An article takes you to get the linear regression model in mathematical modeling (example explanation of the 2005 Yangtze River water quality problem with code)

1. Problem analysis

According to your forecast and analysis, if the proportion of Grade IV and Grade V water in the mainstream of the Yangtze River is required to be controlled within 20% each year for the next 10 years, and there is no water inferior to Grade V, how much sewage will be treated each year

In order to achieve the water quality required in the title, a binary linear regression model between the wastewater discharge volume and the percentage of various types of water can be established to predict the wastewater discharge volume in the next ten years and determine its percentage to the percentage of various types of water. The functional relationship between. Through this relationship, you can calculate the maximum sewage discharge that the Yangtze River can withstand in this case. Compare this discharge with the predicted discharge. The extra part needs to be treated every year.

2. Principle explanation

The amount of sewage that meets the conditions is only related to the water of Category IV, V, and inferior to V. Since the sum of Category IV and V water is not more than 20%, then the sum of the percentages of Category IV and V water y1 and sewage can be considered The relationship between the percentage of water inferior to Grade V y2 and the amount of sewage. Taking into account the interaction and mutual transformation of the water quality of Grade IV, V, and inferior V, the linear regression model of x, y1, and y2 is directly established: