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 X is the age of the crab in months and ˆ Y Y^ is the predicted value of Y Y, the size of the male crab in cm. ˆ Y = 9.1411 + 0.4775 X Y^=9.1411+0.4775X What is the value of ˆ Y Y^ when a male crab is 23.2417 months old? Provide your answer with precision to two decimal places

Question

Mathematics

Pranav Stephenson

25 March, 01:20

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 X is the age of the crab in months and ˆ Y Y^ is the predicted value of Y Y, the size of the male crab in cm. ˆ Y = 9.1411 + 0.4775 X Y^=9.1411+0.4775X What is the value of ˆ Y Y^ when a male crab is 23.2417 months old? Provide your answer with precision to two decimal places

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Answers (1)

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Bethany Lindsey · Answer 1

20.24 cm

Step-by-step explanation:

Here, since the age of the crab is given in months and the regression line was computed using the age in months, we just have to replace the value of the age in the formula to estimate the size.

The formula obtained for the estimated size Y was

Y = 9.1411 + 0.4775X

where X is the age in months

Replacing X with 23.2417, we get

Y = 9.1411 + 0.4775*23.2417 = 20.24 cm