Four factors are thought to influence the taste of the dietary product: A - type of sweetener; B - fruit content; C – percentage fat matter; D – temperature. A full factorial experiment was conducted with these 4 factors. At each run in the design, samples of the dietary product were tested by panel of experts who rated the taste on a scale from 1 to 10, the response variable taken being the sum of individual ratings. The results are listed in the table below, in the standard order of runs. Generate the design for this experiment, analyse the results by producing main effects and interactions plots and discuss the most significant factors that can be used to find a formulation that maximises the total score.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Four factors are thought to influence the taste of the dietary product: A - type of sweetener; B –
fruit content; C – percentage fat matter; D - temperature. A full factorial experiment was
conducted with these 4 factors. At each run in the design, samples of the dietary product were
tested by panel of experts who rated the taste on a scale from 1 to 10, the response variable
taken being the sum of individual ratings. The results are listed in the table below, in the
standard order of runs.
Generate the design for this experiment, analyse the results by producing main effects and
interactions plots and discuss the most significant factors that can be used to find a formulation
that maximises the total score.
Run (std order)
1
2
4
7
8
10
11
12
13
14
15
16
Total score
169
178
168
176
185
189
183
189
174
197
173
195
178 207
180
204
Transcribed Image Text:Four factors are thought to influence the taste of the dietary product: A - type of sweetener; B – fruit content; C – percentage fat matter; D - temperature. A full factorial experiment was conducted with these 4 factors. At each run in the design, samples of the dietary product were tested by panel of experts who rated the taste on a scale from 1 to 10, the response variable taken being the sum of individual ratings. The results are listed in the table below, in the standard order of runs. Generate the design for this experiment, analyse the results by producing main effects and interactions plots and discuss the most significant factors that can be used to find a formulation that maximises the total score. Run (std order) 1 2 4 7 8 10 11 12 13 14 15 16 Total score 169 178 168 176 185 189 183 189 174 197 173 195 178 207 180 204
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