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Customer Loyalty

In: Business and Management

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REGRESSION

In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables.

More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed.

SIMPLE LINEAR REGRESSION

In simple linear regression, we predict scores on one variable from the scores on a second variable. The variable we are predicting is called the criterion variable and is referred to as Y. The variable we are basing our predictions on is called the predictor variable and is referred to as X. When there is only one predictor variable, the prediction method is called simple regression. In simple linear regression, the topic of this section, the predictions of Y when plotted as a function of X form a straight line.
The example data in Table 1 are plotted in Figure 1. You can see that there is a positive relationship between X and Y. If you were going to predict Y from X, the higher the value of X, the higher your prediction of Y.
Table 1. Example data. X | Y | 1.00 | 1.00 | 2.00 | 2.00 | 3.00 | 1.30 | 4.00 | 3.75 | 5.00 | 2.25 |

Figure 1. A scatter plot of the example data

Linear regression consists of finding the best-fitting straight line through the points. The best-fitting line is called a regression line.

MULTIPLE REGRESSION Multiple regression is an extension of simple linear regression in which more than one independent variable (X) is used to predict a single dependent variable (Y). The predicted value of Y is a linear transformation of the X variables such

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