A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data:


People (P) 11 11 9 10 8 7 7 4
Cups of coffee (n) 1 1 2 3 3 4 4 5

Unless otherwise stated, you can round values to two decimal places.

a) Using regression to find a linear equation for P(n)

P(n)P(n) =    

b) Interpret the meaning of the slope of your formula in the context of the problem


c) Interpret the meaning of the P intercept in the context of the problem


d) Use your model to predict the number of people that will complain about his attitude if he drinks 9 cups of coffee.


e) Is the answer to part f reasonable? Why or why not?


f) How many cups of coffee should he drink so that no one will complain about his attitude? It is ok to round to one decimal place.


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1 Answer

G(a) P(n)=12.75-1.52n

(b) The slope means that for each cup of coffee, there’s a reduction of 1.52 complaints. This implies that for every two cups of coffee there are about three fewer complaints.

(c) There will be about 13 complaints (12.75 in the model) if he doesn’t drink any coffee.

(d) The complaints drop below zero if he drinks 9 cups of coffee. The model goes negative, so perhaps he gets compliments instead of complaints!

(e) Yes, this is reasonable, because the model predicts no complaints if he drinks 8 or 9 cups of coffee.

(f) P(n)=0, n=12.75/1.52=8.4 cups.

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