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 12.3 minutes and at 350 degrees. Report your answer with at least 2 decimal places.

Answer 1

Here' the answer to the question. please write back in case you've doubts.

Lets use the linear regression coefficient and the values of the predictors given in the question to sovle the problem

The predicted rating will be = - 24.1 + 18.7*Cook - 0.84*Cook^2 - 17.17*temp350

Now substitute the value of Cook = 12.3 minutes, temp350 = 1 , as we have to calculate for 350 degrees.

Predicted Rating, Y' = - 24.1 + 18.7*12.3 - 0.84*12.3^2 - 17.17*1

Predicted Rating = 61.66

Answer: 61.66