Regression and correlation are closely related statistical techniques that help analyze the relationship between variables. While they are distinct methods, there is a strong connection between the two. Here are the key aspects of their relationship:

1. Purpose: Both regression and correlation aim to measure the relationship between variables. However, they serve different purposes. Regression analysis is used to model and predict the value of a dependent variable based on one or more independent variables. On the other hand, correlation analysis is used to quantify the strength and direction of the linear relationship between two variables without explicitly predicting one variable from another.
2. Variables: In regression analysis, there is a dependent variable that is being predicted or explained by one or more independent variables. Correlation analysis, however, involves studying the relationship between two variables without explicitly distinguishing between dependent and independent variables.
3. Measure of Association: Regression analysis provides the coefficients (slope and intercept) that quantify the relationship between the dependent and independent variables. These coefficients represent the change in the dependent variable for a unit change in the independent variable(s). Correlation analysis provides a correlation coefficient (such as Pearson’s correlation coefficient) that measures the strength and direction of the linear association between two variables. The correlation coefficient does not distinguish between dependent and independent variables.
4. Direction: Regression analysis considers the direction of the relationship between variables based on the signs (positive or negative) of the regression coefficients. Correlation analysis also indicates the direction of the relationship based on the sign of the correlation coefficient (positive or negative). In both cases, a positive sign indicates a positive relationship (as one variable increases, the other tends to increase) and a negative sign indicates a negative relationship (as one variable increases, the other tends to decrease).
5. Strength: Both regression and correlation provide measures of the strength of the relationship between variables. In regression analysis, the coefficient of determination (R-squared) indicates the proportion of variance in the dependent variable that can be explained by the independent variable(s). In correlation analysis, the correlation coefficient ranges between -1 and +1, where values close to -1 or +1 indicate a strong linear relationship, while values close to 0 indicate a weak or no linear relationship.
6. Assumptions: Both regression and correlation have certain assumptions. Regression analysis assumes a linear relationship between variables, independence of observations, homoscedasticity (constant variance of errors), and normality of errors. Correlation analysis assumes linearity, independence of observations, and normality of variables.
7. Interdependence: Regression and correlation are interrelated. Correlation between two variables is the square root of the coefficient of determination (R-squared) from a simple linear regression between the same variables.