Regression is mathematical modelling of the relationship between a dependent variable and a number of independent variables. Correlation is the degree of association between two or more variables. It is measured within the interval from -1 to +1. The sign is an indication of the direction of the association i.e. whether positive or negative. Positive correlation is the tendency for both variables to change in the same direction whereas negative correlation implies that both variables tend to change in opposite directions. The direction of correlation between two variables is usually reflected in the corresponding regression coefficient. For example a person's weight and height are related, the weight being the dependent variable. They are strongly positively correlated and therefore the coefficient of regression is positive and significant.

In simple linear regression (one independent variable X and one dependent variable Y) the regression line is Y = a + (sy rxy/ sx) Y where sx and sy are the standard deviations of X and Y and rxy is the correlation coefficient between X and Y. If the correlation coefficient is significantly different from 0 then the regression coefficient will also be signficant and vice versa.

What I wanted to add before my previous answer was rudely grabbed and posted before I was ready, r is a measure of linear (straight line) dependence between X and Y, while a regression line (straight line) is a model that may be used to predict Y if X is known. Before calculating correlations and regressions, plot a scatter plot to check whether the relationship is linear.

thanks dr Francois for valuable input.

regression measure whether is the independent variable/s effect on the dependent variable or not but correlation just measure the relation between variables only

Regression is statistical modeling which use to predict, interpret and control independent and dependent variable. For example, you can predict the dependent variable using independent variables.

Correlation just explain the association between two variables. For example, If the height grows, weight will also increase.

But in the regression, you can show how much weight you increase on an average with every cm of growing height.

Correlation gives an idea how strongly two variables are related. however, regression analysis represent functional form of this relationship.

you can see examples of correlation coefficient and regression function in following publications

https://www.researchgate.net/publication/324611186_Multiple_linear_regression_and_genetic_algorithm_approaches_to_predict_temporal_scour_depth_near_circular_pier_in_non-cohesive_sediment

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