Question

Multiple Regression

A biologist believes that there is a quadratic relationship between the weight and age of fish, but that there will be different quadratic relationships for male and female fish. Write down a single regression model which explains the weight of a fish as a quadratic function of the fish’s age, and which allows for different quadratic relationships (constant, linear and quadratic terms) for male and female fish. Define each variable carefully.

Answer 1

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Lets write this equation:

Let weight of the fish be y

Lets the variable (age) related to male fish be X1, and the variable (age) related to female fish be X2

Let the constant be k

So, the multiple regression will look like:

y = k + a*X₁ + b*X₁² + c*X₂ + d*X₂²

Now, if the fish is a female a and b become 0 ,

if the fish is a male c and d become 0