Question

In: Statistics and Probability

A particular professor has noticed that the number of people, P, who complain about his attitude...

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 12 10 9 6 6 6 4 Cups of coffee (n) 1 1 2 2 3 3 4 5 Unless otherwise stated, you can round values to two decimal places. Parts d), e) and g) will not be graded by the computer; they will be graded manually. a) Using regression to find a linear equation for P(n). Give your answer in the form y = a + b x y = a + b x . Be sure to use the variable n n . P ( n ) P ( n ) = b) Find the correlation coefficient r 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? 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.

Solutions

Expert Solution

a)

The regression equation is:

y =13.11 - 1.95x

P(n) =13.11 - 1.95n

b)

The correlation coefficient, r = -0.95

c)

The correlation coefficient indicates a strong linear trend.

d)

Slope = -1.95

This means that the number of people who complain (P) decreases by 1.95 with every 1 increase in number of cups of coffee he drinks (n).

e)

P-intercept =13.11

This means that number of people who complain (P) is 13.11 when the number of cups of coffee he drinks (n) is 0.

f)

n =8

The number of people that will complain about his attitude =P =13.11 - 1.95(8) = -2.49

g)

The answer to part f is not reasonable because the number of people cannot be negative.

h)

No one will complain about his attitude =P =0

P =13.11 - 1.95n n =(13.11 - P)/1.95 =(13.11 - 0)/1.95 =13.11/1.95 =6.7

6.7 cups of coffee he should drink so that no one will complain about his attitude.

orchestra answered 1 year ago
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