- Level: International Baccalaureate
- Subject: Maths
- Word count: 1761
Using regression analysis to solve a real time problem
Extracts from this document...
Introduction
QUESTION
Describe a practical problem in any field of interest for which a regression model will be appropriate.Do a research to obtain real data relating to the problem described.
PROBLEM STATEMENT
There has been an upsurge of accidents on the Accra Kumasi Highway in recent times.In spite of this increased occurrence of accidents on the roads little have been done to find out the main causes of the life threatening situation.Although there have been massive reconstruction of the roads at several parts of the highway and in spite of the numerous road safety campaigns that have been undertaken,very little changes have occurred.In order to curb the occurrence of accidents on our roads,there is therefore the need to conduct research to find out the causes of the accidents and to find out the extent to which they do so.
METHODOLOGY
A survey was conducted at the Asafo Accra-Kumasi Lorry Park.In the survey, fifty commercial drivers were selected at random and they were asked questions on their past experiences in the last twelve months.The drivers answered questions on the number of accidents they had encountered, the number of times they maintained their vehicles ,the average speed at which they drove their vehicles and their ages. The number of accidents the drivers encountered was regressed on
Middle
1 5 70 34
1 5 75 27
0 6 70 56
1 3 80 44
0 8 70 53
0 11 75 37
3 1 95 38
2 3 90 43
2 3 85 25
1 6 80 36
0 5 75 54
0 14 70 45
0 10 70 38
1 9 75 57
Number of Accidents vrs Vehicle Maintenance
It is observed that there is a negative linear relationship between the number of accidents and the age of driver.
Number Accidents vrs Average speed of driver
It is observed that there is a positive linear relationship between the number of accidents and the average speed of driver.
Number Accidents vrs Age of Driver
It is observed that there is a negative linear relationship between the number of accidents and the age of driver.
Regression
Correlations
DESCRIPTION OF MODEL
The regression model is of the form
Y = B0 + B1 X1 + B2 X2 + B3 X3
with Y being the number of accidents encountered by the drivers and the dependent variable. X1,X2,X3represents the number of times they maintained their vehicles, the average speed at which they drove their vehicles and their ages respectively;they represent the independent variables.
Y= -1.745-0.0651X1+0.06454X2-0.0311X3 R2 = 0.695
(1.51) (0.028) (0.010) (0.013) S.e
The estimated regression model above depicts the relationship between the predictor variables and the response variable and their standard errors.
The value of R (0.812) depicts a strong linear relationship between all the predictor variables and the response variable.
An R2 value of 0.659 means that the regression model fits well to the set of data points and that 65.9 percent of the variation of the number of accidents the drivers had is explained by the multiple regression model. The Adjusted R2
Conclusion
Y = -1.745-0.06514(4)+0.06454(100)-0.0311(25)
=3.67
Hence a driver of 25 years of age who maintained his vehicle 4 times and drove at an average speed of 100 km/h may encounter 3.67 accidents which is 0.33 away from the observed value of 4.Hence,with a residual error of just 0.33,the regression model can be said to be adequate with vehicle maintenance and average speed of driver being most influencial in the model.
RESIDUAL PLOTS
.
CONCLUSION
The number of accidents encountered by vehicles on the Accra Kumasi highway are related to number of times the drivers maintained their vehicles, the average speed at which they drove their vehicles and their ages.
From the model it is observed that the more a driver did vehicle maintenance,the less he got accidents.Younger drivers got more.The faster a driver drove,the more he encountered accidents.
ROAD SAFETY PROPOSALS
In order to minimize road accidents;
- Drivers who ply the highway must be forced to maintain their vehicles more often by way of conduction of regular checkups at the exit points of the lorry station,so that vehicles that are not in good condition are stopped from embarking on the journey.
- There should be more speed limit indications and road safety signs at various points on the highway.An uncompromising law enforcement agency should be posted at various segments of the highway to make sure defaulters are made to face the law.
- Young drivers must be educated on the dangers they impose on themselves whenever they drive at high speeds.
REFERENCES
Econometric Models and Forecasts (Irwin & Mc-Graw-Hill); Robert S. Pindyck & Danile.
Elementary Statistics (Mc Graw-Hill); Allan G. Bluman
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