In theory, this could be easily done by constructing a simple linear model (e.g. using R's lm()) and, for each point, comparing the actual value $y$ with the one predicted by your model. Consider what a linear regression actually is: a simple function,
$y = Intercept + (beta * x) + noise$
So the Intercept is a constant added to each observation, and beta is the slope of the regression line, or, phrased differently, by how much is the outcome/dependent variable y assumed to be higher than Intercept if the predictor/independent variable is x? So if Intercept is 0 and beta is 1.5, your prediction for y = x is y= 1.5 plus random noise, for x = 5 it's y = 7.5 plus random noise, etc.
So you get the slope/beta and intercept from
summary(lm(y~x)). Then you go through each pair of points $i$ in your data and calculate the result of $Intercept + (beta*x_i)$, and check the absolute (or possibly squared or log) deviance to $y_i$.
What this would basically be equivalent to is doing a scatterplot including the best-fit linear regression line, and checking how far each point diverges from the line on the y axis. This is I think one of the possible answers to your question.
The question is, how meaningful is this? And that greatly depends on your data and question, and I think in very many contexts it would not be especially meaningful.