Data obtained from a random sample of recent years of caribou and wolf population.
Caribou (x): 30, 34, 27, 25, 17, 23, 20
Wolf (y): 66, 79, 70, 60, 48, 55, 60
Sample correlation between x and y is r=.915 for the n=7 data points.
Summary Statistics:
Caribou (x): Mean= 25 and Standard Deviation= 6
Wolf (y): Mean= 63 and Standard Deviation= 10
With the following data, answer these questions. SHOW YOUR WORK!
a. Do the data indicate a linear relationship between x and y?
b. Predict the wolf population when the caribou population is x = 30 using the concept of "regression towards the mean".
c. Predict the wolf population in (b) using the regression line itself.
d. What percentage of the variation in the data is explained by the regression line?