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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 Yˆ is the predicted value of Y, the size of the male crab in cm. Yˆ=9.1411+0.4775X What is the value of Yˆ when a male crab is 23.2417 months old?

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MrRoyal

Answer:

[tex]Y = 20.239[/tex]

Step-by-step explanation:

Given

[tex]Y = 9.1411 + 0.4775X[/tex]

Required

The predicted value of [tex]Y[/tex] when [tex]X = 23.2417[/tex]

To do this, we substitute [tex]X = 23.2417[/tex] in the given equation

So, we have:

[tex]Y = 9.1411 + 0.4775X[/tex]

[tex]Y = 9.1411 + 0.4775 * 23.2417[/tex]

[tex]Y = 9.1411 + 11.0979[/tex]

[tex]Y = 20.239[/tex]

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