BUS 511-Sample Project

2014

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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)


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


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



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


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



Therefore, Population mean of HP is equal to 176

4. Fuel (MPG)


Ho: = 29

HA: 29

Test Statistic:

z = x - o / s n

With = .05



Therefore, Population mean of Fuel (MPG) is equal to 25.

5. Wheel drive


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




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



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


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


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


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


Ho: b 1 = 0

HA: b1 0

Ho = Fuel (MPG) is not a valuable predictor in the presence of the other variables while


Ha = Fuel (MPG) is a valuable predictor in the presence of the other variables while


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


4. Car Selling price and Wheel drive

Hypothesis 1: Wheel drive is a valuable predictor in the presence of the other


Ho: b 1 = 0

HA: b1 0

Ho = Fuel (MPG) is not a valuable predictor in the presence of the other variables while


Ha = Fuel (MPG) is a valuable predictor in the presence of the other variables while


Test Statistic: here, p value = 0.494 n = 33 = 0.05

P value = .494 is larger than .05


So, we conclude that Wheel drive is a not a valuable predictor in the presence of the other


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



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

BUS 511-Sample Project

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