Question 1204980: 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 9 10 6 6 5 3 5
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 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 9 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 by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i used the regression calculator at https://stats.blue/Stats_Suite/correlation_regression_calculator.html
there are many such calculators online.
some are a little too brief.
some are too detailed.
thsi one appeared to be right for the problem at hand as it gives just enough information to answer the question.
a) Using regression to find a linear equation for P(n).
the linear equation is y = −1.9355x + 13.2903.
this equation assumes that y = p(n).
b) Find the correlation coefficient
r = −0.9525
c) Does the correlation coefficient indicate a strong linear trend, a weak linear trend, or no linear trend?
it indicates a strong linear trend.
d) Interpret the meaning of the slope of your formula in the context of the problem.
the slope indicates that, as the value of x increases by 1 unit, the value of y decreases by 1.9355 units.
this is a downward trend, indicating that the more cups of coffee he drinks, the less disagreeable he becomes.
e) Interpret the meaning of the P intercept in the context of the problem.
since y = p(n), the p intercept is the same as the y-intercept.
the y-intercept is the value of y when x = 0.
this means that if he had no cups of coffee, he would be very disagreeable and get even more complaints than if he had just 1 cup of coffee.
f) Use your model to predict the number of people that will complain about his attitude if he drinks 9 cups of coffee.
based on the model, when x = 9, the formula becomes y = y = −1.9355x + 13.2903 becomes y = −1.9355 * 9 + 13.2903.
this makes the number of people complaining to be equal to -4.1292.
g) Is the answer to part f reasonable? Why or why not?
the number in f is not reasonable since the number of people complaining can't be less than 0.
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.
in the equation, you would set y = 0 and solve for x.
you would get:
0 = −1.9355x + 13.2903.
add 1.9355x to both sides of the equation to get:
1.9355x = 13.2903
divide both sides of the equation by 1.9355 to get:
x = 13.2903 / 1.9355 = 6.87 which rounds to 6.9.
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