It is very difficult to say for individual observations, but in general, pretty much all measurement is subject to random measurement error. One way to find out whether and to which extent random noise (random measurement error) waters down ("attenuates") your correlations and/or biases your regression results is by computing the reliability coefficients for X and Y and making an adjustment for attenuation (so-called "correction for attenuation" formula in classical test theory).

An alternative way to correct for error is by using structural equation modeling/confirmatory factor analysis with latent variables in which variance due to measurement error can be separated from true score variance and correlations/regressions can be estimated between latent variables that are free of error. You can check out my YouTube video on this topic:

https://www.youtube.com/watch?v=jJ-qLImQYZs

Hi,

Check for normality in each of the variables.

Scatterplot between them with best fit line and Confidence intervals.Is it linear or not.

I understand the question in a much simper way than Christian Geiser and think that the question is if or when an observed (positive or negative) correlation in some observed values (a sample) from two variables may be interpreted a a (positive or negative) correlation between the variables.

A common way to do this is to test the statistical hypothesis that the correlation is zero. If the observed correlation is too large than would be expected under this hypothesis, one would conclude that the correlation of the variables has the same sign than the observed correlation. Otherwise the data are not conclusive regarding a (possible) correlation between the variables.

Instead of testing the correlation, in a linearregression one can test the hapotheses that the reduction of explained variance is zero or that slope of the regression line is zero, what all turns out to be mathematically equivalent hypotheses in the linear regression model.

If one does linear regression, the most "natural" hypothesis to me seems to test that the slope is zero. Statistical software typically give the slope estimate, its standard error, the ratio of estimate and standard error (=t statistic) and the corresponding p-value (Pr(>|t|), taken from a t-distribution with n-2 degrees of freedom). A p-value close to 0 indicates that "more extreme" t statistics than the observed one are very unexpeced under the tested hypothesis, and thus that the data provide a considerable amount of information to distinguish the estimate from the hypothesized value (and therefore to distinguish a positive from a negative correlation between the variables).