1. An experiment was designed to see what factors affect the cleaning ability of a washing solution. Three factors were used in the experiment - the concentration of detergent, concentration of sodium carbonate, and concentration of sodium carboxymethyl cellulose. A larger value of the response indicates better cleaning ability. Three replicates of the experiment were used. The results were:
Det. Sodium Carb. Sodium Carb. Cellulose Results
-1 -1 -1 106, 93, 116
1 -1 -1 198, 200, 214
-1 1 -1 197, 202, 185
1 1 -1 329, 331, 307
-1 -1 1 149, 169, 135
1 -1 1 243, 247, 220
-1 1 1 255, 230, 252
1 1 1 383, 360, 364
a. Estimate the main effects and interactions. Make sure you clearly indicate to me which values are the estimates.
b. Carry out a complete analysis, indicating exactly what is significant and why, as well as a discussion about whether the assumptions are being met.