Question

In: Math

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) 10 11 9 9 8 6 7 5
Cups of coffee (n) 1 1 2 2 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.

Solutions

Expert Solution

(a) the regression equation is given as  P=11.81-1.34*n

(b) correlation coefficient=r=0.98

(c) strong linear trend

(d) slope=-1.34, it means there will negative change/down in number of people  of 1.34 unit if there is increase in unit number of coffee and vice-versa

(e) intercept=11.81 means , if there will be no coffee then number of people will complain about the attitude is 11.81

(f) for n=10, P=11.81-1.34*10=-1.59

(g) it is not reasonable in part(f), as the number of estimated people should not be negative

(h) required number people can be estimated by the equation if we put P=0

P=11.81-1.34*n

or,11.81-1.34*n=0

or, n=11.81/1.34=8.8

answer is 8.8

following regression analysis information has been generated

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.980824
R Square 0.962016
Adjusted R Square 0.955686
Standard Error 0.427546
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 27.77823 27.77823 151.9632 1.74E-05
Residual 6 1.096774 0.182796
Total 7 28.875
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 11.80645 0.334718 35.27284 3.46E-08 10.98743 12.62548
n -1.33871 0.108597 -12.3273 1.74E-05 -1.60444 -1.07298

milcah answered 1 year ago
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