is this F-test valid Suppose I have a no intercept regression model such as
$Y = \beta x + \epsilon$  where $x$ is univariate and so is $y$.
I want to test the null hypothesis that $\beta = -1.0$.
So, I calculate the sse of the model assuming that $\beta = -1.0$ and call that $sseA$.
Then I estimate the model and call that modelB and get all the sums of
squares of that modelB.
Then I calculate the usual F-test of $(sseA - seeB)/1$ divided by
$sseB/(n-1)$ where $n$ is the number of observations.
I'm not sure if this F-test is valid for 2 reasons.


*

*the intercept is not in the model

*can modelA be viewed as nested in modelB?  F-tests are only valid
for nested models ( assuming normality) and I'm not clear if this
case can be thought of as nested. Usually, the null being true results in a model that is a  subset of the full model but here things are a little different.
 A: An alternative approach is to use an offset (a covariate with known coefficient). So change your model to
$y = \beta x +$ offset($-x$) + $\epsilon$
and then test whether your estimated $\beta = 0$ or establish a confidence interval about it.
A: I see no reason not to estimate the regression coefficient (beta) for the model (zero intercept), then test whether the estimated value is equal to -1 using a t-test.
You would also be interested in how much different your estimate is from the hypothesized value of -1 whatever the test shows. A large but insignificant difference might still be suspicious. It also would suggest your sample size is insufficient to get a good estimate of beta.
If your estimated beta is much different from -1 then you should examine the residuals from both the estimated model and from your hypothesized model (beta = -1, intercept = 0) carefully for the usual stuff but also for differences between the two models. I suspect that either model might work poorly near the ends of the range of x you have observed. 
