Main Project n 33

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 car’s selling price. The variables are used in this report are given below,

Engine displacement- Cubic Centimeters (CC)

Horse power (HP)

Fuel Miles per gallon (MPG)

Preferred Package Accessories ($)

Wheel /Drive

1.3 Objectives of the study:

To find out the level of impact and relationship between Cubic centimeters and Car’s

selling price.

To find out the level of impact and relationship between Horse power and Car’s

selling price.

To find out the level of impact and relationship between Fuel miles per gallon and

Car’s selling price.

To find out the level of impact and relationship between preferred package

accessories and Car’s selling price.

To find out the level of impact and relationship between Wheel drive and Car’s

selling price.

Regression analysis of 5 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. The 33 car models are

used here as a sample variables. After collecting the data we analyzed the data with the help

of statistical software (Minitab 15 and 17). The collected data was first summarized and

presented graphically. Then we tested some hypotheses about the population mean for each

of the variables. After that, we calculated the correlations by using Minitab software among

different variables were, to see the strength of their relationship. Then we tested hypothesis

of correlation coefficient. Then we built a few simple regression equations for Total Pages

Serve and the independent variables. 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:

Fig: Global automobiles sales in 2013

2.3 Car brands used as sample data in the analysis:

3. Variables

3.1 Explanation of test parameters

There are total 6 variables in this project. Among them 1 is dependent variable and other 5 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. 5 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 car’s 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.


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: Car’s 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 car’s selling price.

4.2 Regression Model:

A multiple regression equation was drawn as follows on the basis of Least Square Method:

Ŷ = β0+β1x1+β2x2+β3x3+β4x4

Where, Ŷ = 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 32 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 30 225 2011 NISSAN

SKYLINE5200000 3500 270 17 4

26 Hyundai Eon 1150000 814 95 35 227 2013 KIA

optima6300000 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 30 232 Honda Accord

20132800000 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

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Mean 5813636StDev 7094719N 33

Selling Price in BDT

Freq

uenc

y

Histogram of Selling Price in BDTNormal

http://en.wikipedia.org/wiki/Rectangle

http://en.wikipedia.org/wiki/Frequency_(statistics)

http://en.wikipedia.org/wiki/Continuous_variable

http://en.wikipedia.org/wiki/Probability_distribution

500040003000200010000

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Mean 2350StDev 1052N 33

CC

Freq

uenc

yHistogram of CC

Normal

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6

4

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Mean 176.8StDev 69.52N 33

HP

Freq

uenc

y

Histogram of HPNormal

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Mean 29.06StDev 12.48N 33

Fuel (MPG)

Freq

uenc

yHistogram of Fuel (MPG)

Normal

54321

20

15

10

5

0

Mean 2.788StDev 0.9924N 33

Wheel /Drive

Freq

uenc

y

Histogram of Wheel /DriveNormal

4.6.2 Scatter diagram: The scatterplot 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 scatterplot, 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

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CC

Sellin

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BDT

Scatterplot of Selling Price in BDT vs CC

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40000000

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20000000

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HP

Sellin

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Scatterplot of Selling Price in BDT vs HP

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40000000

30000000

20000000

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Fuel (MPG)

Sellin

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Scatterplot of Selling Price in BDT vs Fuel (MPG)

4.03.53.02.52.0

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30000000

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Wheel /Drive

Sellin

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BDT

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.

400000003000000020000000100000000-10000000-20000000

99

9590

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105

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Mean 5813636StDev 7094719N 33AD 3.855P-Value <0.005

Selling Price in BDT

Perc

ent

Probability Plot of Selling Price in BDTNormal - 95% CI

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Mean 2350StDev 1052N 33AD 0.973P-Value 0.013

CC

Perc

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Probability Plot of CCNormal - 95% CI

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99

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Mean 176.8StDev 69.52N 33AD 1.574P-Value <0.005

HP

Perc

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Probability Plot of HPNormal - 95% CI

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Fuel (MPG)

Perc

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Probability Plot of Fuel (MPG)Normal - 95% CI

6543210

99

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Wheel /Drive

Perc

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Probability Plot of Wheel /DriveNormal - 95% CI

4.6.4 Dot Plot: The dot plot as a representation of a distribution consists of group of data points plotted on a simple scale. Dot plots are used for continuous, quantitative, univariate data. Data points may be labelled if there are few of them. Dot plots are one of the simplest statistical plots, and are suitable for small to moderate sized data sets. They are useful for highlighting clusters and gaps, as well as outliers. Their other advantage is the conservation of numerical information.

http://en.wikipedia.org/wiki/Outlier

http://en.wikipedia.org/wiki/Univariate

http://en.wikipedia.org/wiki/Quantitative_data

http://en.wikipedia.org/wiki/Continuous_function

360000003000000024000000180000001200000060000000Selling Price in BDT

Dotplot of Selling Price in BDT

5600490042003500280021001400700CC

Dotplot of CC

360320280240200160120HP

Dotplot of HP

432Wheel /Drive

Dotplot of Wheel /Drive

4.6.5 BOX PLOT: A box plot is a convenient way of graphically depicting groups of numerical data through their quartiles. Box plots may also have lines extending vertically from the boxes (whiskers) indicating variability outside the upper and lower quartiles, hence the terms box-and-whisker plot and box-and-whisker diagram. Outliers may be plotted as individual points. Box plots display differences between populations without making any assumptions of the underlying statistical distribution: they are non-parametric. The spacings between the different parts of the box help indicate the degree of dispersion (spread) and skewness in the data, and identify outliers.

40000000

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Sellin

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Boxplot of Selling Price in BDT


http://en.wikipedia.org/wiki/Skewness

http://en.wikipedia.org/wiki/Statistical_dispersion

http://en.wikipedia.org/wiki/Non-parametric



http://en.wikipedia.org/wiki/Statistical_population


http://en.wikipedia.org/wiki/Quartile

6000

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CCBoxplot of CC

400

350

300

250

200

150

100

HP

Boxplot of HP

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40

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Fuel

(MPG

)

Boxplot of Fuel (MPG)

4.0

3.5

3.0

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2.0

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rive

Boxplot of Wheel /Drive

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 Q3Selling Price in BDT 33 0 5813636 1235032 7094719 1150000 1850000 4200000 6650000CC 33 0 2350 183 1052 814 1500 2400 2697HP 33 0 176.8 12.1 69.5 95.0 132.0 165.0 208.0Fuel (MPG) 33 0 29.06 2.17 12.48 15.00 21.50 26.00 30.00Wheel /Drive 33 0 2.788 0.173 0.992 2.000 2.000 2.000 4.000

Variable MaximumSelling Price in BDT 40000000CC 5700HP 381.0Fuel (MPG) 66.00Wheel /Drive 4.000

5.2 Summary

1st Quartile 1850000Median 42000003rd Quartile 6650000Maximum 40000000

3297958 8329314

2474103 5451281

5705496 9384136

A-Squared 3.85P-Value <0.005Mean 5813636StDev 7094719Variance 5.03350E+13Skewness 3.8000Kurtosis 17.3185N 33Minimum 1150000

Anderson-Darling Normality Test

95% Confidence Interval for Mean

95% Confidence Interval for Median

95% Confidence Interval for StDev

400000003000000020000000100000000

Median

Mean

8000000700000060000005000000400000030000002000000

95% Confidence Intervals

Summary Report for Selling Price in BDT

1st Quartile 1500.0Median 2400.03rd Quartile 2697.0Maximum 5700.0

1976.9 2723.1

1800.0 2500.0

846.2 1391.8

A-Squared 0.97P-Value 0.013Mean 2350.0StDev 1052.3Variance 1107243.8Skewness 1.26155Kurtosis 2.06613N 33Minimum 814.0





50004000300020001000

Median

Mean

280026002400220020001800


Summary Report for CC


152.11 201.41

132.00 179.00

55.91 91.96

A-Squared 1.57P-Value <0.005Mean 176.76StDev 69.52Variance 4833.44Skewness 1.17036Kurtosis 0.94583N 33Minimum 95.00





40032024016080

Median

Mean

200180160140


Summary Report for HP


24.634 33.488

22.000 29.005

10.040 16.514

A-Squared 2.03P-Value <0.005Mean 29.061StDev 12.485Variance 155.871Skewness 1.71811Kurtosis 2.90649N 33Minimum 15.000





6050403020

Median

Mean

34323028262422


Summary Report for Fuel (MPG)


2.4360 3.1398

2.0000 4.0000

0.7981 1.3126

A-Squared 6.12P-Value <0.005Mean 2.7879StDev 0.9924Variance 0.9848Skewness 0.45507Kurtosis -1.91285N 33Minimum 2.0000





432

Median

Mean

4.03.53.02.52.0


Summary Report for Wheel /Drive

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 you can reject the null hypothesis. In other words, a predictor that has a low p-value is likely to be a meaningful addition to your 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.


http://en.wikipedia.org/wiki/Independent_variable

http://en.wikipedia.org/wiki/Dependent_variable

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:

βo = -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-ValueRegression 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 0.494Error 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 1250000000Total 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 VIFConstant -6269746 4584915 -1.37 0.182CC 4113 2641 1.56 0.131 8.48HP 480 36687 0.01 0.990 7.14Fuel (MPG) -4486 86150 -0.05 0.959 1.27Wheel /Drive 883610 1276072 0.69 0.494 1.76

Fits and Diagnostics for Unusual Observations

Selling StdObs Price in BDT Fit Resid Resid 8 8200000 7361820 838180 0.23 X 17 40000000 15854387 24145613 4.89 R

R Large residualX Unusual X

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S 5175848R-Sq 48.4%R-Sq(adj) 46.8%

CC

Sellin

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Fitted Line PlotSelling Price in BDT = - 5214286 + 4693 CC

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S 5533401R-Sq 41.1%R-Sq(adj) 39.2%

HP

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Fitted Line PlotSelling Price in BDT = - 5746294 + 65400 HP

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S 6917845R-Sq 7.9%R-Sq(adj) 4.9%

Fuel (MPG)

Sellin

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Fitted Line PlotSelling Price in BDT = 10453817 - 159673 Fuel (MPG)

4.03.53.02.52.0

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S 6184330R-Sq 26.4%R-Sq(adj) 24.0%

Wheel /Drive

Sellin

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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 = 0.696P-Value = 0.000

Correlation: Selling Price in BDT, HP

Pearson correlation of Selling Price in BDT and HP = 0.641P-Value = 0.000

Correlation: Selling Price in BDT, Fuel (MPG)

Pearson correlation of Selling Price in BDT and Fuel (MPG) = -0.281P-Value = 0.113

Correlation: Selling Price in BDT, Wheel /Drive

Pearson correlation of Selling Price in BDT and Wheel /Drive = 0.514P-Value = 0.002

8. One way ANOVAs: In statistics, 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.

http://en.wikipedia.org/wiki/Central_limit_theorem

http://en.wikipedia.org/wiki/Null_hypothesis

http://en.wikipedia.org/wiki/Numerical_data

http://en.wikipedia.org/wiki/F_distribution

http://en.wikipedia.org/wiki/Analysis_of_variance

http://en.wikipedia.org/wiki/Statistics

One-way ANOVA: Selling Price in BDT versus CC

Method

Null hypothesis All means are equalAlternative hypothesis At least one mean is differentSignificance level α = 0.05

Equal variances were assumed for the analysis.


Source DF Adj SS Adj MS F-Value P-ValueCC 17 1.56360E+15 9.19763E+13 29.28 0.000Error 15 4.71250E+13 3.14167E+12Total 32 1.61072E+15

Model Summary

S R-sq R-sq(adj) R-sq(pred)1772475 97.07% 93.76% *

Means

CC N Mean StDev 95% CI814 1 1150000 * (-2627940, 4927940)1200 1 1500000 * (-2277940, 5277940)1299 1 1750000 * (-2027940, 5527940)1300 3 1683333 251661 ( -497862, 3864528)1500 3 2466667 621155 ( 285472, 4647862)1600 1 1600000 * (-2177940, 5377940)1800 4 3550000 2030189 ( 1661030, 5438970)2000 1 2300000 * (-1477940, 6077940)2362 1 4200000 * ( 422060, 7977940)2400 4 4700000 1467424 ( 2811030, 6588970)2500 4 5850000 2981890 ( 3961030, 7738970)2694 1 9000000 * ( 5222060, 12777940)2700 1 6900000 * ( 3122060, 10677940)2982 1 13200000 * ( 9422060, 16977940)3500 3 5133333 602771 ( 2952138, 7314528)4000 1 9500000 * ( 5722060, 13277940)4500 1 40000000 * (36222060, 43777940)5700 1 16500000 * (12722060, 20277940)

Pooled StDev = 1772475

One-way ANOVA: Selling Price in BDT versus HP

Method




Source DF Adj SS Adj MS F-Value P-ValueHP 20 1.58203E+15 7.91017E+13 33.09 0.000Error 12 2.86875E+13 2.39062E+12Total 32 1.61072E+15

Model Summary

S R-sq R-sq(adj) R-sq(pred)1546165 98.22% 95.25% *

Means

HP N Mean StDev 95% CI95 1 1150000 * (-2218803, 4518803)98 2 4525000 2651650 ( 2142896, 6907104)105 1 1500000 * (-1868803, 4868803)115 1 5200000 * ( 1831197, 8568803)120 1 1950000 * (-1418803, 5318803)127 1 1600000 * (-1768803, 4968803)132 6 1766667 284019 ( 391358, 3141975)135 2 2825000 35355 ( 442896, 5207104)159 1 4200000 * ( 831197, 7568803)165 1 3450000 * ( 81197, 6818803)169 1 2250000 * (-1118803, 5618803)175 2 6600000 424264 ( 4217896, 8982104)179 3 5816667 2237372 ( 3871687, 7761646)182 1 13200000 * ( 9831197, 16568803)185 1 2800000 * ( -568803, 6168803)231 1 8200000 * ( 4831197, 11568803)266 1 4500000 * ( 1131197, 7868803)268 1 5700000 * ( 2331197, 9068803)270 3 7900000 2351595 ( 5955021, 9844979)310 1 40000000 * (36631197, 43368803)381 1 16500000 * (13131197, 19868803)


One-way ANOVA: Selling Price in BDT versus Fuel (MPG)

Method



Factor Information

Factor Levels ValuesFuel (MPG) 19 15, 17, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 35, 39, 42, 46, 50, 65, 66


Source DF Adj SS Adj MS F-Value P-ValueFuel (MPG) 18 1.23793E+15 6.87738E+13 2.58 0.039Error 14 3.72794E+14 2.66281E+13Total 32 1.61072E+15

Model Summary

S R-sq R-sq(adj) R-sq(pred)5160245 76.86% 47.10% *Means

Fuel(MPG) N Mean StDev 95% CI15 2 28250000 16617009 (20424008, 36075992)17 2 7100000 2687006 ( -725992, 14925992)19 1 9500000 * (-1567624, 20567624)20 1 5700000 * (-5367624, 16767624)21 2 8850000 6151829 ( 1024008, 16675992)22 4 3525000 3259473 (-2008812, 9058812)24 2 3675000 1237437 (-4150992, 11500992)25 2 4275000 3712311 (-3550992, 12100992)26 1 4200000 * (-6867624, 15267624)27 1 6300000 * (-4767624, 17367624)28 4 2937500 1191200 (-2596312, 8471312)30 4 1662500 232289 (-3871312, 7196312)35 1 1150000 * (-9917624, 12217624)39 1 5200000 * (-5867624, 16267624)42 1 6400000 * (-4667624, 17467624)46 1 2300000 * (-8767624, 13367624)50 1 2650000 * (-8417624, 13717624)65 1 3450000 * (-7617624, 14517624)66 1 8200000 * (-2867624, 19267624)


One-way ANOVA: Selling Price in BDT versus Wheel /Drive

Method

Null hypothesis All means are equalAlternative hypothesis At least one mean is differentSignificance level α = 0.05Equal variances were assumed for the analysis.Factor Information

Factor Levels ValuesWheel /Drive 2 2, 4


Source DF Adj SS Adj MS F-Value P-ValueWheel /Drive 1 4.25097E+14 4.25097E+14 11.11 0.002Error 31 1.18562E+15 3.82459E+13Total 32 1.61072E+15

Model Summary

S R-sq R-sq(adj) R-sq(pred)6184330 26.39% 24.02% 13.83%

Means

Wheel/Drive N Mean StDev 95% CI2 20 2920000 1676415 ( 99642, 5740358)4 13 10265385 9713508 (6767161, 13763608)


9. One-Sample Z Test

One-Sample Z (Car Selling Price)

Test of μ = 5800000 vs ≠ 5800000The assumed standard deviation = 7094719

Variable N Mean StDev SE Mean 95% CI Z PSelling Price in BDT 33 5813636 7094719 1235032 (3393018, 8234255) 0.01 0.991

One-Sample Z: CC

Test of μ = 2300 vs ≠ 2300The assumed standard deviation = 1052

Variable N Mean StDev SE Mean 95% CI Z PCC 33 2350 1052 183 (1991, 2709) 0.27 0.785

One-Sample Z: HP

Test of μ = 176 vs ≠ 176The assumed standard deviation = 69.52

Variable N Mean StDev SE Mean 95% CI Z PHP 33 176.8 69.5 12.1 (153.0, 200.5) 0.06 0.950

One-Sample Z: Fuel (MPG)


Variable N Mean StDev SE Mean 95% CI Z PFuel (MPG) 33 29.06 12.48 2.17 (24.80, 33.32) 0.03 0.978

One-Sample Z: Wheel /Drive


Variable N Mean StDev SE Mean 95% CI Z PWheel /Drive 33 2.788 0.992 0.173 (2.449, 3.127) 4.55 0.000

10. 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.

10.1 Hypothesis test for Mean

1. Car selling price

Mean (x) = 5800000, Standard Deviation (S) = 7094719, n = 33Ho: µ = 5800000HA: µ ≠ 5800000

Test Statistic:

z = x - µo / s √ n

With α = .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: µ = 2300HA: µ ≠ 2300

Test Statistic:

z = x - µo / s √ n

With α = .05


Hence the Null Hypothesis Ho is not rejected

Population mean of CC is equal to 2300.

3. HP

Mean (x) = 176, Standard Deviation (S) = 69.52, n = 33

Ho: µ = 176HA: µ ≠ 176

Test Statistic:

z = x - µo / s √ n

With α = .05

And p value 0.950, which is greater than .05Hence the Null Hypothesis Ho is not rejected

Population mean of HP is equal to 176

4. Fuel (MPG)


Ho: µ = 29HA: µ ≠ 29

Test Statistic:

z = x - µo / s √ n

With α = .05


Hence the Null Hypothesis Ho is not rejected

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

5. Wheel drive


Ho: µ = 2HA: µ ≠ 2

Test Statistic:

z = x - µo / s √ n

With α = .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.

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