An amateur brewer has made some experimental batches of beer with the aim of optimizing the taste of future batches. The brewer rates the beer on a scale of 0-10. Except for the brewing temperature, the brewer has already settled on the other aspects of the brewing process. These latest batches are meant to assist in the determination of an optional brewing temperature. The results of the brewers latest experiments are tabled below.
Let R(T) be the mean rating of temperature T
Use the data to estimate a quadratic equation between R(T) and T
On the basis of this relationship, suggest the optimal brewing temperature to the nearest 10th of a degree.
Temp 15 15 15 16 16 16 17 17 17 18 18
Rating 3 5 4 5 7 6 8 7 7 7 9
Temp 18 19 19 19 20 20 20 21 21 21
Rating 8 9 8 7 7 7 8 5 7 9