{"id":152,"date":"2009-03-20T12:00:20","date_gmt":"2009-03-20T19:00:20","guid":{"rendered":"http:\/\/inkofpark.wordpress.com\/?p=152"},"modified":"2024-09-01T20:38:48","modified_gmt":"2024-09-02T02:38:48","slug":"coffee-analysis-results-of-the-response-surface","status":"publish","type":"post","link":"https:\/\/www.inkofpark.com\/?p=152","title":{"rendered":"Coffee: Analysis & Results of the Response Surface"},"content":{"rendered":"

I have executed the experiment design discussed Coffee: Design of the Experiments (Part 2: RSO)<\/a>. This “response surface method” experiment design is carefully crafted to provide the data necessary to fit a formula of the form<\/p>\n

q<\/em> = b<\/em>0<\/sub>T<\/em>2<\/sup> + b<\/em>1<\/sub>t<\/em>2<\/sup> + b<\/em>2<\/sub>r<\/em>2<\/sup> + b<\/em>3<\/sub>Tt<\/em> + b<\/em>4<\/sub>tr<\/em> + b<\/em>5<\/sub>Tr<\/em> + b<\/em>6<\/sub>T<\/em> + b<\/em>7<\/sub>t<\/em> + b<\/em>8<\/sub>r<\/em> + b<\/em>9
\n<\/sub><\/sub><\/p>\n

This model describes quadratic terms (T<\/em>2<\/sup>, t<\/em>2<\/sup>, r<\/em>2<\/sup>), main effects (T, t, r<\/em>), and first-order interactions (Tt, tr, Tr<\/em>). The model basically assumes that quality is locally curved or locally linear, but not an undulating surface. This assumption of local smoothness is a good one in this case\u2014were it not the experience of buying a cup of a coffee would be a dangerous gamble where small changes made by the brewer resulted in big changes in our cup.<\/p>\n

Some possible findings in our analysis<\/p>\n