Trouble with True/False Stats Question

Question

Having trouble determining the truth value of the two above statements. Please let me know if the following reasoning is correct.

I believe the first statement is true, because of this statement I found:

"Since SSE is the minimum of the sum of squared residuals of any linear model, SSE is always smaller than SST(the total sum of squares).

I also believe the second statement to be true, according to:"...it is harder to predict one response than to predict a mean response." Which would suggest a wider interval.

Answer 1

Both of your statements are somewhat informal. The second one is correct. The first is not.

$SST=SSE+SSM$ but there is no reason why most of the total variation needs to be explained by the model...it could be a really poor fitting model, so $SSE>SSM$

Answer 2

For the first part, I have seen data sets that were little more than clouds of dots scattered all over the graph. I have even seen someone present a conference paper in which he presented such a set of data and showed the results of a linear regression on that data set. (It produced a line from left to right with a very slight slope. This was not a mathematics conference.)

The difference in height between the left and right end of that line segment was much less than the distance of most of the data points from the line. Which do you think explained more of the variation, the model or the error term?