It means that the straight-line model through the data explains 0.062²=0.0038 = 0.38% of the variance of the data, and the negative sign indicates that the slope of the line is negatve. There is no more meaning of this value from a statistical point of view. What it may mean practically needs to be interpreted by experts in the field/topic. Usually, there simply is no very sensible interpretation.

Some people may now be concerned if this value of -0.062 for your data is significant. This may or may not be the case - it does nocht change the interpretation/meaning of the value, e.g. if it is "relevant" or not and what we may deduce from this knowledge. These questions are outside of statistics.

It means that the straight-line model through the data explains 0.062²=0.0038 = 0.38% of the variance of the data, and the negative sign indicates that the slope of the line is negatve. There is no more meaning of this value from a statistical point of view. What it may mean practically needs to be interpreted by experts in the field/topic. Usually, there simply is no very sensible interpretation.

Some people may now be concerned if this value of -0.062 for your data is significant. This may or may not be the case - it does nocht change the interpretation/meaning of the value, e.g. if it is "relevant" or not and what we may deduce from this knowledge. These questions are outside of statistics.

Jochen's response is accurate. This correlation may be highly statistically significant (p < 0.001), but regardless the r is very low. Thus it is doubtful that the association is very biologically meaningful, but that may depend on your field, the quality of data, etc.

From my investigations, you are all correct. The correlation is negative. Thanks. 

Jochen is correct, however I would caution the attention to be paid to significance. Failing to accept the null hypothesis  - if the significance below 0.05 (5% margin of error) or 0.01 (1% margin of error) is an important observation in your decision making I.e. Is the correlation significant, also this can be influenced by the sample size and whether data is normally distributed (or not) and whether data is reliable (or not) - which you have not mentioned

1) Jochen's responses are always accurate.

2) Geometrically, Pearson's coefficient is simply a function of the angle between two vectors (more specifically, for vectors x and y, the angle of the cosine (x,y) is the dot product x*y divided by the magnitude of both vectors multiplied together, or Pearson's r).

3) Generally speaking, this correlation coefficient is used to measure the relationship between vectors in some dimensional space well beyond 3D. More importantly, the components of the vectors plotted in whatever Rn are going to be relatively sparse (the curse of dimensionality). This doesn't effect Pearson's correlation coefficient mainly because by itself this coefficient is largely meaningless. Although it's a measure of angular separation, it isn't really a distance measure but a similarity measure that assumes linearity. Thus two basically perfectly correlated sets of observations/measurements/data points can easily yield a very low valued Pearson product-moment correlation coefficient if the correlation is nonlinear. This is one reason why it is always important to plot your data.

4) Statistical significance testing is, in general, questionable at best. It's been criticized since it originated (see e.g. "402 Citations Questioning the Indiscriminate Use of Null Hypothesis Significance Tests in Observational Studies" in the link below). The list in the link lacks some of my favorite criticisms, 2 of which I have uploaded/attached.

http://warnercnr.colostate.edu/~anderson/thompson1.html

If the Pearson's correlation coefficient between two variables is -0.062 this means that the two variables a not linear connected but they can be connected in a nonlinear way. This can be seen if you plot your data. You can use the rank correlation (Spearman) to test a monotonous nonlinear dependence.

The answers provided by Jochen, Robert and Andrew and Aristita are all totally correct and potentially very useful, Rita!

Best wishes

Pieter

Hello,

If both of my Pearson correlations are -.042.Will my outcome or predictor be negative?

I think your outcome or predictor will be positive.

Rita -

r is not always a good measure. It is very volatile for small samples. Even with larger samples, it may not be a strong indicator of the predictive usefulness of such a linear relationship. And if the relationship is not linear, it may also be misleading.

In answer to your question, "...what kind of correlation is it?" I'd say basically it means the data are likely approximately uncorrelated. You can prove this to yourself by plotting the points on a scatterplot graph. In this case "scatter" should take on a more descriptive meaning!

:-)

It should not be obvious that there is any relationship.

Statistics are a guide. They are subject to many influences, sample size being a common one, and you should avoid using a statistic in the absence of other information. Subject matter knowledge is often important. Data are like experimental evidence. You need to see what the data tell you, but remember that anomalous things happen. Here, for example, with enough good data you may find a slightly positive correlation which may be expected from the subject matter. The point is not to make too much over a volatile statistic.

Cheers - Jim

Rita -

I see that you say that "From my investigations ..... The correlation is negative."

If you plot your data, I'm guessing that if there should be a nontrivial negative correlation based on subject matter knowledge, then you probably do not have a great deal of data, and one or two points may be responsible for giving you a near zero r. They may "stick out" on the graph.

At any rate, I think plotting the points might show you something worthwhile.

Jim

PS - I see that this is an old question, but if you still have the data, and can graph it and post the plot here, it might be interesting.

The Pearson correlation coefficient, r, is a measure of the strength and direction of the linear relationship between two variables, most especially continuous or numerical variables. Its size is always between 0 and 1.

A value of 1 implies that a linear equation describes the relationship between the two variables under comparison, with both data pointing lying on a line for which as one increases, the other Increases.

A value of −1 implies that all data points lie on a line for which as one increases, the other decreases.

A value of 0 implies that there is no linear correlation between the two variables.

R-Square (r2) shows the percentage (or proportion) of the relationship.

KEY:

0.00 - 0.19 – very weak

0.20 - 0.39 – weak

0.40 - 0.59 – fairly strong (also called moderate)

0.60 - 0.79 – strong

0.80 - 1.0 – very strong

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To answer your question, r= -0.062, means, (1) the correlation is weak (2) the correlation is in the negative, meaning as the dependent variable is increasing, the independent is decreasing. For example, if Age where your dependent, and BMI where your independent, this means, as Age increases, the BMI values decreases. (3) You didn't state the p-value and so we cannot tell if the correlation is statistically significant nor not. (4) And just for the record, no matter what values your 'r' shows, as long as your p > 0.05, there is no association between the two variables you are comapring

Hello, I am not an expert but I have encountered a similar problem and these are are some of the ideas I had to consider. Plot the data if both variables tend to increase or decrease together, and the line that represents the correlation slopes upward, the coefficient is positive. Keep in mind that it is difficult to conclude that changes in one variable causes changes in another based on the correlation alone. You may want to find the causes by correcting data entries or measurement errors. You may also consider removing data values that are associated with one-time events (outliers). Then, repeat the analysis.

Basically, Pearson's Correlation measures the linear dependency of two quantitative variables. When r = -0.062, the correlation coefficient is close to zero. Yes, there is a negative sign, so one may think about a very slightly negative correlation but the magnitude is closer to zero rather than one. So, it can be considered that there is no linear dependency between that two variables, but it may be happen that the relation between them is quadratic or something except linear.

You can interpret this, in another way. If we fit a simple linear regression equation like, Y = a + bX, then the coefficient of determination is, r2 = 0.003844. This indicates that by the given model, 0.38% of the variability of Y(dependent variable) can be explained by the independent variable, X. That means, that our fitted simple linear model is very bad. Why does this happen? Because there is a few linear dependency between them i.e. r = -0.062. So, the linear fitting should be rejected.

Hola,

El Coeficiente de Correlación de Pearson mide o cuantifica, la asociación entre dos variables, por otra parte, el coeficiente de Regresión (Beta 1) apunta hacia la relación de dos variables.

No es lo mismo "Coeficientes de Regresión" versus "Coeficiente de Correlación de Person" , cada uno, con sus respectivas Prueba de Hipótesis, no olvidad el tamaño del efecto en las Prueba de Hipotesis.

Gracias

It is not r or -r but r-squared that has an interpretation, the amount of variance explained in Y by X. In this case r-squared explains only .13 percent of the variance, that is, almost no variance. Even with a very large sample, a correlation of .062 contains little information and by itself, justifies no kind of inference. .

There are some recommendation on page 4 of this chapter:

http://www.statstutor.ac.uk/resources/uploaded/pearsons.pdf

To determin whether the “negative correlation” should be accepted or rejected，U can make a correlation test to get a P value of “r”.

To carry this test, U can type the code " cor.test(x1, x2)" in R software . Where x1 and x2 is the varibles.