Discussion on Mathematical Models

Discussion on Mathematical function models

Mathematics is an extraordinary exercise of the human mind in abstracting the results of observation to find similarities and differences between phenomena. These relations between phenomena make it possible to organize the natural world into discrete sets of objects that can be studied using similar mathematical objects and methods. Putting all this information into an equation, in a meaningful manner, can be called as mathematical modeling. This, in turn, allows us to summarize, formalize, interpolate, and extrapolate from observations that have been recorded.

The mathematical concept of a function is critical to defining relations between (among) variable phenomena, particularly phenomena that can be described using two (or even more) variables. Mathematical functions can be used for both summarization and prediction. Through this unit, we can explore several types of natural phenomena, and use several types of functions and representations of functions in order to describe the phenomena. We may use these models to make predictions and solve problems related to numerous fields. Understanding these function model is very important since we are going to predict or solve a real world problem (which might end up with incorrect/dangerous results if the analysis is not correct).

The following example demonstrates how to apply the function model concept in marketing data.

Description of data: Following data set represents the amount of sales that particular company had according to the amount they spent on advertising.

Advertising ($) | Sales ($) |

10,000 | 43,000 |

9,000 | 40,500 |

11,000 | 41,000 |

12,000 | 45,900 |

11,000 | 47,000 |

12,000 | 51,000 |

13,000 | 54,000 |

13,000 | 57,000 |

14,000 | 56,000 |

15,000 | 60,000 |

15,800 | 61,000 |

16,700 | 63,000 |

To understand the behavior of the data set, let us consider a plot which demonstrates the relationship between Advertising costs vs....