Question

Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where XX is the age of the crab in months and ˆYY^ is the predicted value of YY, the size of the male crab in cm.ˆY=9.1367+0.4817XY^=9.1367+0.4817X

What is the value of ˆYY^ when a male crab is 22.1725 months old? Provide your answer with precision to two decimal places.

ˆYY^ =

Interpret the value of ˆYY^. The value of ˆYY^ is

the probability that a crab will be 22.1725 months old.

the predicted size of a crab when it is 22.1725 months old.

the predicted number of crabs out of the 1,000 crabs collected that will be 22.1725 months old.

the predicted incremental increase in size for every increase in age by 22.1725 months.

Answer 1

(A) y = 9.1367+0.4817X

put x = 22.1725

y = 9.1367+0.4817*22.1725

y = 9.1367+10.6805

y = 19.82

(B) y variable is the size of male crab in cm and x variable is the age of male crab in years

so, y gives us the value of size of male crab, when it is 22.1725 months old

Hence, option B is correct interpretation.