# Terminology question concerning regression

hopefully you can help me with the meaning of the following, I don't really understand the terminology: "regression of a vector of ones on the matrix $W$", where $W$ is something like $(W_t)' = (w_{1t},w_{2t},w_{3t}, w_{4t})$.

I don't understand, which regression I actually have to compute. If it is of help for you, I'm trying to understand the Godfrey/Wickens test according to this article: Ghosh, S., Gilbert, C. L., & Hallett, A. J. H. (1983). Empirical Economics, 8, 63–69. DOI: 10.1007/BF01973190

Greeting, Julius

• Would be great if you cited whole passage where this occurs. It should be something simple, but I do not have access to the article, so I cannot answer. For example it might mean regression where dependent variable is vector of ones and independent variables are the columns of $W_t$. Usually further formulas in article give hints what authors had in mind. Mar 1 '11 at 14:38
• Thanks for comment. I put up the first three pages here, hoping not to violate any rights too much, but I fear the paragraph is not understandable without the rest (img815.imageshack.us/i/paper0.jpg, img339.imageshack.us/i/paper1d.jpg, img683.imageshack.us/i/paper2a.jpg). The interesting part is on the third page and I don't really see any further information :( Unfortunately I don't have access to the original article by Godfrey and Wickens mentioned there. Mar 1 '11 at 17:21
– whuber
Jan 20 '15 at 22:46

Ordinary least squares regression of $y$ on $X$ involves solving the normal equations $$X'X\hat{\beta} = X'y$$ for $\hat{\beta}$, so I'd assume OLS regression of a vector of ones on $W$ implies solving $$W'W\hat{\beta} = W'\bf{1},$$ where $\bf{1}$ is a vector of ones. If the matrix $X$ itself contained a column of ones, i.e. if the RHS of the regression included a constant, then the solution would be trivial, so I assume none of the $w_{it}$'s are constant in your case.

• +1, it is basically the same as my comment, but much nicer written. Mar 1 '11 at 15:15
• I spent too long LaTeXing that so i didn't see your comment before I submitted this answer. It appears that when you're writing an answer SE alerts you to other answers being posted, but not comments. Mar 1 '11 at 15:23
• Thanks for your explanation, I think I now understand, although I had to reject this anyway as it doesn't fit my needs. Mar 8 '11 at 12:06