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Please help me to interpret this graph in terms of correlation type. Which type involves two vectors in directions observed below (see graph screenshot)? Thanks in advance.

enter image description here

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Check the updated graph. For now I'm saying that y1 and y2 content is directly correlated to the lower content of X. when X is lower, the y1 content decrease while the y2 increase. –  Apopei Andrei Ionut Feb 21 '14 at 13:51
What are y1 and y2 then? Are they separate variables? And what are the dots? Do their coordinates represent observations of two different variables or three? If three, how can one tell the difference? And why do the vectors pass outside the observations rather than through them? –  Nick Stauner Feb 21 '14 at 13:56
y1/(y1+y2) (which is equivalent to that representation y1 and y2) - are to variables on the y-axis, an the third on x-axis. Dots represents the projected values of y1/(y1+y2) vs x. The vectors represent the trend. –  Apopei Andrei Ionut Feb 22 '14 at 17:19
If your y axis is the ratio of two dependent variables, you may wish to also consider graphing them separately, or using other methods to look at the relationship between all three. The change in variation of the data with x may indicate that ONE of the y values is correlated with x, and it becomes more dominant in the total and the ratio at higher x values. But you can't say for sure just based on this plot. –  AmeliaBR Feb 23 '14 at 21:10

1 Answer 1

up vote 12 down vote accepted

Assuming the dots are your observations, the vectors seem to express upper and lower bounds on the range of $y$ as a function of $x$. The correlation appears weakly negative at a glance, but I wouldn't really trust my eyeballs to estimate Pearson's $r$. What does seem clear enough is that $y$ exhibits across $x$. Wikipedia's Consequences section may be of further interest to you. See also for comparison Wikipedia's plot with random data showing heteroscedasticity:

by Q9.

Like most distributional characteristics, heteroscedasticity is a matter of degree, and few real datasets are truly, absolutely homoscedastic. Despite my own behavior here, you may not want to "eyeball" a scatterplot for heteroscedasticity any more than for a correlation. Many tests of homoscedasticity exist, including . Fixes are available, but the best may be methods that tolerate heteroscedasticity. This is not to say heteroscedasticity is only a data-analytic nuisance – it may also be of focal theoretical interest. An example from Wikipedia describes wealth and diet variability:

A classic example of heteroscedasticity is that of income versus expenditure on meals...A poorer person will spend a rather constant amount by always eating inexpensive food; a wealthier person may occasionally buy inexpensive food and at other times eat expensive meals. Those with higher incomes display a greater variability of food consumption.

Interested readers may wish to check the tag wiki for ; I've edited in more info like this.

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Thank you very much! You helped me a lot. –  Apopei Andrei Ionut Feb 21 '14 at 13:56
Note also that there are lots of physical measurements/instrument output/lab procedures where the error will "naturally" come as a relative error rather than an absolute error (or a mix of different absolute and relative error sources). –  cbeleites Feb 22 '14 at 13:08

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