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2014
EEffffeecctt oonn tthhee sseelllliinngg pprriiccee ((ddeeppeennddaanntt vvaarriiaabbllee)) wwiitthh
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Course: BUS 511
BUSINESS STATISTICS
Section: 2
Prepared For: Dr. Kais Zaman
Prepared By:
Date of submission: 25th
April, 2014
Name I.D. NO Imran Hossain
132 1071 660
Abu Hanif Muhammad Saeem Khan
133 0802 660
Rajiv Shamim
112 0542 460
Table of Content
SL Topic Page
1 Introduction 3
2 Background 03 5
3 Variables 05 6
4 Statistical Approaches 08 10
5 Data sheet 11
6 Descriptive statistics 28 21
7 Regression Analysis 32 24
8 Correlations 35 29
9 One way ANOVAs 30
10 Hypothesis testing 32
11 Findings 41
12 Conclusion 42
13 Reference 43
ACKNOWLEDGEMENT
First of all we would like to express our sincere gratitude to almighty Allah that we have
successfully completed our report.
We would like to thank our honorable teacher of the Business Statistics course, Dr.Kais Zaman
for giving us this opportunity and help needed to prepare this report.
Finally, we would like to thanks our class mates for their cooperative attitude which guided us
to recover the problems regarding our report.
25th
April, 2014
To
Dr.Kais Zaman
Associate Professor
Subject: Submission of Project Report
Dear Sir,
It is our great honor to submit our project report on Effect on the selling price (dependant
variable) with changes in independent variables of different cars models. In this endeavor, this
report seeks to identify and analyze the relationships among the variables. The report contains
statistical analysis and some findings and recommendations. It would be our enormous pleasure
if you find this report useful and informative to have an apparent perspective on the issue.
Thanking you
1. Imran Hossain ID - 1321071660
2. Rajiv Shamim ID -1120542460
3. Abu Hanif Muhammad Saeem Khan ID - 1330802660
1. Introduction
1.1Origin of the Report:
BUS 511 is a statistics course offered in the MBA program of NSU in order to equip students
with the statistical tools. The project was initiated so that the students would get a practical
exposure of statistical analysis in a project work. Different types of statistical tools were used
in this project to find out the results.
1.2 Problem Statement:
Automobile is an important and fast growing industry around the globe. So the selling price
of a car is always a good interest for people. In this report we showed different variables of
cars, which are affecting the selling price of a car. We have used different car models and
different models as our sample data. There are many variables that affect the selling price of
a branded car. We have chosen 4 of these for analyzing the selling price of the 33 different
models of car.
Here in this paper a model is to be set up to establish the relationship among the variables
and the different cars selling price. The variables used in this report are given below:
Engine displacement- Cubic Centimeters (CC)
Horse power (HP)
Fuel Miles per gallon (MPG)
Wheel /Drive
1.3 Objectives of the study:
To find out the level of impact and relationship between Cubic centimeters and Cars
selling price.
To find out the level of impact and relationship between Horse power and Cars
selling price.
To find out the level of impact and relationship between Fuel miles per gallon and
Cars selling price.
To find out the level of impact and relationship between Wheel drive and Cars
selling price.
Regression analysis of 4 independent variables with the dependent variable
Testing usefulness of the model
Testing partial regression co efficient
Testing correlation co efficient
To get a practical exposure of statistical analysis
1.4 Methodology:
The data used in this report is collected from different car showrooms in the city. These
include the sole agents of the company in the city such as Pacific Motors BD for Nissan and
Hyundai, Navana 3s for Toyota, Honda and some local car dealers. In total 33 car models are
used as a sample variables. After collecting the data we analyzed the data with the help of
statistical software (Minitab 17). The collected data was first summarized and presented
graphically. Then we tested some hypothesis about the population mean for each of the
variables. After that, we calculated the correlations by using Minitab software among
different variables, to see the strength of their relationship. Then we tested hypothesis of
correlation coefficient. Then we extended the relationships to a multiple regression model.
After that we tested some hypothesis of partial regression coefficient and finally we tested
the usefulness of the regression model.
2. Background
2.1 History of the Automobile industry
The history of the automobile begins as early as 1769, with the creation of steam engine
automobiles capable of human transport. In 1806, the first cars powered by an internal
combustion engine running on fuel gas appeared, which led to the introduction in 1885 of the
ubiquitous modern gasoline- or petrol-fueled internal combustion engine. Cars powered by
electric power briefly appeared at the turn of the 20th century, but largely disappeared from
use until the turn of the 21st century. The early history of the automobile can be divided into
a number of eras, based on the prevalent means of propulsion. Later periods were defined by
trends in exterior styling, and size and utility preferences.
2.2 Global Automobile Sales:
2.3 Car brands used as sample data in the analysis:
3. Variables
3.1 Explanation of test parameters
There are total 5 variables in this project. Among them 1 is dependent variable and other 4 is
independent variables. Car selling is always been an interesting thing for the one who wants
to buy it. So Car selling price is our dependent variable in this report. 4 variables are
affecting the car selling price, so these are the independent variables. These independent
variables are given below:
Engine Displacement- Cubic Centimeters (CC)
Horse power (HP)
Fuel Miles per gallon (MPG)
Wheel /Drive
3.2 Dependent variable
In our case a branded cars selling price is the dependent variable. The price of the car at the
showroom is the selling price. This is a dependent variable, because it may be affected by
several independent variables.
3.3 Independent variables
Factors that are affecting the car selling price are the independent variables. We have 4
independent variables for this report.
Cubic Centimeters (CC)
Cubic Centimeters is the total volume of all cylinders at full stroke. In cars its ci's Cubic
Inches. The higher the cc's, the larger and more powerful the engine.
Horse power (HP)
Horsepower (hp) is the name of several units of measurement of power. Horsepower was
originally defined to compare the output of steam engines with the power of draft horses in
continuous operation. The unit was widely adopted to measure the output of piston engines,
turbines, electric motors, and other machinery. The definition of the unit varied between
geographical regions. Most countries now use the SI unit watt for measurement of power.
Difference between CC and Horsepower (HP):
Many people ask for a relationship between horsepower and cc or how many cc in a hp. The short
answer is about 15 to 17cc = 1 hp or about 1 cu.in. = 1 bhp for a modern car. The full answer is
complex - the power output of an engine depends on the state of tune as well as size, and the definition
of horsepower must be considered, brake horsepower (bhp) or shaft horsepower (shp), and is not
covered here. Horsepower can be increased by engine tuning, more volatile fuel, supercharging or
exhaust turbo boosting. As can be seen from the table below, the top 10 highly tuned engines cover a
wide variety from Formula 1 racing cars and dragsters, through TT and motocross bikes to a tiny 3.5cc
model car engine producing 3.45hp at a screaming 42,600 rpm and weighing in at 340 grams.
Note:-
1 cubic inch ( cu.in. ) = 16.387064 cubic centimetres ( cu.cm. cm3 or cc )
1000 cc = 1 litre
1 hp (UK) = 0.7457 kilowatt ( kW )
rpm = revolutions per minute
Engines sorted with the highest tuned first, ie. with the lowest cu.cm to horsepower ratio
engine cc hp rpm cc / hp
Model car 2 stroke diesel - Rossi 236R21 3.5 3.45 42,600 1.0145
Top fuel dragster V8 supercharged 8194 8000+ 8 200 1.0243
F1 racing car 1987 turbo - qualifying 1494 1400+ 14 000 1.0671
F1 racing car 1987 turbo - race trim - Honda 1494 1000 13 000 1.4940
Honda TT race bike 125 47 2.6596
Model aircraft - Chinese contest diesel 3.5 1.3 26 000 2.6923
Model aircraft - Typhoon Russian diesel 2.47 0.82 27 200 3.0122
BMW F1 racing car 2003 - P83 2998 920 19 200 3.2587
Motocross bike 125 33 3.7879
Honda - stock road bike 125 33 3.7879
F1 racing car 1995 - no turbo 3000 750 4.0000
This table shows that two cars having the same cc can have different horse powers so both cc and
horsepower are not directly related to each other.
Data source: http://www.simetric.co.uk/si_cc2hp.htm
Fuel Miles per gallon (MPG)
Efficiency is defined as output per input. In automobiles it is the distance traveled per unit of
fuel used; in miles per gallon (mpg) or kilometers per liter (km/L), commonly used in the
UK, US (mpg) and Japan, Korea, India, Pakistan, parts of Africa, The Netherlands, Denmark
and Latin America (km/L). If mpg is used the gallon should be identified.
Wheel /Drive
A drive wheel is a road wheel in an automotive vehicle that receives torque from the power
train, and provides the final driving force for a vehicle. A two-wheel drive vehicle has two
driven wheels, and a four-wheel drive has four, and so-on. A steer wheel is one that turns to
change the direction of a vehicle. A trailer wheel is one that is neither a drive wheel nor a
steer wheel.
Two wheel drive
For four-wheeled vehicles, this term is used to describe vehicles that are able to transmit
torque to at most two road wheels, referred to as either front- or rear-wheel drive. The term
4x2 is also used, to indicate four total road-wheels with two being driven.
Four-wheel drive or All-wheel drive
Four-wheel drive, 4WD, 4x4 ("four-by-four"), all-wheel drive, and AWD are terms used to
describe a four-wheeled vehicle with a drive train that allows all four road wheels to receive
torque from the internal combustion engine simultaneously. While some people associate the
term with off-road vehicles - powering all four wheels provides better control, and therefore
safety on slick ice, and is an important part of rally racing on mostly-paved roads.
Front-wheel drive
Front-wheel drive (or FWD for short) is the most common form of internal combustion
engine / transmission layout used in modern passenger cars, where the engine drives the front
wheels. Most front wheel drive vehicles today feature transverse engine mounting, whereas
in past decades engines were mostly positioned longitudinally instead. Rear-wheel drive was
the traditional standard, and is still widely used in luxury cars and most sport cars. Four-
wheel drive is also sometimes used. See also Front-engine, front-wheel drive layout.
Rear-wheel drive
Rear-wheel drive (or RWD for short) was a common internal combustion engine /
transmission layout used in automobiles throughout the 20th century.
4. Statistical Approaches
4.1 Theoretical Model:
Dependent variable: Cars selling price (Y)
Independent variable: X1, X2, X3, X4
Car selling price, Y= f (X1, X2, X3, X4)
The analysis would be based on different variables of cars and the internal relationship of
their characteristics with the cars selling price.
4.2 Regression Model:
A multiple regression equation was drawn as follows on the basis of Least Square Method:
= b0+b1x1+b2x2+b3x3+b4x4
Where, = Car selling price ($)
X1= Cubic Centimeters (CC)
X2 = Horse power (HP)
X3 = Fuel Miles per gallon (MPG)
X4 = Wheel /Drive
4.3 Hypothesis:
H1: Cubic Centimeters (CC) has impact on car selling price
H2: Horse power (HP) has impact on car selling price
H3: Fuel Miles per gallon (MPG) has impact on car selling price
H4: Wheel /Drive has impact on car selling price
4.4 Sample size
Considering time and other limitations, we found that it would be most appropriate to work
with 33 car model of different brands.
Number of observations, n= 33
Variables: {X1, X2, X3, X4, }
4.5 Data Sheet
No. Car Model Selling
Price in
BDT
CC HP Fuel
(MPG)
Wheel
/Drive
1 2013 NISSAN
PATROL
16500000 5700 381 15 4
2 2012 NISSAN
MURANO
9500000 4000 270 19 4
3 2012 Toyota
Premio G
2850000 1500 135 28 2
4 2012 Toyota Allion 2800000 1500 135 28 2
5 2012 NISSAN
SUNNY
1650000 1300 132 25 2
6 2013Toyota Yaris 1750000 1299 132 30 2
7 2013 Toyota Prius
Hybrid
3450000 1800 165 65 2
8 2013 Toyota Camry
Hybrid
8200000 2500 231 66 4
9 2012 NISSAN
SYLPHY
2300000 2000 132 46 2
10 2012 NISSAN
BLUEBIRD
2650000 1800 98 50 4
11 Kia Sportage 2013 5200000 2400 115 39 4
12 2012 NISSAN X-
TRAIL
6400000 1800 98 42 2
13 2012 NISSAN
CEFIRO
4550000 2500 179 24 2
14 Toyota Avanza 1450000 1300 132 30 2
15 2012 NISSAN
PATHFINDER
Hybrid
4500000 3500 266 21 4
16 2013 Toyota Rav4 4200000 2362 159 26 4
17 Toyota Landcruiser
200
40000000 4500 310 15 4
18 Toyota Prado 2013 13200000 2982 182 21 4
19 2012 NISSAN
SUNNY 1.5
1750000 1500 132 22 2
20 2012 Toyota
Fortuner
9000000 2694 270 17 4
21 2011 NISSAN
DUALIS
5700000 3500 268 20 2
22 2011 NISSAN
TEANA
2250000 2500 169 22 2
23 2013 Hyundai
Sonata
4500000 2400 179 28 2
24 Hyundai i10 1500000 1200 105 30 2
25 2011 NISSAN
SKYLINE
5200000 3500 270 17 4
26 Hyundai Eon 1150000 814 95 35 2
27 2013 KIA optima 6300000 2400 175 27 2
28 Toyota Vista 2000 1700000 1800 132 22 2
29 Toyota Corolla G
2012
1600000 1600 127 28 2
30 Honda 2014 CRV 8400000 2500 179 22 4
31 Honda City 1950000 1300 120 30 2
32 Honda Accord 2013 2800000 2400 185 24 2
33 Mitsubishi Pajero
Sport 2013
6900000 2700 175 25 4
4.6 Graphs
4.6.1Histogram: A histogram is a graphical representation of the distribution of data. It is an
estimate of the probability distribution of a continuous variable. A histogram is a representation
of tabulated frequencies, shown as adjacent rectangles, erected over discrete intervals, with an
area proportional to the frequency of the observations in the interval. The total area of the
histogram is equal to the number of data.
400000003000000020000000100000000-10000000
16
14
12
10
8
6
4
2
0
Mean 5813636
StDev 7094719
N 33
Selling Price in BDT
Fre
quency
Histogram of Selling Price in BDTNormal
500040003000200010000
12
10
8
6
4
2
0
Mean 2350
StDev 1052
N 33
CC
Fre
quency
Histogram of CCNormal
40032024016080
12
10
8
6
4
2
0
Mean 176.8
StDev 69.52
N 33
HP
Fre
quency
Histogram of HPNormal
6050403020100
9
8
7
6
5
4
3
2
1
0
Mean 29.06
StDev 12.48
N 33
Fuel (MPG)
Fre
quency
Histogram of Fuel (MPG)Normal
54321
20
15
10
5
0
Mean 2.788
StDev 0.9924
N 33
Wheel /Drive
Fre
quency
Histogram of Wheel /DriveNormal
4.6.2 Scatter diagram: The scatter plot is widely used to present measurements of two or more
related variables. It is particularly useful when the variables of the y-axis are thought to be
dependent upon the values of the variable of the x-axis (usually an independent variable).In a
scatter plot, the data points are plotted but not joined; the resulting pattern indicates the type and
strength of the relationship between two or more variables.
600050004000300020001000
40000000
30000000
20000000
10000000
0
CC
Sellin
g P
rice in
BD
T
Scatterplot of Selling Price in BDT vs CC
400350300250200150100
40000000
30000000
20000000
10000000
0
HP
Sellin
g P
rice in
BD
T
Scatterplot of Selling Price in BDT vs HP
70605040302010
40000000
30000000
20000000
10000000
0
Fuel (MPG)
Sellin
g P
rice in
BD
T
Scatterplot of Selling Price in BDT vs Fuel (MPG)
4.03.53.02.52.0
40000000
30000000
20000000
10000000
0
Wheel /Drive
Sellin
g P
rice in
BD
T
Scatterplot of Selling Price in BDT vs Wheel /Drive
4.6.3Probability Plot: The normal probability plot is a graphical technique for normality testing:
assessing whether or not a data set is approximately normally distributed. The data are plotted
against a theoretical distribution in such a way that the points should form approximately a
straight line. Departures from this straight line indicate departures from the specified distribution.
5. Descriptive statistics
5.1 Descriptive Statistics: Selling Price, CC, HP, Fuel (MPG), wheel drive
Descriptive Statistics: Selling Price in BDT, CC, HP, Fuel (MPG), Wheel /Drive Variable N N* Mean SE Mean StDev Minimum Q1 Median
Q3
Selling Price in BDT 33 0 5813636 1235032 7094719 1150000 1850000 4200000
6650000
CC 33 0 2350 183 1052 814 1500 2400
2697
HP 33 0 176.8 12.1 69.5 95.0 132.0 165.0
208.0
Fuel (MPG) 33 0 29.06 2.17 12.48 15.00 21.50 26.00
30.00
Wheel /Drive 33 0 2.788 0.173 0.992 2.000 2.000 2.000
4.000
Variable Maximum
Selling Price in BDT 40000000
CC 5700
HP 381.0
Fuel (MPG) 66.00
Wheel /Drive 4.000
5.2 Summary
1st Quartile 1850000
Median 4200000
3rd Quartile 6650000
Maximum 40000000
3297958 8329314
2474103 5451281
5705496 9384136
A-Squared 3.85
P-Value
1st Quartile 132.00
Median 165.00
3rd Quartile 208.00
Maximum 381.00
152.11 201.41
132.00 179.00
55.91 91.96
A-Squared 1.57
P-Value
6. Regression Analysis: A regression analysis is a statistical process for estimating the
relationships among variables. It includes many techniques for modeling and analyzing several
variables, when the focus is on the relationship between a dependent variable and one or more
independent variables. More specifically, regression analysis helps one understand how the
typical value of the dependent variable changes when any one of the independent variables is
varied, while the other independent variables are held fixed. In regression analysis, it is also of
interest to characterize the variation of the dependent variable around the regression function
which can be described by a probability distribution. The p-value for each term tests the null
hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 0.05) indicates that
we can reject the null hypothesis. In other words, a predictor that has a low p-value is likely to be
a meaningful addition to our model because changes in the predictor's value are related to
changes in the response variable. Conversely, a larger (insignificant) p-value suggests that
changes in the predictor are not associated with changes in the response. Typically, we use the
coefficient p-values to determine which terms to keep in the regression model.
1st Quartile 2.0000
Median 2.0000
3rd Quartile 4.0000
Maximum 4.0000
2.4360 3.1398
2.0000 4.0000
0.7981 1.3126
A-Squared 6.12
P-Value
Regression Analysis: Selling Price in BDT versus CC, HP, Fuel (MPG), Wheel /Drive
Regression Equation:
Selling Price in BDT = -6269746 + 4113 CC + 480 HP - 4486 Fuel (MPG)
+ 883610 Wheel /Drive
Explanation:
bo = -6269746, it will always remain constant.
For a single unit change of CC, the Car Selling Price will be changed 4113 units, and
the variables share a positive relationship to each other.
For a single unit change of HP, the car Selling Price will be changed 480units, and the
variables share a positive relationship to each other.
For a single unit change of Fuel (MPG), the car Selling Price will be changed 446 units,
and the variables share a negative relationship to each other.
For a single unit change of Wheel/Drive, the Car Selling Price will be changed
883610units, and the variables share a positive relationship to each other.
Predictor Coef SE Coef T-value P-value
Constant -6269746
4584915 -1.37 0.182
CC 4113
2641 1.56 0.131
HP 480 36687 0.01 0.990
Fuel (MPG) -4486 86150 -0.05 0.959
Wheel/Drive 883610 1276072 0.69 0.494
Regression Table
S = 5398952 R-Sq = 49.33% R-Sq(adj) = 42.09% R-sq(pred) = 27.36%
The coefficient of determination (R2) and the adjusted value was found to be 49.33% and
42.09% respectively. That means the Selling Price can be explained 49.33% by CC, HP, Fuel
(MPG) and Wheel/Drive.
Minitab Output:
Regression Equation
Selling Price in BDT = -6269746 + 4113 CC + 480 HP - 4486 Fuel (MPG) + 883610 Wheel /Drive
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 4 7.94558E+14 1.98640E+14 6.81 0.001
CC 1 7.06797E+13 7.06797E+13 2.42 0.131
HP 1 4993542516 4993542516 0.00 0.990
Fuel (MPG) 1 79043102586 79043102586 0.00 0.959
Wheel /Drive 1 1.39762E+13 1.39762E+13 0.48 0.494
Error 28 8.16163E+14 2.91487E+13
Lack-of-Fit 27 8.16162E+14 3.02282E+13 24182.58 0.005
Pure Error 1 1250000000 1250000000
Total 32 1.61072E+15
Model Summary
S R-sq R-sq(adj) R-sq(pred)
5398952 49.33% 42.09% 27.36%
Coefficients:
Term Coef SE Coef T-Value P-Value VIF
Constant -6269746 4584915 -1.37 0.182
CC 4113 2641 1.56 0.131 8.48
HP 480 36687 0.01 0.990 7.14
Fuel (MPG) -4486 86150 -0.05 0.959 1.27
Wheel /Drive 883610 1276072 0.69 0.494 1.76
Fits and Diagnostics for Unusual Observations
Selling Std
Obs Price in BDT Fit Resid Resid
8 8200000 7361820 838180 0.23 X
17 40000000 15854387 24145613 4.89 R
R Large residual
X Unusual X
The graph shows that for 1 unit increase in CC the selling price increases by 4693 units.
The graph shows that for 1 unit increase in HP the selling price increases by 65400 units.
600050004000300020001000
40000000
30000000
20000000
10000000
0
S 5175848
R-Sq 48.4%
R-Sq(adj) 46.8%
CC
Sellin
g P
rice in
BD
TFitted Line Plot
Selling Price in BDT = - 5214286 + 4693 CC
400350300250200150100
40000000
30000000
20000000
10000000
0
S 5533401
R-Sq 41.1%
R-Sq(adj) 39.2%
HP
Sellin
g P
rice in
BD
T
Fitted Line PlotSelling Price in BDT = - 5746294 + 65400 HP
The graph shows that for 1 unit increase in Fuel (MPG) the selling price changes by -159673
units.
The graph shows that for 1 unit increase in WHEEL/DRIVE the selling price increases by
3672692 units.
70605040302010
40000000
30000000
20000000
10000000
0
S 6917845
R-Sq 7.9%
R-Sq(adj) 4.9%
Fuel (MPG)
Sellin
g P
rice in
BD
TFitted Line Plot
Selling Price in BDT = 10453817 - 159673 Fuel (MPG)
4.03.53.02.52.0
40000000
30000000
20000000
10000000
0
S 6184330
R-Sq 26.4%
R-Sq(adj) 24.0%
Wheel /Drive
Sellin
g Pr
ice
in B
DT
Fitted Line PlotSelling Price in BDT = - 4425385 + 3672692 Wheel /Drive
7. Correlations: The correlation coefficient is a measure of linear association between two
variables. Values of the correlation coefficient are always between -1 and +1. A correlation
coefficient of +1 indicates that two variables are perfectly related in a positive linear sense; a
correlation coefficient of -1 indicates that two variables are perfectly related in a negative linear
sense, and a correlation coefficient of 0 indicates that there is no linear relationship between the
two variables.
Correlation: Selling Price in BDT, CC
Pearson correlation of Selling Price in BDT and CC = 0.696
P-Value = 0.000
Correlation: Selling Price in BDT, HP
Pearson correlation of Selling Price in BDT and HP = 0.641
P-Value = 0.000
Correlation: Selling Price in BDT, Fuel (MPG)
Pearson correlation of Selling Price in BDT and Fuel (MPG) = -0.281
P-Value = 0.113
Correlation: Selling Price in BDT, Wheel /Drive
Pearson correlation of Selling Price in BDT and Wheel /Drive = 0.514
P-Value = 0.00
8. One way ANOVAs: One-way analysis of variance (one-way ANOVA) is a technique used to
compare means of two or more samples (using the F distribution). This technique can be used
only for numerical data.
The ANOVA tests the null hypothesis that samples in two or more groups are drawn from
populations with the same mean values. To do this, two estimates are made of the population
variance. These estimates rely on various assumptions. The ANOVA produces an F-statistic, the
ratio of the variance calculated among the means to the variance within the samples. If the group
means are drawn from populations with the same mean values, the variance between the group
means should be lower than the variance of the samples, following the central limit theorem. A
higher ratio therefore implies that the samples were drawn from populations with different mean
values.
One-way ANOVA: CC, HP, Fuel (MPG), Wheel /Drive
Method
Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level = 0.05
Equal variances were assumed for the analysis.
Factor Information
Factor Levels Values
Factor 4 CC, HP, Fuel (MPG), Wheel /Drive
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Factor 3 129296737 43098912 155.00 0.000
Error 128 35591490 278059
Total 131 164888228
Model Summary
S R-sq R-sq(adj) R-sq(pred)
527.313 78.41% 77.91% 77.04%
Means
Factor N Mean StDev 95% CI
CC 33 2350 1052 ( 2168, 2532)
HP 33 176.8 69.5 ( -4.9, 358.4)
Fuel (MPG) 33 29.06 12.48 ( -152.57, 210.69)
Wheel /Drive 33 2.788 0.992 (-178.841, 184.417)
Pooled StDev = 527.31
Result: Since the p-value is less than .05 level of significance, so the null
hypothesis is rejected that is all means are not equal.
Wheel /DriveFuel (MPG)HPCC
2500
2000
1500
1000
500
0
Data
Interval Plot of CC, HP, ...95% CI for the Mean
The pooled standard deviation was used to calculate the intervals.
9. Hypothesis testing: Hypothesis testing or significance testing is a method for testing a claim
or hypothesis about a parameter in a population, using data measured in a sample. In this
method, we test some hypothesis by determining the likelihood that a sample statistic could have
been selected, if the hypothesis regarding the population parameter were true.
9.1 Hypothesis test for Mean
1. Car selling price
Mean (x) = 5800000, Standard Deviation (S) = 7094719, n = 33
Ho: = 5800000
HA: 5800000
Test Statistic:
z = x - o / s n
With = .05
And p value 0.991, which is greater than .05
Hence the Null Hypothesis Ho is not rejected.
Population mean of car selling price is equal to BDT 5800000.
2. CC
Mean (x) = 2300, Standard Deviation (S) =1052, n = 33
Ho: = 2300
HA: 2300
Test Statistic:
z = x - o / s n
With = .05
And p value 0.785, which is greater than .05
Hence the Null Hypothesis Ho is not rejected
Therefore the Population mean of CC is equal to 2300.
3. HP
Mean (x) = 176, Standard Deviation (S) = 69.52, n = 33
Ho: = 176
HA: 176
Test Statistic:
z = x - o / s n
With = .05
And p value 0.950, which is greater than .05
Hence the Null Hypothesis Ho is not rejected
Therefore, Population mean of HP is equal to 176
4. Fuel (MPG)
Mean (x) = 29, Standard Deviation (S) = 29.061, n = 33
Ho: = 29
HA: 29
Test Statistic:
z = x - o / s n
With = .05
And p value 0.978, which is greater than .05
Hence the Null Hypothesis Ho is not rejected
Therefore, Population mean of Fuel (MPG) is equal to 25.
5. Wheel drive
Mean (x) = 2, Standard Deviation (S) = 0.9942, n = 33
Ho: = 2
HA: 2
Test Statistic:
z = x - o / s n
With = .05
And p value 0.000, which is less than .05
Hence reject the Null Hypothesis Ho
Population mean of Wheel drive is not equal to 2.
9.2 Hypothesis Test for correlation coefficient
1. Car Selling price and CC
Hypothesis 1: Correlation exists between car selling price and CC
Ho: = 0
Ha: 0
Ho = There is no relationship between car selling price and CC
Ha = There is relationship exists between car selling price and CC
Test Statistic: here, r = 0.696 n = 33 = 0.05
P value 0.00 is less than .05
Hence Reject the Null Hypothesis Ho
So, there is relationship exists between car selling price and CC
2. Car Selling price and HP
Hypothesis 2: Correlation exists between car selling price and HP
Ho: = 0
HA: 0
Ho = There is no relationship between car selling price and HP
Ha = There is relationship exists between car selling price and HP
Test Statistic: here, r = 0.641 n = 33 = 0.05
P value 0.00 is less than .05
Hence Reject the Null Hypothesis Ho
So, there is relationship exists between car selling price and HP
3. Car Selling price and Fuel (MPG)
Hypothesis 3: Correlation exists between car selling price and Fuel (MPG)
Ho: = 0
HA: 0
Ho = There is no relationship between car selling price and Fuel (MPG)
Ha = There is relationship exists between car selling price and Fuel (MPG)
Test Statistic: here, r = -0.281 n = 33 = 0.05
P value 0.00 is less than .05
Hence Reject the Null Hypothesis Ho
So, there is relationship exists between car selling price and Fuel (MPG)
4. Car Selling price and Wheel drive
Hypothesis 5: Correlation exists between car selling price and Wheel drive
Ho: = 0
HA: 0
Ho = There is no relationship between car selling price and Wheel drive
Ha = There is relationship exists between car selling price and Wheel drive
Test Statistic: here, r = 0.514 n = 30 = 0.05
P value 0.061 is greater than .05
Hence accept the Null Hypothesis Ho
So, there is no relationship between car selling price and Wheel drive.
9.3 Hypothesis Test for partial regression coefficient
1. Car Selling price and CC
Hypothesis 1: CC is a valuable predictor in the presence of the other variables while
predicting cars selling price.
Ho: b 1 = 0
HA: b1 0
Ho = CC is not a valuable predictor in the presence of the other variables while predicting
cars selling price.
Ha = CC is a valuable predictor in the presence of the other variables while predicting
cars selling price.
Test Statistic: here, p value = .131 n = 33 = 0.05
P value .131 is larger than .05
Hence do not reject the Null Hypothesis Ho
So, we conclude that CC is a not a valuable predictor in the presence of the other
variables while predicting cars selling price.
2. Car Selling price and HP
Hypothesis 1: HP is a valuable predictor in the presence of the other variables while
predicting cars selling price.
Ho: b 1 = 0
HA: b1 0
Ho = HP is not a valuable predictor in the presence of the other variables while predicting
cars selling price.
Ha = HP is a valuable predictor in the presence of the other variables while predicting
cars selling price.
Test Statistic: here, p value =. 0.990 n = 33 = 0.05
P value = 0.990 is larger than .05
Hence do not reject the Null Hypothesis Ho
So, we conclude that HP not is a valuable predictor in the presence of the other variables
while predicting cars selling price.
3. Car Selling price and Fuel (MPG)
Hypothesis 1: Fuel (MPG) is a valuable predictor in the presence of the other
variables while predicting cars selling price.
Ho: b 1 = 0
HA: b1 0
Ho = Fuel (MPG) is not a valuable predictor in the presence of the other variables while
predicting cars selling price.
Ha = Fuel (MPG) is a valuable predictor in the presence of the other variables while
predicting cars selling price.
Test Statistic: here, p value = 0.959 n = 33 = 0.05
P value = 0.959 is larger than .05
Hence Do not Reject the Null Hypothesis Ho
So, we conclude that Fuel (MPG) is a not a valuable predictor in the presence of the other
variables while predicting cars selling price.
4. Car Selling price and Wheel drive
Hypothesis 1: Wheel drive is a valuable predictor in the presence of the other
variables while predicting cars selling price.
Ho: b 1 = 0
HA: b1 0
Ho = Fuel (MPG) is not a valuable predictor in the presence of the other variables while
predicting cars selling price.
Ha = Fuel (MPG) is a valuable predictor in the presence of the other variables while
predicting cars selling price.
Test Statistic: here, p value = 0.494 n = 33 = 0.05
P value = .494 is larger than .05
Hence do not reject the Null Hypothesis Ho
So, we conclude that Wheel drive is a not a valuable predictor in the presence of the other
variables while predicting cars selling price.
9.4 Testing the usefulness of the regression model
We are testing the F test for finding the regression model is useful or not.
Regression Analysis: Selling Price in BDT versus CC, HP, Fuel (MPG), Wheel /Drive
Ho: regression model is not useful in predicting the car selling price
HA: regression model is useful in predicting the car selling price
Ho: 1= 2= 3= 4= 5=0
HA: 1= 2= 3= 4= 50
Test statistics F = MSR/MSE
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 4
7.94558E+14
1.98640E+14 6.81
0.001
CC 1
7.06797E+13 7.06797E+13 2.42 0.131
HP
1 4993542516 4993542516 0.00 0.990
Fuel (MPG)
1 79043102586 79043102586 0.00 0.959
Wheel
1 1.39762E+13 1.39762E+13 0.48 0.494
Error
28 8.16163E+14 2.91487E+13
Lack-of-Fit
27 8.16162E+14 3.02282E+13 24182.58 0.005
Pure Error
1 1250000000 1250000000
Total
32 1.61072E+15
So F value is 6.81 and P value is 0.001
P value is less than .05
Hence reject the null hypothesis
So we can conclude that regression model is useful in predicting the car selling price.
10. Findings
In this report we tried to find out the relationship and impact on the car selling price with 4
independent variables. We had 4 hypotheses about this report, these are given below,
H1: Cubic Centimeters (CC) has impact on car selling price
Pearson correlation of Selling Price in BDT and CC = 0.696, so it a partial positive
relationship
H2: Horse power (HP) has impact on car selling price
Pearson correlation of Selling Price in BDT and HP = 0.641, so it a partial positive
relationship
H3: Fuel Miles per gallon (MPG) has impact on car selling price
Pearson correlation of Selling Price in BDT and Fuel (MPG) = -0.281, so it a partial
negative relationship
H4: Wheel /Drive has impact on car selling price
Pearson correlation of Selling Price in BDT and Wheel /Drive = 0.514, so it a negative
positive relationship.
Therefore we can say that all hypotheses are true.
The regression equation is:
Selling Price in BDT = -6269746 + 4113 CC + 480 HP - 4486 Fuel (MPG)
+ 883610 Wheel /Drive
The coefficient of determination (R2) and the adjusted value was found to be 49.33% and
42.09% respectively. That means the Selling Price can be explained 49.33% by CC, HP,
Fuel (MPG) and Wheel/Drive.
From the Hypothesis Test for correlation coefficient we can conclude that among 4
independent variables fuel miles (MPG) have inverse relation with the selling price and
the other 3 CC, HP and Wheel drive have positive relationship with the car selling price.
From the Hypothesis Test for partial regression coefficient we can conclude that all
independent variables are not a valuable predictor in the presence of the other variables
while predicting cars selling price. That means the selling price of a car cannot be found
using the relationship with just one independent variable as the other variables plays a
great role as well.
And after testing the usefulness of the regression model we can say that this regression
model is useful in predicting the car selling price.
11. Conclusion:
There are other variables such as the brand image, the type of tires used in the car, the interior
decoration type of car, the type of engine used etc. All these and others factors play a major role
in determining the selling price. Due to time constraints and data constraints we need to work
with the available factors and that is explained by the value of R2 in the report. The report could
have been more realistic if the other variables could be included.
13. References:
Pacific Motors BD Ltd.
Navana 3s centre
Car retailers:
Car selection
KK automobiles
Sal Sabeel cars
http://www.toyota.com
http://www.nissan-global.com/EN/index.html
http://worldwide.hyundai.com/WW/Main/index.html
http://www.simetric.co.uk/si_cc2hp.htm