Second, your likelihood will look different from what you think anyway. Assuming normal distributions and only one covariate x, letting y denote the response with n total observations, it will be:
%5E2%20\right))
Where sigma is your standard error, NOT the forecast standard error. Your likelihoods might look different depending on the particular models you are using. Multiple regression, for example, will have more covariates and thus more regression parameters in the mean function.
D is your data.
First, I misspoke—you don’t want the likelihood, you want the marginal distribution of the data. See http://www-personal.umich.edu/~bnyhan/montgomery-nyhan-bma.pdf especially the first 5 or so pages.
Second, your likelihood will look different from what you think anyway. Assuming normal distributions and only one covariate x, letting y denote the response with n total observations, it will be:
Where sigma is your standard error, NOT the forecast standard error. Your likelihoods might look different depending on the particular models you are using. Multiple regression, for example, will have more covariates and thus more regression parameters in the mean function.