Question

Because ecological disruption can put native species in contact with humans and livestock, it is believed that an increased number of threatened species in an area leads to a greater risk of novel disease transmission. A team of ecologists is investigating this relationship and records the number of threatened species and the number of novel diseases in different biogeographical regions. The following is their data set:

Region	Number of threatened species	Number of novel diseases
1	12	20
2	10	12
3	6	4
4	5	7
5	3	6
Mean	7.2	9.8
SD	3.7	6.4

(a) Calculate the correlation between these two variables.

(b) What are the slope and intercept for a linear regression model with number of diseases as the response variable?

(c) Predict how many diseases we would expect for a region that has 10 threatened species.

(d) Can we conclude from this data that ecological disruption causes an increase in the transmission of novel diseases? Explain.

Answer 1

a.

X Values
∑ = 36
Mean = 7.2
∑(X - M_x)² = SS_x = 54.8

Y Values
∑ = 49
Mean = 9.8
∑(Y - M_y)² = SS_y = 164.8

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = 84.2

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 84.2 / √((54.8)(164.8)) = 0.886

b.

Sum of X = 36
Sum of Y = 49
Mean X = 7.2
Mean Y = 9.8
Sum of squares (SS_X) = 54.8
Sum of products (SP) = 84.2

Regression Equation = ŷ = bX + a

Slope =b = SP/SS_X = 84.2/54.8 = 1.5365

Intercept = a = M_Y - bM_X = 9.8 - (1.54*7.2) = -1.2628

ŷ = 1.5365X - 1.2628

c. For x=10, ŷ = (1.5365*10)- 1.2628=14.1022

d. As r is positive and slope is also positive so we conclude that ecological disruption causes an increase in the transmission of novel diseases