Question

The deadly Ebola virus is a threat to both people and gorillas in Central Africa. An outbreak in 2002 and 2003 killed 91 of the 95 gorillas in seven home ranges in the Congo. To study the spread of the virus, measure "distance" by the number of home ranges separating a group of gorillas from the first group infected. Here are data on distance and time in number of days until deaths began in each later group. (Data set may be found here.) Distance 1 3 4 4 4 5 Time 4 21 33 41 43 46

(a) Make a scatterplot. Which is the explanatory variable? distance time either distance or time Correct: Your answer is correct. What kind of pattern does your plot show? There is a strong positive linear association between distance and time. There is a strong negative linear association between distance and time. There is little to no association between distance and time. Correct: Your answer is correct. (

b) Find the correlation r between distance and time. (Round your answer to four decimal places.)

(c) If time in days were replaced by time in number of weeks until death began in each later group (fractions allowed so that 4 days becomes 4/7 weeks), would the correlation between distance and time change? Explain your answer. Correlation would change, since it depends on units. Correlation would not change, since it does not depend on units.

As you can see, I only need to find the correlation r between distance and time.

Answer 1

a) Scatter plot:

There is a strong positive linear association between distance and time.

b)

X	Y	XY	X²	Y²
1	4	4	1	16
3	21	63	9	441
4	33	132	16	1089
4	41	164	16	1681
4	43	172	16	1849
5	46	230	25	2116
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
21	188	765	83	7192

n =	6
SSxx = Ʃx² - (Ʃx)²/n =	9.5
SSyy = Ʃy² - (Ʃy)²/n =	1301.33
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	107

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 0.9623

c) Correlation would not change, since it does not depend on units.