In the simple linear regression model, y=Bo +B1x + u, suppose that E(u) is not equal to 0

In the simple linear regression model, y=Bo +B1x + u, suppose that E(u) is not equal to 0. Letting a₀ = E(u), show that the model can always be written with the same slope, but a new intercept and error has a zero expected value.

Expert Solution

y = B0 + B1*x + u
E(u) = a0
u = a0 + h, where E(h) = 0

y = B0 + B1*x + a0 + h
y = (B0 + a0) + B1*x + h

here, the new intercept is: (B0 + a0)
The slope is the same, B1
The new error term is h, which has a zero expected value.

Rahul Sunny answered 2 years ago

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