Linear Regression Question

May 2010
1
0
Hi, yesterday I sat my Stats exam at Reading University. One of the questions was about Linear Regression lines. For the data given there were was one x value(namely 5) corresponding to two y values (as in when x=5 y=3.5 and x=5 y=3.7). Now some of the values had for example 3 and 3.5, which made me think maybe this was a mistake in the paper. Can linear regression lines have points which correspond with two values? Obviously when you plot your line of best fit then two values also correspond with the same value which meant one point didn't fit the line properly.

Just wondering really
 
Aug 2007
3,171
860
USA
If you've two points that the regression line cannot possibly pass through simultaneously, this is quite acceptable. In fact, it is very likely that you will take measurements from the same place. This is not a problem at all.

You do not seem to be thinking about this regression line properly. It is not the point's fault where it is. Leave the poor thing alone and just use its value.

The regression line is a line that minimizes the error from all points simultaneously, based on some minimization criteria (often least squares). It is NOT an effort at collocation. If it hits one point, that is interesting, but not very signiticant. If it fails to hit some point, that is normal.