84

5 79 81 80 88

? Construct an ANOVA table to analysis these data to determine whether the treatment affect the yield.

? Also, give a 95% confidence interval for the standard deviation of the 'errors'.

See attached for full question.

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#### Solution Preview

An experiment was conducted to investigate the effect of four treatments, A, B, C and D on the yield of penicillin in a manufacturing process. It was necessary to use a different blend for each application if the four treatments. The results of the yields for this randomised block experiment are given in the table below.

Construct an ANOVA table to analysis these data to determine whether the treatment affect the yield.

Hence, fill in the missing values, denoted (**) in the GLIM report below (I have been given the solutions that I have included in red, please show me manually, showing all working, that those answers are correct).

Also, give a 95% confidence interval for the standard deviation of the 'errors'.

Blend A B C D

1 89 88 97 94

2 84 77 92 79

3 81 87 87 85

4 87 92 89 84

5 79 81 80 88

Blend A B C D

1 89 88 97 94

2 84 77 92 79

3 81 87 87 85

4 87 92 89 84

5 79 81 80 88 Grand total

Total=T i= 420 425 445 430 1720

ni= 5 5 5 5 20

Total number of treatments=k= 4

Null Hypothesis: H0: u1=u2=u3=u4 (All population means are equal)

Research (Alternative) Hypothesis: H1: At least two of the population means are different

1) Calculation of CM

CM= correction for mean=( total of all observations )^2 / n = ( sigma yi )^2 / n

total of all ...

#### Solution Summary

The solution provides a regression analysis. Also ANOVA table is prepared.