Slope parameter info if intercept known?

[Anonymouse3]

Consider the SLR y = b +mx + e

Where the intercept b is known.

a) Find least squares estimator of m for this model.

b) What's the variance of the value from a.

Thanks

[fed1]

1.)


Model: y - b = mx + e = y*

sum( err^2 ) = E = sum[ ( y*_i - m x_i)^2 ]

go through the motiions, i get

m_hat = sum( x_i y*_i ) / sum( x_i^2 )

2)

the Var(m_hat) = sigma^2 / sum(x_i^2)

Enjoy smiles

[statsdude100]

Sorry to dig up this old thread, but are you implying that even if the intercept is known, it makes no difference on the least square estimate of the slope?

[Dason]

Sorry to dig up this old thread, but are you implying that even if the intercept is known, it makes no difference on the least square estimate of the slope?

How did you arrive at the conclusion? Notice that the estimate m_hat depends on the values of y*_i = y_i - b.

[statsdude100]

I thought that the m_hat obtained was very similar to the m_hat I obtained when the intercept was unknown. Could you help me see the difference

[Dragan]

Sorry to dig up this old thread, but are you implying that even if the intercept is known, it makes no difference on the least square estimate of the slope?

What fed1 wrote is correct.

That said, if you want to force the error terms to have a mean of zero, then that's another story.

For example, if you want to assume that the intercept term is zero where the mean of the error terms is zero, then the slope coefficient simply becomes the mean(Y)/mean(X).

[statsdude100]

I don't want to force the intercept term to be any constant in particular. I was just wondering whether the final outcome of m_hat would be impacted knowing whether or not the intercept was known.

[Dason]

How is that not the same as forcing the intercept term to be a set value?

[statsdude100]

Ok. I think I'm in way over my head here. I know that if the intercept was unknown, then the LSE of the slope is Sxy/Sxx. Will this still be the case if the intercept was a known parameter?