Business statistics

Question

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)	10	12	9	10	7	5	6	6
Cups of coffee (n)	1	1	2	2	3	4	5	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 = _____

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

1. strong linear trend
2. weak linear trend
3. 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. ________

Answer 1

Hi Salma,

To get the regression line, you need either a TI-83 Plus, an online calculator, or statistical software. The formula to compute that manually is very complex and error-prone. I made errors with it myself while working with another student.

From online calculator--make sure you put cups of coffee on x axis and complaints on y axis:

A. P(n)= -1.371n + 12.066

B. Same goes with the correlation coefficient--manual formula involves squares and sums of squares for eight data points--it gets cumbersome. I'll use a calculator and help you interpret the correlation coefficient we get:

r= -0.9096

This indicates a strong linear trend. General cutoffs are, in absolute value, 0.1-0.3 is weak trend, 0.4-0.6 is moderate trend, and 0.7 or above is strong trend. 0.9096 certainly qualifies as strong.

D. For every cup of coffee the professor drinks, he will get 1.371 fewer complaints.

E. For p-intercept, typically designated as y-intercept, this is the value of the equation when x (or n, in this case) is 0. So, the p-intercept, 12.066, is the number of complaints the professor would get if he drank no coffee at all.

F. Just plug 10 in for n in regression equation:

P(n)= -1.371n + 12.066

P(10)= -1.371(10) + 12.066

P(10)= -13.71 + 12.066

P(10)= -1.644

G. No. There is no such thing as a negative number of complaints.

H. This is similar to above--plug 0 in for P:

0= -1.371n + 12.066

Add 1.371n on both sides:

1.371n=12.066

Divide by 1.371 on both sides:

n=8.9

In practice, he might go straight to 9 cups, but 8.9 is accurate to one decimal. I hope this helps.