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Explanation of the problemI have been given a problem in which I am asked to calculate the SST of $Y$ while only being given the SSE of each model (there are $3$ variables, $X_1 ,X_2 ,X_3$ and I have been given the SSE of all possible models that can be created with these three variables. all of them have constants). No $R^2$ is given, only the sample number $n=30$. How do I calculate the SST of $Y$?

Petros Xristodoulou
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    What do you mean by SST and SSE? Where did this problem come from? And what have you done so far? – cpiegore Jul 07 '23 at 18:25
  • Can you post a snapshot of the exercise? Are the three functions $Y_i=aX_i+b$? It is not totally clear. – callculus42 Jul 07 '23 at 18:32
  • I added a snapshot. Sorry but i had to handwrite it as it was in greek and i had to translate it for you – Petros Xristodoulou Jul 07 '23 at 19:00
  • You may not have enough information to solve this problem. To find the SST of $Y$ you need to know the SSR in addition to SSE, so unless SSR is $0$ it may not be possible to continue the analysis any further. – cpiegore Jul 07 '23 at 19:43

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I think this might be just some non-standard notation that the student is expected to understand and apply. In a model with a constant value for Y (the top row in your table), that constant value will just be the mean value for Y. There is no regression in that constant value model (SSR=0), so the sum-of-squares total for other models is the same as the sum-of-squares error for that model.

Marc Shelikoff
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  • I do not think $Y$ is supposed to be constant. It represents sales data that the OP is trying to model using the explanatory variables $X_1, X_2$ and $X_3$. – cpiegore Jul 07 '23 at 19:39
  • Yes. Y represents the response variable. Rows 5-8 of the table represent SSE outcomes from multiple linear regression, and rows 2-4 represent SSE outcomes from three simple linear regressions. Row 1 is where the non-standard notation comes in and seems to represent comparison of the data to a constant-value model. – Marc Shelikoff Jul 07 '23 at 19:44
  • I may be wrong, but perhaps column 1 refers to the constant term in the linear regression model. – cpiegore Jul 07 '23 at 19:51
  • There are no explanatory variables in in the top row of that table. They are all white, so the model isn't really a regression model any longer. It makes this a somewhat semantic and silly thing to consider. But that's what I think is happening. – Marc Shelikoff Jul 07 '23 at 19:56