Fundamentally speaking, such instruments are based on the hypothesised arguments and are not free from errors. Thus I feel results of such instruments need further validations including case based methods.

Well...sort of.  This is not really a question that can be addressed in a single thread, but I will try.  Please note that what you're asking is really suitable for several lectures of a single introductory statistics course.  With that said...

A simple correlation coefficient (and the p-value testing whether it is different from zero) provides the answer to a very specific question: is there a linear relationship between the two variables in question?  A correlation coefficient near zero would suggest that the variables do not have a linear relationship with one another.  A correlation coefficient near 1 or -1 would suggest that there is a strong linear relationship between the two variables.

Please note that this simple first step does not take into account the effect of additional confounding variables.  For example, if I believe that there is a strong relationship between tobacco smoking (measured as daily number of cigarettes smoked) and severity of chest pain during exercise (measured on a linear scale from 0 to 100 by the participant), I may find a strong correlation between the two variables just by calculating the correlation coefficient.  

However, it is also possible that age is a confounder in this relationship - suppose that older participants are more likely to smoke AND more likely to have chest pain during exercise.  In that case, I could be finding that smoking is very strongly predictive of chest pain during exercise when, in fact, the true effect is due to age.

This is where a multivariate regression comes in handy.  You could create a model with the dependent variable = degree of chest pain during exercise, the independent variable = number of cigarettes smoked daily, and age is included as a second independent variable.  This would provide an estimate of the effect of tobacco smoking on chest pain during exercise WHILE ADJUSTING FOR age, meaning that (ideally) the effect of smoking on chest pain would now be "independent" of any age effects.

This, also, must be done carefully, because if the correlation between your two independent variables is too strong, the model will have some undesirable properties.  But that really goes beyond the scope of a ResearchGate thread, and should be addressed in person by a professional statistician.

We also have not covered non-linear relationships (which cannot be adequately found by just calculating a correlation coefficient or a simple linear regression).

Everything depends on the case because these methods are based on assumptions therefore can cause errors

Hello, AsI see it, dependent and independent variables may be connected to each other  and the statistic correlation between them will be significant.

but if you want to study casuation, you need regression based not only on the results but on a theory. Good luck!

I think use of R is preferred.  Capital R is the multiple correlation coefficient that tells us how strongly the multiple independent variables are related to the dependent variable.

http://academic.udayton.edu/gregelvers/psy216/SPSS/reg.htm

Some of the answers getting posted here are far, far too simplistic to answer this question.  Folks, please, don't try to boil this down to one sentence.  It is much more complicated than that.

A correlation coefficient is one piece of the puzzle.

A simple linear regression is another piece of the puzzle.

They are just that - pieces.  If you're trying to teach introductory students how to assess the relationship between two variables, they are essential building blocks, and may be sufficient to get the very basic point across.  But comprehensive understanding of this issue requires a LOT more than just those two things.

Thank you for your prompt response to my question, which helped to clarify how "effect" should be measured regarding the phenomena being studied.

Kind regards,

Debra

 Dear Hassan

Tiu are right. R is a very important test, but ie tells us about a conection and less about effect

This is very comprehensive

http://www.statisticalassociates.com/assumptions.pdfhttp://www.statisticalassociates.com/assumptions.pdf

I believe Correlation and Regression do different jobs! Correlation does NOT tell anything about the effect of y (independent variable) and x (dependent variable). Even when correlation is highly significantly positive (or negative), it tells nothing about cause and effect relationship between y and x. Correlation indicates only the strength of relationships between y and x. 

Regression has the power of prediction and showing cause-effect relationship. Yet, to have a clear picture of this relationship between independent and dependent in terms of cause-effect, all extraneous variables must be excluded. 

A linear relationship can also predict some randomly generated numbers, so it cannot easily tell you the cause and effect. However, to find the cause and effects, a good statistical models (i.e. Bayesian models)  should be used. Thanks

They will get at relations between the variables.  As has been pointed out, correlation does not necessarily show effect, as you asked about.  The only way true effect is determined is by experimental manipulation of your independent variable.  Simply correlating them does not prove effect, only that the two are related.  "Proof", although that word should be used very cautiously in statistics, comes from the design.  If you look at the equations for both, you can see that correlation is relationship, where as regression is modeling change in independent and resulting change in dependent. 

Regression equations are more based on cause and effect (for every increase in x, what is the change in y).  I think they are more useful because they can be used to both explain and predict variance in your outcome.  But again, these are just generic descriptions of correlation and regression because it really depends on your situation.  In general, I think most people who read an article with regression coefficients would interpret that as you trying to see the cause and effect link of the two variables (which seems to be your goal), whereas correlation coefficients would be interpreted as simply looking at the relation between the two without implying cause and effect.  Which is most appropriate and what should drive your decision depends entirely upon your hypothesis and design (i.e., your question) and not what the analyses do (i.e., the answer).  The tail shouldn't wag the dog so to speak.   Hope that helps, best of luck. 

Dear Debra

Correlation and regression give different meaning and used in different purpose.

Correlation coefficient ( denoted = r ) describe the relationship between two independent variables ( in bivariate correlation ) , r ranged between +1 and - 1 for completely positive and negative correlation respectively , while r = 0 mean that no relation between variables, so we can calculate correlation between paired data, the data must normally distributed and scale type variables , if one or two variables are ordinal , or in case of not normal distribution , then spearman correlation is suitable for this data .

Regression describe the relationship between independent variable ( x ) and dependent variable ( y ) , and we can use regression equation to predict for y by using x value .

 Good Luck

Correlation is used to compare two independent variables (x1, x2) whereas regression is used to describe the relationship between an independent variable (x) and dependent variable (y). In addition, correlation is not causation (does not show cause and effect) where as regression shows to what extend variable (x) can be used as a predictor of variable (y).

Uses of multiple linear regression analysis

First, it might be used to identify the strength of the effect that the independent variables have on a dependent variable.

Second, it can be used to forecast the effects or impacts of changes. 

Third, multiple linear regression analysis predicts trends and future values.