Question

A 22 factorial design was used to investigate the effects of stearate concentration and mixing time on the hardness of a tablet formulation. The results are presented in the attached table (Hardness vs time and stearate.mtw). Calculate the regression equation and present the ANOVA table. Test the main effects and interaction effect (ab) for significance. Graph the data and comment on whether or not the plots indicate the possible interaction between the effects or the mixing time and stearate concentration on hardness.

StdOrder	RunOrder	CenterPt	Blocks	Time	Stearate	Hardness
40	1	1	1	30	1	6.9
21	2	1	1	15	0.5	9.7
14	3	1	1	30	0.5	7.4
38	4	1	1	30	0.5	7.2
37	5	1	1	15	0.5	9.3
34	6	1	1	30	0.5	7.8
15	7	1	1	15	1	7.4
25	8	1	1	15	0.5	9.9
10	9	1	1	30	0.5	7.2
29	10	1	1	15	0.5	9.5
3	11	1	1	15	1	7.6
28	12	1	1	30	1	6.8
4	13	1	1	30	1	7.2
33	14	1	1	15	0.5	9.3
20	15	1	1	30	1	7
26	16	1	1	30	0.5	7.1
16	17	1	1	30	1	6.9
7	18	1	1	15	1	7.9
35	19	1	1	15	1	8
23	20	1	1	15	1	7.3
17	21	1	1	15	0.5	9.2
27	22	1	1	15	1	7.1
13	23	1	1	15	0.5	9.8
1	24	1	1	15	0.5	9.5
2	25	1	1	30	0.5	7.6
24	26	1	1	30	1	6.8
8	27	1	1	30	1	7.1
9	28	1	1	15	0.5	10
22	29	1	1	30	0.5	7.3
31	30	1	1	15	1	7
39	31	1	1	15	1	7.3
32	32	1	1	30	1	7.2
18	33	1	1	30	0.5	7
19	34	1	1	15	1	7.8
36	35	1	1	30	1	7.3
12	36	1	1	30	1	6.9
30	37	1	1	30	0.5	7.1
5	38	1	1	15	0.5	9.4
6	39	1	1	30	0.5	7.3
11	40	1	1	15	1	7.6

Answer 1

Solution...

The Regression Equation is:

Hardness = 11.67 - 0.091*Time - 2.35*Stearate

As the P value for Anova (significance F) is less than 0.05, so it can be stated that the data is statistically significant...

Time vs Stearate:

The correlation between the two variables is 0... So a significant relationship is not seen between them...

End of the Solution...