Correlation analysis seeks to establish whether or not two variables are correlated. That is to say, whether an increase in one is accompanied by either an increase (or decrease) in the other most of the time. It is a measure of the degree to which they change together.
Regression analysis goes further and seeks to measure the extent of the change. Using statistical techniques, a regression line is fitted to the observations and this line is the best measure of how changes in one variable affect the other variable.
Although the first of these variables is frequently called an independent or even explanatory variable, and the second is called a dependent variable, the existence of regression does not imply a causal relationship.
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The strength of the linear relationship between the two variables in the regression equation is the correlation coefficient, r, and is always a value between -1 and 1, inclusive. The regression coefficient is the slope of the line of the regression equation.
A correlation coefficient is a value between -1 and 1 that shows how close of a good fit the regression line is. For example a regular line has a correlation coefficient of 1. A regression is a best fit and therefore has a correlation coefficient close to one. the closer to one the more accurate the line is to a non regression line.
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Correlation is a measure of association between two variables and the variables are not designated as dependent or independent. Simple regression is used to examine the relationship between one dependent and one independent variable. It goes beyond correlation by adding prediction capabilities.
A linear regression