# Interpretation of Scatter Plot

I am have been looking over my undergraduate statistics notes about the relationship between two numeric variables, but I am baffled regarding what the relationship this graph is showing.

From my perspective, I would say this is a non-linear (possibly logarithmic relationship).

Any inputs?

• I do not see a clear relationship. Can you add some transparency to the dots? – user2974951 Mar 27 at 7:00
• Try a logarithmic scale for sodium. If there are any exact zeros, you need to tell us. – Nick Cox Mar 27 at 8:22
• Hi, I have resized the plot. gyazo.com/ccc0f1f8fcabca75d307cd2e4b49c253 – John Mar 27 at 8:24
• Yes there are several points that have 0 for sodium level. No point is 0 for calories – John Mar 27 at 8:26
• For those of you that want hexagonal binning graph; link here gyazo.com/76106af5676c08c9dc830a7bce3181b0 – John Mar 27 at 8:33

Well, it's hard to see any relationship between sodium level to the rating but that most people have low sodium and very few have very high.

One more insightful plot you might want to try is freezing the sodium level and looking at the distribution of the rating given this sodium level , i.e. P(rating|sodium level).

Hope that helps. Cheers.

First of all, it's good to realize that there is no reason any two variables should follow some specific relation.

More to the point of your question, judging from the plot alone, which is probably not a great idea (both fitting a real formula and checking statistics and coming up with a data story that explains any relationship are important steps), it is tempting to look for something based on the outliers that determine the overal shape when you look at this blob, I mean, the measurements with high sodium and high rating, however, I want to list some other explanations for this shape

• there are many more measurements with high rating, so also more outliers
• the relationship itself could be linear, the shape of the outliers coming from more measurements
• the error could be lognormal which could explain such a shape
• the error could be higher for higher values of rating

For consideration.

EDIT, after staring a bit more at the plot, it seems rating is cut off at 40. That's suspicious as well, you could imagine a (log)normal distribution in both directions without any correlation, then cutting it of there and you get this shape. Using that recipe, I created the scatterplot below. So the point is, there is no relation at all, but if you're looking at it you may be tempted to think there is something going on.

• When you suspect a "lognormal distribution in both directions" think of applying a logistic transformation to normalized data. In this case, one of the first plots to view would use something like $\log((\epsilon+\text{rating})/(\epsilon+40-\text{rating}))$ on the vertical axis and the log of sodium on the horizontal axis, where you might vary the small positive number $\epsilon$ in an exploratory way. – whuber Mar 27 at 14:41
• Good advice, this data is actually only lognormal in the horizontal axis, the vertical axis is a clipped normal distribution. – Gijs Mar 27 at 16:08
• Thank you, just to confirm, for this particular plot there is no relationship? – John Mar 28 at 9:00
• Indeed, no relation – Gijs Mar 30 at 7:04