Thread: Which SSR (Regression sum of squares) is theoretically larger?

1. Which SSR (Regression sum of squares) is theoretically larger?

Dear all,
I have 3 fitted lines:
1. Y = b0 + (b1)X
2. Y = (0.5)b0 + (b1)X
3. Y = b0 + 0.5(b1)X
Where
b0 = the y-intercept
and
b1 = the slope of the fitted line
In addition to the the 3 equations above, using the information provided by the image attached I would like to determine (theoretically), which one of the three fitted lines (listed above) would have the largest SSR and why. This is to be done without physically calculating the SSR values for each and every fitted line equation, but rather by studying the formula in hand with the equations above, to determine which would be largest.

Additionally, I believe (correct me if I am wrong) that the SST should technically remain constant across all the fitted line equations (shown above). This is because, the equation for SST does not depend on the values created by the fitted line equations, but instead relies upon the observed values of Y (Yi) and the mean value of the observed values (Y-bar). And thus if the SST were to remain constant, then surely the fitted line with the highest SSR will be that which has the lowest SSE. To check my theory, I physically calculated the SSE and SSR values using a data set for each of the fitted line equations, but I found that the SSR is higher for the fitted lines that have a higher SSE, and that therefore the SST (which is SSR+SSE) is not constant. Am I wrong in assuming that the SST would be constant irrespective of what the fitted line equation is? or does the SST differ from each linear equation to equation? What am I doing wrong here?

2. Re: Which SSR (Regression sum of squares) is theoretically larger?

hi,
my guess is that SST= SSR + SSE is only valid if the Yhat_i points are calculated with the regression equation, but I might be wrong (it has been a long time)

regards

3. Re: Which SSR (Regression sum of squares) is theoretically larger?

Originally Posted by rogojel
hi,
my guess is that SST= SSR + SSE is only valid if the Yhat_i points are calculated with the regression equation, but I might be wrong (it has been a long time)

regards
Thank you for your reply. However, given that there is uncertainty in your answer, I would prefer to wait for further replies (from other members), in order to confirm whether or not your answer is correct.

 Tweet