Question

[3:26 PM, 7/29/2020] Demety: 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   8   7   6   5   4   3   2
Cups of coffee (n)   1   2   3   3   4   4   5   5

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

a) Use technology (such as Excel or lock5stat) to find a linear equation for P (Just enter the part after the equal sign, and use n as the variable. For example 3.4n+15.1

P
=
  

b) Find the correlation coefficient. (use technology, such as lock5stat or Excel)

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 regression line equation to predict the number of people that will complain about his attitude if he drinks 3 cups of coffee.

Answer 1

(a) P = -2.2n + 13.3

(b) r = -0.977

(c) strong linear trend

(d) For every additional cup of coffee, the number of people who complain about his attitude would decrease by 2.2.

(e) For 0 cup of coffee, the number of people who complain about his attitude would be 13.3 on average.

(f) y = -2.2*3 + 13.3 = 7

	r²	0.954
	r	-0.977
	Std. Error	0.739
	n	8
	k	1
	Dep. Var.	P
ANOVA table
Source	SS	df	MS	F	p-value
Regression	67.5957	1	67.5957	123.68	3.15E-05
Residual	3.2793	6	0.5465
Total	70.8750	7
Regression output				confidence interval
variables	coefficients	std. error	t (df=6)	p-value	95% lower	95% upper
Intercept	13.3
n	-2.2	0.1985	-11.121	3.15E-05	-2.6928	-1.7216