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Question:

(1)This is an INDIVIDUAL Assignment. We strongly discourage plagiarism, as it will be penalized as much as possible. However, it is not collusion if you discuss the questions with other students, but you need to submit your own original work. Note that we may request you come in and explain your assignment in person if we feel your assignment is too similar to another students’ work.

(2)This assignment in total has 30 marks that correspond to 20% of your final grade.

(3)Once completed, you will need to submit your ‘Microsoft Word’ document via CloudDeakin. You must submit a single file only that contains a cover page with your name and student ID.

If you are submitting your assignment as a PDF document, please ensure that you are also submitting as a Word document to enable word counting.  

Please ensure the Word document is self-contained (i.e. all your tables and figures should be in the word document). You will not need to submit a hardcopy.

Answer:
  1. Descriptive statistics of Sale Price, Length and Weight

According to Goos &Meintrup (2015), descriptive statistics includes the measure of central tendency and measure of dispersion. The measures of central tendency are mean, median and mode, while dispersion is measured using variance, standard deviation, maximum and minimum, range, quartiles, and interquartile range. The descriptive statistics of the sales price, length and weight of the car were determined on Microsoft Excel and results are shown below.

Statistics

 

Sales Price

Length

Weight

Central Tendency

 

 

 

Mean

39699

469

1562

Median

34842

471

1545

Mode

29424

449

1716

 

 

 

 

Dispersion

 

 

 

Variance

387164687

1000

96985

Standard Deviation

19677

32

311

Maximum

126908

557

2575

Minimum

13042

366

916

Range

113866

192

1660

Quartile(Q3)

47913

491

1733

Quartile(Q1)

26792

449

1363

Inter-quartile Range

21121

42

371

The mean is greater than the median, which is greater than the mode for the three variables. This indicates that the distributions for the three are positively skewed (Sharma 2007; Data& Using Descriptive Statistics Bartz 1988). The variances and standard deviations of the three variables are very high. Higher variance and standard is an indicator of much-dispersed data points from the mean (Bernstein& Bernstein 1998).  According to Brase& Brase (2011), a big range indicates a greater dispersion of data points, whereas a small range shows a less dispersion. Comparing the three variables, sales price has the biggest range and interquartile range, what makes its data to have the greatest dispersion among the three.

  1. Estimation of a simple regression model of the Sale price on Length,

The values of   and  were determine using Microsoft Excel, regression analysis. The results are shown below.

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

 

 

 

 

Multiple R

0.330323

 

 

 

 

 

 

 

R Square

0.109113

 

 

 

 

 

 

 

Adjusted R Square

0.105535

 

 

 

 

 

 

 

Standard Error

18609.28

 

 

 

 

 

 

 

Observations

251

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

 

 

 

df

SS

MS

F

Significance F

 

 

 

Regression

1

1.06E+10

1.06E+10

30.49674

8.4E-08

 

 

 

Residual

249

8.62E+10

3.46E+08

 

 

 

 

 

Total

250

9.68E+10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 99.0%

Upper 99.0%

Intercept

-56711.5

17497.65

-3.24109

0.001353

-91173.8

-22249.3

-102131

-11292.6

Length

205.5067

37.2134

5.522385

8.4E-08

132.2136

278.7999

108.9112

302.1022

From the above results, the simple regression model for estimate sale price is given

  • Estimation of a simple regression model of the Sale price on Length with the log-log specification.

are estimated on Excel, the results are shown below

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

 

 

 

 

Multiple R

0.418226

 

 

 

 

 

 

 

R Square

0.174913

 

 

 

 

 

 

 

Adjusted R Square

0.171599

 

 

 

 

 

 

 

Standard Error

0.177349

 

 

 

 

 

 

 

Observations

251

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

 

 

 

df

SS

MS

F

Significance F

 

 

 

Regression

1

1.660274

1.660274

52.78635

4.77E-12

 

 

 

Residual

249

7.831726

0.031453

 

 

 

 

 

Total

250

9.491999

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 99.0%

Upper 99.0%

Intercept

-2.79362

1.011322

-2.76234

0.006167

-4.78546

-0.80178

-5.41873

-0.16851

Log Length

2.751461

0.378706

7.265421

4.77E-12

2.005585

3.497338

1.768447

3.734476

The estimated log sale price is given by

The coefficient of log length is 2.751, which is positive. According to Francis (2004) and Hassett& Stewart (2006), a positive coefficient indicates that the regression line has a positive gradient. Therefore, the estimated log sale price has a positive gradient, thus increase in length will lead to an increase in sales price.

I expected the coefficient to be a positive value above 2. The sign of the coefficient is a real representation of my expectation.

  1. The Model relating the Sale price to Length and Weight;

were estimated on Excel, the results are shown below

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

 

 

 

 

Multiple R

0.606309658

 

 

 

 

 

 

 

R Square

0.367611401

 

 

 

 

 

 

 

Adjusted R Square

0.362511493

 

 

 

 

 

 

 

Standard Error

15710.28447

 

 

 

 

 

 

 

Observations

251

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

 

 

 

Df

SS

MS

F

Significance F

 

 

 

Regression

2

35581538227

1.78E+10

72.08197

2.1E-25

 

 

 

Residual

248

61209633442

2.47E+08

 

 

 

 

 

Total

250

96791171669

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 99.0%

Upper 99.0%

Intercept

-705.1735874

15784.45647

-0.04468

0.964402

-31793.9

30383.51

-41678.4

40268.1

Length

-51.78489734

40.496887

-1.27874

0.202185

-131.547

27.97679

-156.907

53.33686

Weight

41.40869765

4.112717181

10.06845

3.26E-20

33.30839

49.50901

30.73291

52.08448

The estimated sale price is given by

This model has a better goodness of fit than model in II above, its significance F, 2.1E-25, is less than that of model in II, 8.4E-08,which is less than  0.05.

  1. Estimating the model in IV above using log of each variable.

The value of were estimated on Excel, results are shown below.

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

 

 

 

 

Multiple R

0.725841

 

 

 

 

 

 

 

R Square

0.526846

 

 

 

 

 

 

 

Adjusted R Square

0.52303

 

 

 

 

 

 

 

Standard Error

0.134572

 

 

 

 

 

 

 

Observations

251

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

 

 

 

df

SS

MS

F

Significance F

 

 

 

Regression

2

5.00082

2.50041

138.071

5.02E-41

 

 

 

Residual

248

4.49118

0.01811

 

 

 

 

 

Total

250

9.491999

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 99.0%

Upper 99.0%

Intercept

0.507216

0.804954

0.630118

0.529198

-1.0782

2.092633

-1.58228

2.596713

Log Length

-0.61182

0.379339

-1.61285

0.10805

-1.35895

0.135322

-1.5965

0.372873

Log Weight

1.783179

0.131293

13.58171

8.74E-32

1.524588

2.04177

1.44237

2.123989

The estimated log sale price model is given by;

  1. Testing whether length has a negative effect on sale price at 1% significance level.

Null hypothesis: Length has a negative effect on sale price.

From the above table, the P-value of Log length is 0.10805 which is greater than 0.05. This suggests that the length is not statistically significant at 1% level, the null hypothesis will be rejected (Aiken, West & Reno 1991). As a result, length does not have negative effects on the sale price.

  • Adding Horsepower and luggage size to the log-log model in V.

The values of were determined on Excel, the results are shown below.

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

 

 

 

 

Multiple R

0.895914

 

 

 

 

 

 

 

R Square

0.802662

 

 

 

 

 

 

 

Adjusted R Square

0.799453

 

 

 

 

 

 

 

Standard Error

0.08726

 

 

 

 

 

 

 

Observations

251

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

 

 

 

Df

SS

MS

F

Significance F

 

 

 

Regression

4

7.618868

1.904717

250.1481848

2.04037E-85

 

 

 

Residual

246

1.873131

0.007614

 

 

 

 

 

Total

250

9.491999

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 99.0%

Upper 99.0%

Intercept

3.442802

0.557211

6.178627

2.66178E-09

2.345287893

4.5403157

1.99630194

4.8893017

Log Length

-0.95977

0.24875

-3.85838

0.000145868

-1.449720201

-0.4698191

-1.605514

-0.31402526

Log Weight

1.041427

0.116977

8.902839

1.22434E-16

0.811022984

1.2718314

0.73775938

1.345094981

Horsepower

0.001962

0.000118

16.58606

5.58703E-42

0.001728996

0.002195

0.00165491

0.00226907

Luggage Size

-0.00164

0.000582

-2.81992

0.005194904

-0.002789204

-0.0004952

-0.00315393

-0.00013042

The estimate log sale price will be

 From the information in the table above, Horsepower is statistically significant at 1% level, since its P-value, 5.58703E-42 is less than 0.05. Similarly, Luggage size is significant because its P-value, 0.005194904 is also less than 0.05. The two variables are jointly significant at 5%, as 0, which is null the hypothesis is not within their 95% confidence interval brackets are above.

  • The overall significance of the model in VII above at 1%.

The overall significance is determined using the significance F. The significance F, 2.04037E-85, is less than 0.05. This indicates that one of the variables is statistically significant. This means the model is good for the estimation of the sale price.

  1. Testing whether Luxury cars are more expensive than other types of cars

Null hypothesis: Luxury car are not more expensive than other types of cars

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

 

 

 

 

Multiple R

0.846518

 

 

 

 

 

 

 

R Square

0.716593

 

 

 

 

 

 

 

Adjusted R Square

0.713151

 

 

 

 

 

 

 

Standard Error

0.10436

 

 

 

 

 

 

 

Observations

251

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

 

 

 

Df

SS

MS

F

Significance F

 

 

 

Regression

3

6.801904

2.267301

208.1797

2.52E-67

 

 

 

Residual

247

2.690096

0.010891

 

 

 

 

 

Total

250

9.491999

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0.393903

0.624303

0.630948

0.528658

-0.83573

1.623538

-0.83573

1.623538

Log Length

-0.06938

0.297186

-0.23347

0.815591

-0.65473

0.515958

-0.65473

0.515958

Log Weight

1.345826

0.107347

12.53713

3.12E-28

1.134393

1.557258

1.134393

1.557258

Luxury

0.196725

0.015298

12.85972

2.58E-29

0.166594

0.226856

0.166594

0.226856

The P- value for luxury is less than 0.05, therefore, Luxury is statistically significant at 5%, hence Luxury cars are more expensive than other types of cars.

References

Aiken, L.S., West, S.G. and Reno, R.R., 1991. Multiple regression: Testing and interpreting interactions. Sage

Bernstein, S. and Bernstein, R., 1998. Schaum's Outline of Elements of Statistics I: Descriptive Statistics and Probability. McGraw-Hill Companies.

Brase, C.H. and Brase, C.P., 2011. Understandable statistics: Concepts and methods. Cengage Learning.

Data, S. and Using Descriptive Statistics Bartz, A.E., 1988. Basic statistical concepts. New York: Macmillan. Devore, J., and Peck.

Francis, A., 2004. Business mathematics and statistics. Cengage Learning EMEA.

Goos, P. and Meintrup, D., 2015. Statistics with JMP: graphs, descriptive statistics and probability. John Wiley & Sons.

Hassett, M.J. and Stewart, D., 2006. Probability for risk management. Actex Publications

Sharma, J.K., 2007. Business statistics. Pearson Education India.

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My Assignment Help (2021) Descriptive Statistics And Regression Analysis [Online]. Available from: https://myassignmenthelp.com/free-samples/mae256-analytical-methods-in-economics-and-finance/descriptive-statistics-and-probability.html
[Accessed 17 July 2024].

My Assignment Help. 'Descriptive Statistics And Regression Analysis' (My Assignment Help, 2021) <https://myassignmenthelp.com/free-samples/mae256-analytical-methods-in-economics-and-finance/descriptive-statistics-and-probability.html> accessed 17 July 2024.

My Assignment Help. Descriptive Statistics And Regression Analysis [Internet]. My Assignment Help. 2021 [cited 17 July 2024]. Available from: https://myassignmenthelp.com/free-samples/mae256-analytical-methods-in-economics-and-finance/descriptive-statistics-and-probability.html.

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