Question

Rain and Hantavirus in Mice

Hantavirus is carried by wild rodents and causes severe lung disease in humans. A recent study¹ on the California Channel Islands found that increased prevalence of the virus was linked with greater precipitation. The study adds "Precipitation accounted for 79% of the variation in prevalence."


^1"More Rain, More Virus," Nature, April 28 2011, p. 392.

(a) What notation or terminology do we use for the value 79% in this context?

β

r

p-value

b

Standard error

p

R2

(b) What is the response variable?

Choose the answer from the menu in accordance to item (b) of the question statement: Prevalence Variation Precipitation


What is the explanatory variable?

Choose the answer from the menu in accordance to item (b) of the question statement: Variation Prevalence Precipitation

(c) What is the correlation between the two variables?

Round your answer to three decimal places.

r=

Answer 1

(A) 79% is explained variation

we know that explained variation is the coefficient of determination or R^2

So, answer is R2

(B) Response variable is dependent variable

In this case, response variable prevalence because 79% of variation is explained by precipitation for prevalence

It is clear that precipitation is responsible for variation in the prevalence, so explanatory variable is precipitation

(C) correlation r = sqrt(R^2)

where R^2 = 0.79

so, we get

r = sqrt(0.79)

= 0.889