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.

Question

From eight days of tracking he compiled the following data:

People (P) 12,10,8,8,7,5,4,2

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) =

b) Find the correlation coefficient

r =

c) Does the correlation coefficient indicate a strong linear trend, a weak linear trend, or no linear trend?

• strong linear trend

• weak linear trend

• no linear trend

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

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

f) Use your model to predict the number of people that will complain about his attitude if he drinks 10 cups of coffee.

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

h) 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.

Answers using a calculator are welcome as long as they have explanations of how they are found please.

Answer 1

You will need to have Excel sheet and put in the data points by column. One column should be the number of people complained and another column is the number of cups of coffee.

a.) Go to Data Analysis and click on Regression. You should have number of people complained as the y-value and the number of cups of coffee as the x-value.

P(n) = 13.1848739495798 - 2.15126050420168*n

b.) Correlation Coefficient: r = 0.930274812627754

c.) This is a strong linear trend because r is closed to +1. There is a strong relationship between the number of cups of coffee and the number of people complained about their teacher's attitude.

d.) For every cup of coffee drank, about 2 people complained less about their teacher's attitude.

e.) If the teacher didn't drink any cups of coffee to start with, then about 13 people will complain about the teacher's attitude.

f.) P(10) = 13.1848739495798 - 2.15126050420168*(10) = -8.327731092437

If he drinks 10 cups of coffee, then 8 people will complain less about his attitude.

g.) This is not reasonable because you can't have a negative number of people complaining.

h.) 13.1848739495798 - 2.15126050420168*n = 0

- 2.15126050420168*n = -13.1848739495798

n = 6.128906249999987071533203124996

He should drink about 6 cups of coffee so that no one will complain about his teacher.