• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15
  16. 16
    16

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

...read more.

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

image00.png

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

image01.png

          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

image06.png

It is observed that there is a negative linear relationship between the number of accidents and the age of driver.

Regression

image07.png

image08.png

image09.png

image10.png

Correlations

image11.png

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

...read more.

Conclusion

3  

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

image03.png

image04.png

image05.png

.

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

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Mathematics (EE): Alhazen's Problem

    5 My primary reason for choosing to investigate this focus question is that the I.B Higher Level Mathematics Programme at our school is at times limited with regards to the study of geometry and trigonometry. Investigating this problem gave me an opportunity to fill this void.

  2. A logistic model

    With a considerably large growth rate, r=2.9, the long-term sustainable limit is reached after already 3 years, and since this limit cannot be surpassed over a long time, the fourth year is characterized by a drop in population (ie. the death of roughly thirty thousand fish), followed by a demographic explosion.

  1. Creating a logistic model

    Since we know that in every case, when time = 0, that is, initially our population is 10000, substituting x = 0 in the logistic function, it must be the case that y = 10000. In other words: a = 5 Although the initial growth rate should not affect the

  2. Maths Project. Statistical Analysis of GCSE results at my secondary school summer 2010 ...

    10 46 f 46 128 Fi 7.5 34 m 34 127 Fl 10 46 f 46 126 Fo 8 34 f 34 125 Fo 8.5 28 m 28 124 Fo 12 40 f 40 123 Ga 11 52 f 52 122 Ge 9 46 f 46 121 Ge 9 46

  1. The speed of Ada and Fay

    After finding Fay's average time, which is 12.5 seconds. Then, I am going to define the speed of Fay's runs, by the speed formula. The calculation will be as follow, After the calculation, the outcome of Fay's running velocity is 8 m/s.

  2. Statistics project. Comparing and analyzing the correlation of the number of novels read per ...

    This shows that the middle amount of books read was 1, which is even lesser than the median number of books by boys. As shown, there is no correlation between number of books read and modal mark for girls Step 2 The next step was to do the chi squared test.

  1. Networks - Konigsberg Bridge Problem.

    All these will be better explained when I tell what the rule is. And finally in the third section, there is another map of the bridges in Kaliningrad except with two more bridges across the Pregel. For this part, I have to apply my rule and tell if the network is traversable.

  2. Barbara & Allen's Compound Interest

    To calculate a 12.68% interest rate (r) with a yearly frequency, one must the value 1 for n, resulting in the following formula: A= P(1+0.1268/1)(1)(t) It is clear that 12% interest per year compounded monthly is approximately the same as 12.68% interest per year compounded annually. At first, each formula produces the same interest, however, as time

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work