Question

Question 2: (15 pts) To determine the relationship between the amount of precipitation and the number of trees that grow in area, an ecologist has recorded the yearly rainfall x (mm) and the amount of ground covered by tree (measured on a scale from 49.6,sy -7.1. The sample correlation between x and y is 0.673. to 100) for 49 locations. In this sample, 1182.4,S 226.9,5 a) Calculate the regression equation (5 pts) Can we conclude that the tree cover depends on the amount of raintfal? Explain why? (5 pts) research believes that an increase in average yearly precipitation of one mm will increase ne mee amount of tre covers by 0.025. Does the data support this statement? Why? (5 pts) Question 3: (15 pts)

Answer 1

Ans:

a)

slope,b=r*sy/sx

   =0.673*(7.1/226.9) =0.0211

y-intercept,a=49.6-0.0211*1182.4=24.65

Regression equation:

y'=0.0211x+24.65

b)n=49

df=n-2

df=49-2=47

Test statistic:

t=0.673*sqrt((49-2)/(1-0.673^2))

t=6.238

p-value=tdist(6.238,47,2)=0.0000

Yes,we can conclude that tree cover depends on the amount of rainfall.

c)No,data does not support the above statement.

As,slope=0.0211,which means that an increase in average yearly precipitation of one mm will increase average amount of tree covers by 0.0211