Question

In: Statistics and Probability

Because ecological disruption can put native species in contact with humans and livestock, it is believed...

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.

Solutions

Expert Solution

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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