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Correlation and Regression

  • Correlation is the statistical measure that quantifies the linear relationship between two variables. If you look at a scatter plot of two variables, their correlation is the slope of the ‘best fitting’ straight line that can be drawn through the points. If the line rises (traveling left to right) the slope is positive, which means that as one variable increases, the other also increases. If the line falls, the opposite is true: the slope is negative and as one variable increases, the other decreases. Further, the size of the correlation measures the size of the resulting rise or fall. So if a correlation was .5, that would mean that for each unit one variable increases, the other variable will increase by half a unit. A correlation of -.75 would mean that for each unit one variable increases, the other decreases by ¾ of a unit.
  • Regression is an extension of correlation analysis that will predict the value of one variable (the dependent variable) based on the values of one or more predictor or ‘independent’ variables. In a bi-variate regression (i.e., the dependent variable and one independent variable), the main difference between regression and correlation is that regression adds an ‘intercept’ term. Thinking of the line, the intercept is the point where the line crosses the Y-axis. A bi-variate regression produces a the general formula for a line:
  • y = a + bx where: y is the predicted value of the dependent variable
  • a is the intercept
  • b is the slope of the line
  • x is the value of the independent variable to be predicted
  • A multiple regression analysis adds more independent variables, and extends the equation above to include additional independent variables, each having their own slope.
  • Regression is typically used whenever a prediction is required. Typical uses of regression in market research include predicting market share, coupon redemption rates, product acceptance scores, customer satisfaction or awareness and so on.
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