## Correlation and regression analysis methods

Analysis and synthesis of marketing research data is carried out by manual or computer processing methods. For processing, both descriptive and analytical methods are used. Among the analytical methods in marketing research, the following are mainly used: trend analysis, non-linear regression and correction methods, discriminant analysis, cluster analysis, factor analysis, etc.

Considering the dependencies between the signs, it is necessary to distinguish first of all two categories of dependence: functional and correlation.

* Functional relations * are characterized by a complete correspondence between the change in the factor sign and the change in the resultant value, and to each value of the characteristic-factor there correspond quite definite values of the effective characteristic.

In * correlations *, there is no complete correspondence between the change of the factor and the resultant attribute, the effect of individual factors is manifested only on average in the mass observation of actual data. In the simplest case of applying the correlation dependence, the magnitude of the effective attribute is considered as a consequence of a change in only one factor (for example, the advertising budget is the reason for the growth in sales volume).

* Correlation analysis * provides an opportunity to calculate the level of confidence in the results of the analysis. In the process of this analysis, correlation indices are calculated, which include correlation coefficients and correlation ratios.

When comparing functional and correlation dependencies, it should be borne in mind that in the presence of a functional relationship between the signs, knowing the magnitude of the factor sign, you can accurately determine the magnitude of the resultant trait. In the presence of the correlation dependence, only the tendency of the change in the resultant attribute is established with a change in the value of the factor sign. Unlike the rigidity of a functional connection, correlation links are characterized by a variety of causes and effects and only their trends are established.

Let's consider an example * of correlation dependence. * Let's analyze and confirm or deny the statement that the number of promotions held by the company to promote a new product increases sales. To do this, we will sample territories (Table 6.8).

* Table 6.8 *

** Product sales data for different areas of the city **

Territory (territory code) |
The volume of sales of packages, pcs. |
Number of promotions |

I |
30 |
2 |

2 |
60 |
5 |

3 |
40 |
3 |

4 |
60 |
7 |

5 |
40 |
2 |

6 |
80 |
6 |

7 |
60 |
4 |

8 |
90 |
9 |

9 |
90 |
8 |

10 |
50 |
4 |

The simplest way to detect a connection is to match two parallel rows. From the general analysis it is clear that an increase in the number of promotions contributes to an increase in sales.

Another way is to construct a scattering field on the diagram (Figure 6.2).

* Fig. 6.2. * ** Dispersion field **

The nature of the distribution in Fig. 6.2 indicates that the volume of sales increases with the increase in the number of promo actions. Consequently, there is a positive relationship between the factors.

* Regression analysis * will give an opportunity to answer the question about the quantitative measure of the influence of various factors, for example, on demand (the volume of possible sale). It is a selection and solution of mathematica