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 0.86 & 0.74 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. Based on 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. 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.
Thank you.
Sincerely
Suraj
Maharjan (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 colour
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: 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
-.294
68.061
.770
-383.969
1306.702
-2991.409
2223.471
Appendix 2: 2 of Part C
Regression
Variables Entered/Removed 'a'
Model
Variables Entered
Variables Removed
Method
1
Age 'b'
.
Enter
a. Dependent Variable: Price
b. All requested variables entered.
Model
Summary 'b'
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
ANOVA
'a'
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
3624863478.806
1
3624863478.806
337.278
.000b
Residual
1278939753.276
119
10747392.885
Total
4903803232.083
120
a. Dependent Variable: Price
b. Predictors: (Constant), Age
Coefficients 'a'
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 Statistics 'a'
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