Regression analysis is a statistical method used to establish a relationship between two variables: independent and dependent variables. The main objective of regression analysis is to find the best fit line that represents the relationship between the two variables. The dependent variable is the one that is being predicted, while the independent variable is the one that is used to make the prediction.

Establishing mathematical relationship between two variables
One of the primary objectives of regression analysis is to establish a mathematical relationship between two variables. The mathematical relationship is derived by fitting a line through a set of data points, which represents the relationship between the two variables. The line can be linear or non-linear, depending on the type of regression analysis being used.

Measuring the extent of association between two variables
Regression analysis also helps in measuring the extent of association between two variables. The correlation coefficient is used to measure the degree of association between the two variables. The correlation coefficient ranges from -1 to +1, where -1 represents a perfect negative correlation, 0 represents no correlation, and +1 represents a perfect positive correlation.

Predicting the value of dependent variable for a given value of independent variable
Regression analysis is also used to predict the value of the dependent variable for a given value of the independent variable. This is done by using the equation of the line that represents the relationship between the two variables. Once the equation is derived, the value of the dependent variable can be predicted for any given value of the independent variable.

Conclusion
In summary, regression analysis is concerned with establishing a mathematical relationship between two variables, measuring the extent of association between the two variables, and predicting the value of the dependent variable for a given value of the independent variable. Therefore, the correct answer is option D, which states that regression analysis is concerned with both establishing a mathematical relationship between two variables and predicting the value of the dependent variable for a given value of the independent variable.