INTRODUCTION S. 2005). Resistance 1 – Light duty

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).

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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