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 - Mx)2 = SSx = 54.8

Y Values
∑ = 49
Mean = 9.8
∑(Y - My)2 = SSy = 164.8

X and Y Combined
N = 5
∑(X - Mx)(Y - My) = 84.2

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

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 (SSX) = 54.8
Sum of products (SP) = 84.2

Regression Equation = ŷ = bX + a

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

Intercept = a = MY - bMX = 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.

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