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 X is the age of the crab in months and ˆ Y is the predicted value of Y , the size of the male crab in cm. ˆ Y = 9.1367 + 0.4817 X What is the value of ˆ Y when a male crab is 22.1725 months old? Provide your answer with precision to two decimal places. ˆ Y = Interpret the value of ˆ Y . The value of ˆ Y is the predicted size of a crab when it is 22.1725 months old. the probability that a crab will be 22.1725 months old. the predicted incremental increase in size for every increase in age by 22.1725 months. the predicted number of crabs out of the 1,000 crabs collected that will be 22.1725 months old.

Answer 1

Answer: 19.82 months

Step-by-step explanation:

Usually in regression analysis candidates are provided with data and they are asked to determine the equation of the line of regression. This is not the case here. The question is pretty much straight forward.

Provided the line equation:-

$Y= 9.1367 + 0.4817X\\= 9.1367 + 0.4817(22.1725)\\= 19.81719325 \\=19.82$

This shows the that the predicted size of the male crab will be 19.82 cm when the crab is 22.1725 months old.