Independent sample T test
hypothesis): There is no significant difference
in the mean price of cars for sale privately and by a used car dealer
hypothesis): There is no significant
difference in the mean price of cars for sale privately and by a used car
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.
Presenting linear regression analysis related to age and price
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.
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.
Presenting multiple regression analysis of variables like price, age, odometer
hypothesis): There is no significant
relationship of price pertaining to Mazda-3 with age, odometer and
H1 (Null hypothesis): There is a significant linear relationship price pertaining to
Mazda-3 with age, odometer and transmission.
Calculation depicted in appendix 4.
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