Regression Analysis of Used Car Prices

The provided document is an SPSS output for a regression analysis on used car prices. The analysis includes a model summary, ANOVA table, and coefficients table. The results show that transmission type, odometer reading, and age have significant effects on car price. The study aims to help buyers make informed decisions by understanding the factors that influence used car prices.

Statistical Analysis Project

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................3
PART A...........................................................................................................................................3
QUESTION A.................................................................................................................................3
Stating the descriptive statistics of the price of two and three years old car...............................3
QUESTION B..................................................................................................................................5
To,....................................................................................................................................................5
PART B...........................................................................................................................................6
Question 1 Stating the proportion of car available for sale is white............................................6
Question 2 Assessing two and years used car having odometer less than 50000 km.................6
TASK 3: WRITTEN ANSWER......................................................................................................7
PART C...........................................................................................................................................8
TASK 1............................................................................................................................................8
Question 1 Independent sample t test..........................................................................................8
Question 2 Presenting linear regression analysis related to age and price..................................8
Question 3 Presenting multiple regression analysis of variables like price, age, odometer and
transmission.................................................................................................................................9
TASK 2............................................................................................................................................9
Presenting results of evaluation to the client via business letter.................................................9
CONCLUSION APPENDIX.........................................................................................................10
APPENDIX....................................................................................................................................11
Appendix 1: Question 2 of part b..............................................................................................11
Question 1 Stating the proportion of car available for sale is white..........................................12
Question 2 Assessing two and years used car having odometer less than 50000 km...............12
Appendix 2: 1 of Part C.............................................................................................................12

Appendix 3: 2 of Part C.............................................................................................................13
Appendix 4: 3 of Part C.............................................................................................................19

INTRODUCTION
Statistical analysis implies for the process of collecting, exploring and analyzing large
data set which in turn helps in discovering suitable pattern or trend. Such analysis is highly
significant which in turn provides assistance in evaluating quantitative data set in an appropriate
manner and thereby aid in decision making. On the basis of cited case situation, individual
wishes to purchase two and three year old cars such as Mazda 3 pertaining to the state of New
South Wales. In this context, report will provide deeper insight about the manner in which
statistical tools namely regression, one sample and independent t test helps in taking appropriate
decision.
PART A
QUESTION A
Stating the descriptive statistics of the price of two and three years old car
Descriptive statistics of the price range of 2014 and 2015
Particulars
Two years time period
(2015)
Three years period
(2014)
Mean 22385.53 21551.13
Standard Error 667.33 617.6097
Median 21990 20500
Mode 19888 20500
Standard Deviation 2908.84 2961.95
Sample Variance 8461367.15 8773160
Kurtosis 0.39 -0.26

Skewness 0.93 -0.028
Range 10790 12000
Minimum 17990 14990
Maximum 28780 26990
Sum 425325 495676
Count 19 23
Quartile 1 and 25th percentile 19989.5 19945
Quartile 2 and 50th percentile 21990 21125
Quartile 3 and 75th percentile 23657.5 24454.5
Estimated price range
Particulars Price (in $) Price (in $)
Price
Range
(class
interva
l)
2015 model (2 years
used car)
22385.53 + 2908.84 =
25294.37
22385.53 + 2908.84 =
19476.68
19476.
68 -
25294.
37
2014 model (3 years
used car)
21551.13 + 2961.95 =
24513.08
21551.13 - 2961.95 =
18589.18
18589.
18 -
24513.
08

QUESTION B

To,
ABC
Date: 18th January 2018
Subject: Descriptive analysis
Introduction: On the basis of your requirement,
Methods: With the motive to assess mean, minimum and maximum prices of two and two years
old car descriptive statistic tool has applied. This in turn helps in making assessment of data set
from several perspectives and helps in making judgment.
Results: From descriptive analysis, it has found that average price of two and three years used
car accounts for $22385.53 & $21551.13 respectively. This aspect shows that mean price of 2
years used car is higher as compared to other. The rationale behind this, depreciation is charged
on asset every year which in turn may result into reduction in the prices of same. Due to this,
average price of two years used Mazda 3 is greater than other alternative option. Along with this,
statistical evaluation clearly exhibits that out of 121 sample, number of two and year used car
implies for 19 and 23. In the context of model 2015, 19 cars, minimum and maximum prices of
car account for $17990 & $14990 respectively. On the other side, minimum price of three year
used cars (2014) implies for $14990 which is less as compared to 2015 model. From analysis, it
has assessed that out of 121 samples, count of three year used car imply for 23 which shows that
maximum price is $26990. Further, statistical evaluation also shows that price range of 2 years
used car fall within the range of $19476.68 - $25294.37. In contrast to this, price of Mazda 3 (2014
model) accounted for $18589.18 - $24513.08. Hence, considering all such aspects it can be depicted that
price of two and three years used car differs but not to the significant level. Thus, it is suggested that lays
emphasis on purchasing 3 years old Mazda 3.
Conclusion: From overall evaluation, it has been concluded that he needs to make focus on
investing money in two years old Mazda 3 related to New South Wales.
Sincerely
Analyst

PART B
Question 1 Stating the proportion of car available for sale is white
Row Labels Count of White
No 88
Yes 33
Grand Total 121
Proportion
Particulars Figures (in %)
Car for sale is white 33 / 121 * 100 = 27%
Car for sale is not white 88 / 121 * 100 = 73%
Question 2 Assessing two and years used car having odometer less than 50000 km
Particulars Figures (in %)
Cars having odometer less than 50000 km 90%
Cars having odometer greater than 50000 km 10%
On the basis of given case scenario, concerned individual or buyer wishes to purchase 2
and 3 years old car having odometer less than 50000 km. For getting suitable result of such
aspect one sample t test has been applied to check whether significant difference takes place in
the odometer of cars pertaining to model 2014 and 2015. Considering given case situation
following hypothesis has been formulated.
Hypothesis
H0 (Null hypothesis): There is no significant difference in the odometer (less than 50000) of
Mazda-3, of the specified make and model, in the context of two and three years used or old car.
H1 (Null hypothesis): There is a significant difference in the odometer (less than 50000) of
Mazda-3, of the specified make and model, in the context of two and three years used or old car.

Statistical evaluation enclosed in appendix 1.
Interpretation: Tabular presentation depicted in appendix 1 clearly exhibits that average
odometer of cars related to 2014 and 2015 model accounts for 32907.55 km. Further,
significance value entails that p<0.05 which in turn shows that null hypothesis is true and other
one rejected. Considering all such aspect it can be depicted that there is no significant difference
take place in the odometer of two and three year’s old car as per specific value such as 50000
km.
TASK 3: WRITTEN ANSWER
To
Client
Date:18th January 2018
Subject: Assessment of availability regarding white car and odometer
By doing analysis of 121 car samples (Mazda 3), it has identified that only 27% having white color. Out
of 121, 73% cars having different colors rather than white which in turn shows that on the basis of color
less options are available in new South Wales. In addition to this, through applying statistical tools on
data set it has identified that out of 121 Mazda 3, available in New South Wales, only 42 cars were two
and three years old. Hence, from the evaluation of data set pertaining to such 42 cars, it has identified that
approximately 90% having odometer less than 50000 km. Car that was 2 and 3 years old has an odometer
greater than 5000 0 km accounts for 10%. Along with this, statistical evaluation also presents that mean
values of odometer do not differ significantly pertaining to 2014 and 2015 model of Mazda-3. Hence,
considering all the aspects it can be depicted that majority of two and three years used cars, in a state of
new South Wales have an odometer less than 50000 km. Thus, you have wide options for purchasing
Mazda-3, in New South Wales, with both 2014 and 2015 model.
Thanks!
Sincerely
Analyst

PART C
TASK 1
Question 1 Independent sample t test
Hypothesis
H0 (Null hypothesis): There is no significant difference in the mean price of cars for sale
privately and by a used car dealer
H1 (Null hypothesis): There is no significant difference in the mean price of cars for sale
privately and by a used car dealer
Calculation depicted in appendix 2.
Interpretation: Results of independent sample t test shows that average prices accounts
for $16048.53 when car is sold by dealer. On the other side, in the case of private seller mean
value implies for $16432.50 significantly. In addition to this, p>0.05 that entails that average
price level of cars significantly vary as per seller. Hence, from evaluation it can be stated that
null hypothesis is true.
Question 2 Presenting linear regression analysis related to age and price
H0 (Null hypothesis): There is no significant linear relationship between age and price of
Mazda-3.
H1 (Null hypothesis): There is a significant linear relationship between age and price of Mazda-
3.
Calculation depicted in appendix 3.
Interpretation: Model summary table, referring appendix 3, it can be mentioned that R
and R square accounts for .86 & .74 respectively. Level of R entails that both age and price
variable of car is highly correlated. Along with this, it has assessed from evaluation that
significance value is 0.00 that falls within standard limit such as 0.05. Hence, all the aspects or
outcome indicates that alternative hypothesis is true. On the basis of overall evaluation, it can be

presented that significant relationship exists between age and price of Mazda-3 in a state of New
South Wales.
Question 3 Presenting multiple regression analysis of variables like price, age, odometer and
transmission
H0 (Null hypothesis): There is no significant relationship of price pertaining to Mazda-3 with
age, odometer and transmission.
H1 (Null hypothesis): There is a significant linear relationship price pertaining to Mazda-3 with
age, odometer and transmission.
Calculation depicted in appendix 4.
Interpretation: Statistical evaluation of multiple regressions shows that price of Mazda-3
is highly and positively correlated with age, odometer and transmission. Results of evaluation
present that R accounts for .896 significantly. In addition to this, significance value in the case of
age and odometer implies for 0.00, whereas p in the context of transmission variable is .01.
Overall, p<0.05 which presents that alternative hypothesis has accepted. Hence, statistical
significant correlation takes place between price and age, odometer as well as transmission.
Further, graphical presentation of appendix 4 shows that all the values or results are in line with
scatter plot.
TASK 2
Presenting results of evaluation to the client via business letter
To
Client
Date:18th January 2018
Subject: Determining relationship of price with other variables
From assessment of data set, it is reported that you will find significant difference in the price if car will
be purchased through dealer. Moreover, dealers charge commission for the deal or services offered so it
so it is recognized as main cause due to which prices of car will be higher in such case over private

selling. Thus, for saving an additional cost emphasis should be placed on purchasing Mazda -3, in New
South Wales, from private entity rather than dealer. This in turn provides you with Mazda-3 at suitable
prices and thereby offers financial benefits. Along with this, value of car depreciates significantly
according to its age. In order to assess the impact of other variables like age, odometer, transmission on
price regression model has been applied. Hence, considering the evaluation of 121 cars it has identified
that prices of the car are getting highly influenced from age, odometer and transmission. Due to usage
level value of asset such as car decreases over the time frame. Along with this, transmission or diffusion
also has significant impact on price. Thus, while taking decision in relation to purchasing Mazda-3 you
need to consider all the variables that have an impact on price level.
Thanks!
Sincerely
Analyst
CONCLUSION
From the above report, it has been concluded that prices of car in relation to model 2014
and 2015 varies but not to a great extent. Besides this, it can be inferred that concerned buyer has
no more option regarding color specifically white. Along with this, it has been articulated that
prices of car are highly affected from age, odometer and transmission variable. Thus, buyer
should purchase Mazda-3, in New South Wales, by taking into consideration all the aspects that
have influence on price of car.

APPENDIX
Appendix 1: Question 2 of part b
Year Odometer (kms)
2015 44,863
2015 23,540
2015 40,108
2015 36,717
2015 35,598
2015 22,600
2015 31,529
2015 10,660
2015 28,001
2015 23,320
2015 9,228
2015 47,150
2015 44,801
2015 34,882
2015 14,200
2015 36,467
2015 12,800
2015 15,604
2015 33,532
2014 23,000
2014 54,455
2014 53,401
2014 37,854
2014 52,390
2014 19,978
2014 42,058
2014 74,900
2014 40,100
2014 46,000
2014 29,500
2014 40,100
2014 25,900
2014 24,267
2014 30,506
2014 19,627

2014 23,299
2014 22,490
2014 19,870
2014 36,141
2014 37,100
2014 40,100
2014 43,481
Question 1 Stating the proportion of car available for sale is white
Row Labels Count of White
No 88
Yes 33
Grand Total 121
Proportion
Particulars Figures (in %)
Car for sale is white 33 / 121 * 100 = 27%
Car for sale is not white 88 / 121 * 100 = 73%
Question 2 Assessing two and years used car having odometer less than 50000 km
Particulars Figures (in %)
Cars having odometer less than 50000 km 90%
Cars having odometer greater than 50000 km 10%
Appendix 2: 1 of Part C
T-Test
Group Statistics
Seller N Mean Std. Deviation Std. Error Mean

Price
Dealer 81 16048.53 6067.582 674.176
private 40 16432.50 7079.424 1119.355
Independent Samples Test
Levene's Test
for Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
Price
Equal
variances
assumed
2.865 .093 -.310 119 .757 -383.969 1240.048 -
2839.387 2071.449
Equal
variances not
assumed
-.29468.061 .770 -383.969 1306.702 -
2991.409 2223.471
Appendix 3: 2 of Part C
Regression

Variables Entered/Removeda
Model Variables
Entered
Variables
Removed
Method
1 Ageb . Enter
a. Dependent Variable: Price
b. All requested variables entered.
Model Summaryb
Model R R Square Adjusted R
Square
Std. Error of
the Estimate
1 .860a .739 .737 3278.322
a. Predictors: (Constant), Age
b. Dependent Variable: Price
ANOVAa

Model Sum of Squares df Mean Square F Sig.
1
Regression 3624863478.80
6 1 3624863478.80
6 337.278 .000b
Residual 1278939753.27
6 119 10747392.885
Total 4903803232.08
3 120
a. Dependent Variable: Price
b. Predictors: (Constant), Age
Coefficientsa
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig. 95.0% Confidence
Interval for B
B Std. Error Beta Lower
Bound
Upper
Bound
1
(Constant) 25133.597 571.621 43.969 .000 24001.732 26265.463
Age -1717.804 93.536 -.860 -18.365 .000 -1903.015 -1532.593
a. Dependent Variable: Price
Residuals Statisticsa

Minimum Maximum Mean Std. Deviation N
Predicted Value 2802.15 23415.79 16175.46 5496.107 121
Std. Predicted Value -2.433 1.317 .000 1.000 121
Standard Error of
Predicted Value 298.706 786.818 407.769 107.062 121
Adjusted Predicted Value 2606.74 23506.86 16169.10 5504.027 121
Residual -8644.578 11587.618 .000 3264.633 121
Std. Residual -2.637 3.535 .000 .996 121
Stud. Residual -2.648 3.551 .001 1.002 121
Deleted Residual -8716.946 11698.354 6.368 3307.478 121
Stud. Deleted Residual -2.718 3.740 .002 1.015 121
Mahal. Distance .005 5.921 .992 1.172 121
Cook's Distance .000 .060 .007 .009 121
Centered Leverage Value .000 .049 .008 .010 121
a. Dependent Variable: Price
Charts

Appendix 4: 3 of Part C
Regression
Variables Entered/Removeda
Model Variables
Entered
Variables
Removed
Method

1
Transmission,
Odometerkms,
Ageb
. Enter
a. Dependent Variable: Price
b. All requested variables entered.
Model Summaryb
Model R R Square Adjusted R
Square
Std. Error of the
Estimate
1 .896a .803 .797 2876.724
a. Predictors: (Constant), Transmission, Odometerkms, Age
b. Dependent Variable: Price
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1
Regression 3935564870.497 3 1311854956.832 158.522 .000b
Residual 968238361.585 117 8275541.552
Total 4903803232.083 120
a. Dependent Variable: Price
b. Predictors: (Constant), Transmission, Odometerkms, Age
Coefficientsa
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig. 95.0% Confidence Interval
for B
B Std. Error Beta Lower Bound Upper Bound
1
(Constant) 23293.497 838.107 27.793 .000 21633.671 24953.323
Age -1145.231 136.656 -.573 -8.380 .000 -1415.871 -874.590
Odometerkms -.041 .007 -.392 -5.736 .000 -.055 -.027
Transmission 1421.940 548.514 .110 2.592 .011 335.637 2508.243
a. Dependent Variable: Price
Residuals Statisticsa

Minimum Maximum Mean Std. Deviation N
Predicted Value 936.65 24665.45 16175.46 5726.812 121
Std. Predicted Value -2.661 1.482 .000 1.000 121
Standard Error of Predicted
Value 343.365 1098.360 504.599 138.236 121
Adjusted Predicted Value 494.39 24898.35 16172.81 5748.206 121
Residual -7109.951 9457.408 .000 2840.537 121
Std. Residual -2.472 3.288 .000 .987 121
Stud. Residual -2.504 3.340 .000 1.004 121
Deleted Residual -7297.085 9759.313 2.648 2935.549 121
Stud. Deleted Residual -2.563 3.496 .003 1.016 121
Mahal. Distance .718 16.502 2.975 2.540 121
Cook's Distance .000 .089 .008 .014 121
Centered Leverage Value .006 .138 .025 .021 121
a. Dependent Variable: Price
Charts