

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 bivariate 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 Yaxis. A bivariate 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.



