INTRODUCTION

Fuel loss in automobiles

has turned into the real worry, because of the expansion in its cost and the

absence of resources. One-third of the fuel utilization in the auto are because

of the Frictional losses (ScienceDaily, 12 January 2012). The main reason for

these friction, wear and lubrication was set up by scientists like Hertz (H.

Hertz,1882), Reynolds (O. Reynolds,1886), and Bowden and Tabor (F.P. Bowden, D.

Tabor,1950). If the reason behind these losses are found, the wastage of fuel

can be reduced drastically. This analysis was conducted on the fuel loss due to

friction in car, where my dependent variable is gallons per vehicle and

independent variable is MPG (miles per gallon) and resistance (Espey, M., &

Nair, S. 2005).

PARAMETERS AND SAMPLE

Parameters of interest are

mean Gallons per vehicle and mean miles per gallon. The sample population

consists for year 2005 – 2015 (Espey, M., & Nair, S. 2005).

COLLECTED DATA

The data is collected

from U.S. Energy Information Administration which was released on December 22, 2017

(Espey, M., & Nair, S. 2005).

Resistance 1 – Light duty

vehicles with short wheel base

Resistance 2 – light duty

vehicles with long wheel base

Resistance 3 – Heavy duty

trucks

Year

MPG

Resistance

(Gallons per Vehicle)

2005

22.1

1

567

2006

22.5

1

554

2007

22.9

1

468

2008

23.7

1

435

2009

23.5

1

442

2010

23.3

1

456

2011

23.2

1

481

2012

23.3

1

484

2013

23.4

1

480

2014

23.2

1

476

2015

23.9

1

475

2005

17.7

2

617

2006

17.8

2

612

2007

17.1

2

877

2008

17.3

2

880

2009

17.3

2

882

2010

17.2

2

901

2011

17.1

2

702

2012

17.1

2

694

2013

17.2

2

683

2014

17.1

2

710

2015

17.3

2

684

2005

6

3

4385

2006

5.9

3

4304

2007

6.4

3

4398

2008

6.5

3

4387

2009

6.5

3

4037

2010

6.4

3

4180

2011

6.3

3

4128

2012

6.4

3

3973

2013

6.4

3

4086

2014

6.3

3

4036

2015

6.4

3

3904

The above tabulation

stats are the MPG (miles per gallon) run by each vehicle between the year 2005 –

2015 and the number of gallons each vehicle used between the years.

DESCRIPTIVE STATISTICS

The descriptive

statistics for Gallons per vehicle and miles per gallon as conducted in excel

is given below.

MPG

(Gallons per Vehicle)

Mean

15.59697

1799.333

Median

17.2

702

Mode

6.4

#N/A

Skew

-0.36013

0.73394

Stdev

7.104333

1706.699

The mean MPG and Gallons

per vehicle Is 15.59 units and 1799.33 units. The mean of MPG is solid as its

estimation of standard deviation in less. However, with high estimation of

standard deviation of Gallons per vehicle, I can state that mean gallons per

vehicle isn’t dependable. The information for gallons per vehicle is skewed to

right, showing there are not very many perceptions with high estimations of

gallons per vehicle. The best measure of central tendency for Gallons per

Vehicle is median with 702 (Thompson,

B. 2004).

CORELATION ANDREGRESSION

The scatter-plot between

resistance and Gallons per Vehicle is given below.

SUMMARY OUTPUT

Regression

Statistics

Multiple

R

0.997816

R

Square

0.995636

Adjusted

R Square

0.995185

Standard

Error

118.4279

Observations

33

ANOVA

df

SS

MS

F

Significance F

Regression

3

9280363

30934534

2205.644

2.64E-34

Residual

29

406729.9

14025.17

Total

32

93210333

Coefficients

Standard

Error

t Stat

P-value

Lower

95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept

4930.599

393.7137

12.52331

3.19E-13

4125.364

5735.834

4125.364

5735.834

MPG

-121.131

62.05759

-1.95191

0.060665

-248.053

5.791221

-248.053

5.791221

resistance_1

-1639.11

1047.734

-1.56444

0.128564

-3781.97

503.7449

-3781.97

503.7449

resistance_2

-2086.86

682.8109

-3.05629

0.004776

-3483.37

-690.36

-3483.37

-690.36

RESULTS

DISCUSSION

There is a strong positive linear relationship between

resistance and gallons per vehicle observed from scatterplot. That is as the

value of resistance increases the value of gallons per vehicle also increases.

Ho: model is not significant. v/s h1: model is

significant. With F = 1105.34 and p-value < 0.05, I reject ho and conclude
that model is significant (Draper, N. R., & Smith, H. 2014).
Ho1: coefficient of MPG is not significant. v/s h1:
coefficient of MPG is significant. With t = -1.95 and p-value < 0.10, I
reject ho and conclude that coefficient of MPG is significant at 10% level of
significance (Draper, N. R., & Smith, H. 2014).
Ho2: coefficient of Resistance_1 is not significant. v/s h2: coefficient of Resistance_1 is
significant. With t = -1.56 and p-value > 0.1, I reject ho and conclude that

coefficient of Resistance_1 is not significant (Draper, N. R., & Smith, H. 2014).

Ho3: coefficient of Resistance_2 is not significant.

v/s h13: coefficient of Resistance_2 is significant. With t = -3.056 and

p-value > 0.1, I reject ho and conclude that coefficient of Resistance_2 is

significant (Draper, N. R., & Smith, H. 2014).

Regression equation is given by: gallons per vehicle =

4930.59 -121.13*MPG -1639.112 *resistance_1 -2086.86*resistance_2

Gallons per vehicle for Light-Duty Vehicles, Short

Wheelbase (low resistance vehicle) is 1639.112 units less as compared to Heavy-Duty

Trucks (higher resistance vehicle).

Gallons per vehicle for Light-Duty Vehicles, Long

Wheelbase (low resistance vehicle) is 2086 units less as compared to Heavy-Duty

Trucks (higher resistance vehicle).

CONCLUSION

Model is significant. Regression equation is given by:

gallons per vehicle = 4930.59 -121.13*MPG -1639.112 *resistance_1

-2086.86*resistance_2. Gallons per vehicle for Light-Duty Vehicles, Short

Wheelbase (low resistance vehicle) is 1639.112 units less as compared to

Heavy-Duty Trucks (higher resistance vehicle). Gallons per vehicle for

Light-Duty Vehicles, Long Wheelbase (low resistance vehicle) is 2086 units less

as compared to Heavy-Duty Trucks (higher resistance vehicle). Hence, I can say

that as rolling resistance increases, fuel loss also increases (Loewenstein,

G., & Ubel, P. 2010).

Reference

VTT Technical Research Centre of Finland. “One-third of

car fuel consumption is due to friction loss.” ScienceDaily. ScienceDaily,

12 January 2012. www.sciencedaily.com/releases/2012/01/120112095853.htm

H. Hertz, Über die behrörung fester elastische Körper und

über die harte (On the contact of ridge elastic solids and on hardness)

Verhandlungen des Vereins zur Beforderung des Gewerbefleisses, Leipzig, Germany

(1882)

O. Reynolds On the theory of lubrication and its application

to Mr. Beauchamp Tower’s experiments, including experimental determination of

the viscosity of olive oil Philosophical Transactions of the Royal Society, 177

(1886), pp. 157-234

F.P. Bowden, D. Tabor Friction and lubrication of solids,

part I, Oxford University Press, Oxford (1950)

Espey, M., & Nair, S. (2005). Automobile fuel economy:

What is it worth?. Contemporary Economic Policy, 23(3), 317-323.

http://ageconsearch.umn.edu/bitstream/20102/1/sp04es12.pdf?origin%3Dpublication_detail

Thompson, B. (2004). Exploratory and confirmatory factor

analysis: Understanding concepts and applications. American Psychological

Association.

Draper, N. R., & Smith, H. (2014). Applied regression

analysis. John Wiley & Sons.

https://books.google.com.au/books?hl=en&lr=&id=uSReBAAAQBAJ&oi=fnd&pg=PT12&dq=Applied+regression+analysis.+John+Wiley+&ots=Pa5BvBNftX&sig=NZoxAocHtF2Y2yHl1NtrKSS908o#v=onepage&q=Applied%20regression%20analysis.%20John%20Wiley&f=false

Loewenstein, G., & Ubel, P. (2010). Economics behaving

badly. New York Times, 14.

http://bear.warrington.ufl.edu/williams/MAR_6930/Readings_files/Loewenstein%20%26%20Ubel.pdf