In reading the following scatterplot

enter image description here

Would it be correct to say there is a strong positive linear relationship between the two axis? If not, could you please explain why?

Also is it correct to consider the ringed point as outlier?

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    $\begingroup$ It really depends on context, but assuming this is homework, I would say that here is a strong linear relationship and the ringed point is an outlier. However, in real life, one should take a good look at outliers, especially one that is 'way off'. $\endgroup$ – copper.hat Jan 28 '15 at 17:15
  • $\begingroup$ @copper.hat You might want to put that up as an answer, since it basically covers everything ;) (+1) $\endgroup$ – AlexR Jan 28 '15 at 17:22
  • $\begingroup$ @copper.hat Thanks a lot for advice. How would you interpret such data if not in a homework context? Given that x-axis represent number of source code lines in thousands and y-axis the amount of bugs in tens? $\endgroup$ – ZeroCool Jan 28 '15 at 17:28
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    $\begingroup$ Without more info. I would say that it is hard to infer much other than more lines more bugs. How do you associate a bug with a particular number of lines, how mature is the code, do the bugs arise from a particularly delicate piece of code, etc, etc. It really depends on context. $\endgroup$ – copper.hat Jan 28 '15 at 17:34
  • $\begingroup$ @copper.hat Brilliant! Thanks a lot. $\endgroup$ – ZeroCool Jan 28 '15 at 17:40

I would say that a linear relation is a reasonable first guess for the relationship, as it's simple, so avoids much of the with of overfitting, but describes a lot of the variance in the data.

However, it isn't a very robust conclusion. If you removed the top-right point and bottom-left points (considering them outliers), then you would remove the apparent linear relation, and would probably consider either a linear relation through the top-left point, or consider that there is no relation, and consider it an outlier.

If you added a point around (5, 0.5), then another negative linear relation starts to look equally plausible. Perhaps you would have both, so an x value would have two corresponding y values, if they are generated by different processes.

Also, if you start having more points around (5,0.5), or more near the top-left, top-right and bottom-left points, perhaps each of them is part of a cluster of values, rather than being following a linear relationship.

To sum up, I think a linear relationship is a good first approximation, but given the low sample size, you probably need more data points to test it, and see what are genuine outliers, and what are recurring clusters. You might also consider additional variables, that might explain the outlier, but if you include more variables, you risk overfitting.


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