Question

A cookie shop conducted a study to determine the ideal cook time for their cookies along with the ideal temperature for their cookies. The goal was create a model to predict the customer Rating of the cookies based on both the time and the Temperature. The amount of cook time was recorded on a numerical scale ranging between 9 and 13 minutes. The temperature level was recorded as a categorical variable with 2 levels (325 and 350 degrees). The company collected 100 Ratings from the randomly selected customers. The customers were given a cookie with a predetermined combinations of cook time and temperature.
Y = Rating (between 0 and 100)
cook = Cook time (numerical recorded with units of minutes)
temp350 is an Indicator Variable for temperature level

temp350 = 1 if the Temperature is 350 degrees
temp350 = 0 if the Temperature is 325 degrees

JMP was used to produce the following estimated model.

	Estimate
Intercept	-24.1
cook	18.7
cook*cook	-0.84
temp350	-17.17

Report the predicted rating for a cookie baked at 9.5 minutes and at 350 degrees. Report your answer with at least 2 decimal places.

Answer 1

We have given JMP output.

	Estimate
Intercept	-24.1
cook	18.7
cook*cook	-0.84
temp350	-17.17

From the JMP output, the regression equation is

Rating=-24.1 +18.7*cook-0.84 *cook*cook-17.17*temp350

Rating For a cookie baked at 9.5 minutes and at 350 degrees

Rating =-24.1 +18.7*9.5-0.84 *9.5*9.5-17.17*0

=77.74

the predicted rating for a cookie baked at 9.5 minutes and at 350 degrees is 77.74