Correlation and Regression
Correlation is a specialized procedures from a larger family of regression procedures. Regression procedures examine the relationship between two or more sets of paired variables. The basic linear regression formula
y = a + β x
Where:
y is the set of dependent variable
values
a is the intercept, the value of y when x is 0
β is the change in y for each unit of x.
In words this formula says that the predicted value of the dependent variable y is the intercept value a plus the coefficient β times the value of x. It is possible to add more βs for additional independent variables.
Lets first compare the specifics of correlation with the most general linear regression.
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Correlation |
Linear Regression |
| Correlation examines the relationship between two variables using a standardized unit. However, most applications use raw units as an input. | Regression examines the relationship between one dependent variables and one or more independent variables. Calculations may us either raw unit values, or standardized units as input. |
| The calculation is symmetrical, meaning that the order of comparison does NOT change the result. | The calculation is NOT symmetrical. So one variable is assigned the dependent role (the values being predicted) and one or more the independent role (the values hypothesize to impact the dependent variable). |
| Correlation coefficients indicate the strength of a relationship. | Regression shows the effect of one unit change in an independent variable on the dependent variable. |
| Correlation removes the effect of different measurement scales. Therefore, comparison between different models is possible since the rho coefficient is in standardized units. | Linear regression using raw unit measurement scales can be used to predict outcomes. For example, if a model shows that spending more money on advertising will increases sales, then one can say that for every added $ in advertising our sales will increase by β. |
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A next step is to examine statistical control |
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OR to consider an example of Correlation being applied to the relationship between Unemployment and Crime. |
