# Have conducted a bivariate correlation - want to identify the outlier - is there a 'statistical' way to do this?

I run correlation (on SPSS) between a governance indicator 1996 and the same governance indicator in 2012. As would be expected there is a near perfect correlation.

What I am interested in, however, are the cases that are not as closely correlated - are furthest from the line (because those would be cases of genuine governance change).

Is there a way I can motivate my selection of these outliers 'statistically'? or is legitimate for me to identify them visually?

I am a complete novice - so simple answers help.

Perhaps some sort of multivariate outlier test is needed, but in this context it seems reasonable to me to think of trying to predict the 2012 indicators, $y$, based on the 1996 indicators, $x$ -- i.e., putting the data in roles of dependent and independent variables. If you fit a linear regression line using software that can compute the "$t$ residuals", AKA "Studentized deleted residuals", then that is the formal way of testing for an outlier in the $y$ direction. A absolute $t$ residual greater than $t_{\alpha/2,d}$ would be significant,'' where $d$ is the error degrees of freedom.
Another way to do the above is to fit a regression model with $y$ as the response and predictors $x$ and $I_i$, where $I_i$ is an indicator variable for the $i$th observation ($1$ for the $i$th observation, $0$ for all others). Then in the table of coefficients, the $t$ statistic for $I_i$ is the negative of the $i$th $t$ residual. This approach also reveals the substance of what is being done: this $t$ statistic measures the significance of accounting for the $i$th observation separately, over and above what is explained by $x$.