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) 12 10 9 8 4 4 4 4

Cups of coffee (n) 1 2 2 3 4 4 5 5

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

a) Using Google Sheets to find a linear equation for P. P = 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 8 cups of coffee. g) Is the answer to part f reasonable? Why or why not?

Answer 1

a) Regression equation is y=-2.1129x+13.7419

i.e. People = -2.1129 * Cups of coffee + 13.7419

b) the correlation coefficient r =0.9613

c) the correlation coefficient indicate a strong linear trend

d) Interpretation for slope

If the cups of coffee increase by 1 unit then model predicts People decreases approximately by

-2.1129

e)Interpretation for intercept

If the cups of coffee is 0 then model predicts that the people is approximately will be 13.7419

f)

Substitute x=8 into regression equation

=> y = -2.1129*8 + 13.7419

=-3.16

g) I think it is not reasonable. Since is 8 is considered to be outlier for given regression .