Economic processes are characterized by quantitative characteristics that are subject to mathematical modeling, in particular, using multi-factor regression analysis. For example, the cost of a car depends on the brand, model, year of issue (age), fuel (gasoline, diesel, gas, gas / gasoline, hybrid, electric), gearboxes (mechanical, automatic, tiptronic, adaptive, variator), drive type (full, front, rear), engine volume, engine power, mileage, color, status, etc.
To illustrate the possibilities of regression analysis we select the basic (basic): brand, model, year of issue (age), mileage. In our case, the dependence of value on other factors is a regression. Given that the cost of a car depends on several factors (year of issue (age) and mileage), an example of economic modeling will be carried out with the help of a multivariable regression model. For example, we will construct separate multi-factor regression models depending on the market value of the Toyota Land Cruiser Prado (further-car) from the year of issue (age) and mileage for diesel and gasoline versions. We will get statistical information from open sources of the Internet. The analysis of gasoline cars 441 units and diesel 167 units with the period of release from 1997 to 2019 years.
Multi-factor regression model will be constructed using the following algorithm
1. Selection of factors that affect the cost of the car
The main factors affecting the market value of a car are year of issue (age) and mileage. That is, the variable Y (car cost) depends on X1 (age) and X2 (mileage)
2. Selection and construction of regression model
The construction of a regression model will be carried out using modern software products and the consequences of which the regression model will look like:
Petrol kit
Y = 43 156.73 - 1 808.71 * X1- 0.0053 * X2
Diesel kit
Y = 48 483.35 - 1 724.37 * X1-0.021 * X2
3. Estimation of the regression model and its factors
Petrol kit
The coefficient of multiple determination is (R Square) is 0.85, hence the result, and the cost depends on the factors (age, mileage) by 85 percent. Multiple R multiplier factor is 0.92, which indicates a strong (close) relationship between the indicators
Diesel kit
The coefficient of multiple correlation is (Multiple R) is 0.89, hence the effective index, and the cost depends on the factors (age, mileage) by 89 percent. The Multiple R ratio is 0.94, indicating a strong (close) relationship between the indicators. Other indicators, in particular Fischer F-criterion and the Student t-criterion, confirm the significant link between the indicators included in the two-factor regression model
4. Using a regression model (examples)
4.1. Definition by the seller of the market price at the sale
The seller plans to sell the petrol Toyota Land Cruiser Prado 2015 with a mileage of 120,000 km and uses a regression model to determine the recommended value
Y = 48 483.35 - 1 724.37 * X1-0.021 * X2
or
Y = 48 483.35 - 1 724.37 * 5-0.021 * 120.000
or
Y = 37,342
So the recommended cost is $ 37,342
4.2. Checking the reliability of the car's run
The Toyota Land Cruiser Prado 2012 Diesel Buyer, using a regression model, wants to check the reliability of the car's run, which plans to buy. The announcement runs 42,000 km, the cost of the car is $ 44,195
Y = 48 483.35 - 1 724.37 * X1-0.021 * X2
or
X2 = (48 483.35 - 1 724.37 * X1 - Y) / 0.021
or
X2 = 39,981
Thus, the mileage according to the regression model is 39,981 km and is close to that declared by the seller in the announcement
4.3. Calculation of cost loss during the use period
The buyer bought 2019 petrol Toyota Land Cruiser Prado in 2017 for a price of $ 39,300 with a mileage of 40,000 km and wants to calculate how much he will lose after 5 years of use, flooding each year 20,000 km
Y = 43 156.73 - 1 808.71 * X1- 0.0053 * X2
The year 2024 will be 140,000 km
The cost of the car according to the regression model
Y = 43 156.73 - 1 808.71 * X1- 0.0053 * X2
Y = 43 156.73 - 1 808.71 * 7 0.0053 * 140.000
Y = 29,754
Consequently, during 5 years of operation a loss of value is possible
$ 9,546 = $ 39,300 - $ 29,754
4.4. The calculation of the comparison of the cost of a car with a gasoline and diesel engine
The buyer, in order to decide on the purchase of petrol or diesel Toyota Land Cruiser Prado, with the help of a regression model wants to calculate in which car, during the 10 years of operation will be less cost loss.
Output: The buyer has two alternative purchase options
The 2014 gasoline version, running 150,000 km, costs $ 33,300
Diesel version of 2014, running 150,000 km cost $ 36,200
During 10 years of operation the mileage will be 350,000 km = 20,000 km * 10 years + 150,000 km
The cost of the gasoline version
Y = 43 156.73 - 1 808.71 * X1- 0.0053 * X2
Y = 14 171
Losing cost of the gasoline version
$ 33,300 - $ 14,171 = $ 19,129
The cost of the diesel version
Y = 48 483.35 - 1 724.37 * X1-0.021 * X2
Y = 15,268
Loss of cost of the diesel version
$ 36,200 - $ 15,268 = $ 20,932
Thus, the petrol Toyota Land Cruiser Prado will lose 10 years of equal operating costs of $ 1,803 less than diesel
Summing up, it can be argued that the car is not only a means of transportation and a source of pleasure, but also an investment object. We will invest efficiently.