Foreigners in Romania

8/3/2019 Foreigners in Romania

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Academy of Economic Studies Bucharest

FABIZ

Coordinator : Prof. Univ. Dr. Daniela SerbanStudent : CusturaRuxandra-Gabriela

Group 139

-2012-

Romanian Tourism for foreign visitors


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Table of contents

Part 1 Introduction

1.1Introduction about the domain..................................................................31.2Data description.........................................................................................4

Part 2 Methods and formulas

2.1 Hypothesis testing.....................................................................................4

2.2 Regression models.....................................................................................4

Part 3. Problem solving

Problem nr.1....................................................................................................5

Problem nr.2....................................................................................................8

Problem nr.3..................................................................................................10

Problem nr.4..................................................................................................17

References...............................................................................................................29


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Romanian Tourism for foreign visitors

1.1 Introduction about the domain

Tourism is one of the world's fastest growing industries as well as the major source offoreign exchange earning and employment for many developing countries. Tourism is vital to the

well being of many countries, because of the income generated by the consumption of goods andservices by tourists, the taxes levied on businesses in the tourism industry and the opportunity for

employment and economic advancement by working in the industry.The tourism industry is based on many different components and interrelated parts. For

example, transport, accommodation, attractions, activities, marketing and government regulation.Many businesses span more than one sector and the impacts in one part of the tourism industry

have significant implications for other sectors.Tourism is travel for recreational, leisure or business purposes. The World Tourism

Organization defines tourists as people "travelling to and staying in places outside their usualenvironment for not more than one consecutive year for leisure, business and other purposes".

Tourism is a key sector of the European economy. It comprises a wide variety of products anddestinations and involves many different stakeholders, both public and private, with areas of

competence very decentralised, often at regional and local levels.The EU tourism industry generates more

than 5% of the EU GDP, with about 1,8 millionenterprises employing around 5,2% of the total

labour force (approximately 9,7 million jobs).When related sectors are taken into account, the

estimated contribution of tourism to GDP creation

is much higher: tourism indirectly generates morethan 10% of the European Union's GDP andprovides about 12% of the labour force.

Tourism Industry Growth in any country isprone to the changing economic conditions. In the

event when a country is passing through a lowphase or an individual's job is at stake, not many people choose to travel. This poses a limitation

in the spending power of the individuals. People under these circumstances tend to settle for lowbudget restaurants, hotels or opt for amusement parks and nearby places.

Tourism in Romania focuses on the country's natural landscapes and its rich history.Tourism is a significant contributor to the Romanian economy. In the 1990s the government

heavily promoted the development of skiing in the Romanian Carpathians. Domestic andinternational tourism generates about 4% of gross domestic product (GDP) and 0.8 million jobs.

Following commerce, tourism is the second largest component of the services sector. Two-thirdsof all major trade fairs from Central Europe are held in Romania, and each year they attract 2 to

3 million business travellers, about 20% of whom are foreigners. The four most important tradefairs take place in Bucharest, Cluj-Napoca, Iai, Timioara.


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1.2 Data description

Following commerce, tourism is the second largest component of the services sector.The database used in this project focuses on the arrival of foreign tourists from Europe

who registered at the borders, at turistical units and those who spend at least one night in

Romania during 2006-2010, with a situation of every month from those years.In order to facilitate the operation of computing, Microsoft Excel software has been usedin order to obtain an output for the problems developed along the project.

Part 2. Methods and formulas

1.1Hypothesis testingHypothesis testing is one of the most important tools of application of statistics to real life

problems. Most often, decisions are required to be made concerning populations on the basis of

sample information. Statistical tests are used in arriving at these decisions.There are five parts of any statistical test :

(a) Null Hypothesis = It is a hypothesis which states that there is no difference between theprocedures and is denoted by H0. Always the null hypothesis is tested, i.e., we want to either

accept or reject the null hypothesis because we have information only for the null hypothesis.(b) Alternate Hypothesis = It is a hypothesis which states that there is a difference between the

procedures and is denoted by H1.(c) Test Statistic = It is the random variable X whose value is tested to arrive at a decision. A z

statistic is usually used for large sample sizes (n > 30), but often large samples are not easy toobtain, in which case the t-distribution can be used. In case of performing multiple comparisons

by one way Anova, the F-statistic is normally used.

n = sample size, = sample mean, = population standard deviation

(d) Rejection/Critical Region = It is the part of the sample space (critical region) where the nullhypothesis H0 is rejected.

(e) Conclusion = If the test statistic falls in the rejection/critical region, H0 is rejected, else H0 isaccepted.

2.2 Regression models

Linear regression is an approach to 4odelling the relationship between a scalar variable y

and one or more explanatory variables denoted X. The case of one explanatory variable is calledsimple regression. More than one explanatory variable is multiple regression.

Linear regression attempts to model the relationship between two variables by fitting alinear equation to observed data. One variable is considered to be an explanatory variable, and

the other is considered to be a dependent variable.


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Linear regression attempts to model the relationship between two variables by fitting alinear equation to observed data. One variable is considered to be an explanatory variable, and

the other is considered to be a dependent variable.A linear regression line has an equation of the form Y = a + bX, where X is the

explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the

intercept (the value of y when x = 0).The goal of regression analysis is to determine the values of the parameters thatminimize the sum of the squared residual values for the set of observations. This is known as a

least squares regression fit. It is also sometimes referred to as ordinary least squares (OLS)regression.

The residual, , is the difference between the value of the dependentvariable predicted by the model, and the true value of the dependent variable yi. One method of

estimation is ordinary least squares. This method obtains parameter estimates that minimize thesum of squared residuals, SSE,also sometimes denoted RSS:

In the case of simple regression, the formulas for the least squares estimates are

, where is the mean (average) of the x

values and is the mean of the y values. This is called the mean square error (MSE) of theregression.

Problem nr. 1

A hotel manager wants to expand his business. He bases on the assumption that theaverage monthly number of foreign tourists that spent a night in Romania was 4000 00. In order

to check it, a sample of 2006-2010 period was taken, meaning all foreign tourists who passed anight in Romania, taken every month. The sample mean was found To be 272383,5333 tourists

with a standard deviation of 95173,92047. Test the manager view and decide if he is right.

Year Months

Marca

timp

Number of

tourists that

slept in RO

2006 1 1 188700

2 2 161900

3 3 191400

4 4 204500

5 5 275100

6 6 353600

7 7 423000

8 8 489100

9 9 317200


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10 10 272500

11 11 205000

12 12 160200

2007 1 13 339400

2 14 360700

3 15 218800

4 16 255700

5 17 341100

6 18 394600

7 19 468800

8 20 473000

9 21 364100

10 22 295500

11 23 233200

12 24 171300

2008 1 25 2024002 26 203900

3 27 233500

4 28 260700

5 29 343800

6 30 353400

7 31 386600

8 32 397700

9 33 339500

10 34 285600

11 35 20720012 36 144200

2009 1 37 158400

2 38 151000

3 39 179100

4 40 193900

5 41 343800

6 42 353400

7 43 387400

8 44 397700

9 45 339500

10 46 285600

11 47 207200

12 48 144200

2010 1 49 141200

2 50 137900

3 51 177800

4 52 191900


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5 53 282500

6 54 138500

7 55 309200

8 56 326800

9 57 311300

10 58 252900

11 59 257932

12 60 156980

Table nr.1

: = 400 000

In the null hypothesis, we say that the average monthly number of foreign tourists that

spent a night in Romania is 400 000.

: 400 000

In the alternative hypothesis, the average monthly number of foreign tourists that spent anight in Romania is different than 400 000.

=5% => We have two cut of values, so the rejection region will be (-;-1,96)U(1,96;+) =>

RR (-;-1,96)U(1,96;+)It will be a both sided test.

=

=

= - 10,4 RR

Where = sample mean= population mean=standard deviationn=sample size

AR

RR RR

- -10,4 -1,96 1,96 +


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-10,4< -1,96 => < -

falls into the rejected region (RR). As a consequence, we have enough sampleevidence to reject . The managers belief is wrong, so he should not expand his businessbecause there are less foreign tourists that spend a night in Romania than he assumed, which

stands in 95% of the cases.

Problem nr. 2

The Romanian Minister of Tourism believes that after so many campaigns, the average

number of foreign tourists registered at the Romanian boarders is 800 000. But according tosome European statistics, the foreign tourists from Europe that have visited our country is lower.

In order to test it, the last 60 months (2006-2010) were taken as a sample, with a mean of624295,85 and a variance of 31426404144. Which side is right ?

Year Months

Marca

timp

Arrivals offoreign tourists

registered at Ro

borders

2006 1 1 337703

2 2 329320

3 3 379772

4 4 428185

5 5 445655

6 6 518700

7 7 590197

8 8 608047

9 9 462711

10 10 468559

11 11 434322

12 12 521600

2007 1 13 339400

2 14 360700

3 15 477100

4 16 535900

5 17 626800

6 18 665000

7 19 962800

8 20 1016800

9 21 753600

10 22 704600

11 23 632200

12 24 646700


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2008 1 25 536700

2 26 582400

3 27 604000

4 28 645700

5 29 793600

6 30 789700

7 31 1041300

8 32 1097400

9 33 800600

10 34 745200

11 35 612500

12 36 613000

2009 1 37 494700

2 38 459100

3 39 531200

4 40 5976005 41 660300

6 42 707700

7 43 847400

8 44 897400

9 45 645500

10 46 638400

11 47 527000

12 48 568600

2010 1 49 470000

2 50 4274003 51 530100

4 52 586700

5 53 633100

6 54 685500

7 55 633100

8 56 977700

9 57 651600

10 58 589500

11 59 792239

12 60 797441

Table nr.2

: = 800 000

In the null hypothesis, we say that the average monthly number of foreign tourists that

registered at the Romanian boarders is 800 000.


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: < 800 000

In the alternative hypothesis, the average monthly number of foreign tourists registered at

the Romanian boarders are less.

=5% => We have one cut of value, so the rejection region will be (-;-1,645) => RR (-;-

1,645) => left-hand tail test

= 31426404144 => = = 177274,93

Where =variance=standard deviation

=

=

= -0,8 AR

Where = sample mean= population mean=standard deviationn=sample size

RRAR

- -1.645 -0,8 +

-0,8> -1,645 => > -

falls into the acceptance region (AR). As a consequence, we don not have enoughsample evidence to reject . The Romanian Minister of Tourisms belief is valid, supporting

that the previous campaigns were successful, which stands in 95% of the cases.

Problem nr. 3

A travel agency is investigating the relationship between Arrivals of foreign touristsregistered at Ro borders and Arrivals of foreign tourists at turistical units within 2006-2010,

which was counted every month.. For the situation in table nr. 2, it is asked to characterize therelation between them.


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Year Months

Marca

timp

Arrivals of

foreign tourists

registered at Ro

borders

Arrivals of foreign

tourists at

turistical units

2006 1 1 337703 75500

2 2 329320 72500

3 3 379772 87000

4 4 428185 98900

5 5 445655 127700

6 6 518700 144000

7 7 590197 161600

8 8 608047 179100

9 9 462711 136600

10 10 468559 128400

11 11 434322 96400

12 12 521600 72200

2007 1 13 339400 77000

2 14 360700 80100

3 15 477100 99000

4 16 535900 115100

5 17 626800 153200

6 18 665000 166700

7 19 962800 183200

8 20 1016800 194900

9 21 753600 161900

10 22 704600 139400

11 23 632200 106000

12 24 646700 73400

2008 1 25 536700 82800

2 26 582400 89500

3 27 604000 104500

4 28 645700 118200

5 29 793600 154600

6 30 789700 149600

7 31 1041300 1624008 32 1097400 165800

9 33 800600 151800

10 34 745200 130800

11 35 612500 90400

12 36 613000 65300

2009 1 37 494700 67600


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2 38 459100 72500

3 39 531200 87500

4 40 597600 93400

5 41 660300 154600

6 42 707700 149600

7 43 847400 162700

8 44 897400 165800

9 45 645500 151800

10 46 638400 130800

11 47 527000 90400

12 48 568600 65300

2010 1 49 470000 66400

2 50 427400 69300

3 51 530100 87800

4 52 586700 94600

5 53 633100 1390006 54 685500 286200

7 55 633100 144100

8 56 977700 152800

9 57 651600 131100

10 58 589500 126400

11 59 792239 91560

12 60 797441 75439

Table nr.3

1.The variables are identified, meaningArrivals of foreign tourists registered at Ro borders

Arrivals of foreign tourists at turistical units

2.After, we specify the variables :Arrivals of foreign tourists registered at Ro borders = y(dependent variable)

Arrivals of foreign tourists at turistical units = x (regressor)

3.General formula of regression modelThe one corresponds to the simple linear model, because we have one regressor and the

points in the scatter diagram are spread along the first degree equation.

=+x+, where , =parameters

X= Arrivals of foreign tourists at turistical units

With the help of Data Analysis from MS Excel, I obtained the following results :

Regression Statistics

Multiple R 0,602881461

R Square 0,363466056


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Adjusted R Square 0,352491333

Standard Error 142649,4621

Observations 60

ANOVA

df SS MS F

Significance

F

Regression 1 6,73923E+11 6,74E+11 33,11847 3,44E-07

Residual 58 1,18023E+12 2,03E+10

Total 59 1,85416E+12

Coefficien

ts

Standard

Error t Stat

P-

valu

e

Lower

95%

Upper

95%

Lower

95,0%

Upper

95,0%

Intercept

321050,2

002

55819,20

216

5,7516

09

3,49

E-07

20931

5,9

43278

4,5

20931

5,9

43278

4,5

Arrivals of foreign

tourists at turistical

units

2,508858

208

0,435954

309

5,7548

65

3,44

E-07

1,6362

01

3,3815

16

1,6362

01

3,3815

16

RESIDUAL OUTPUT

Observatio

n

Predicted Arrivals of foreign tourists registered at Ro

borders Residuals

Standard

Residuals1 510468,9949 -172765,995 -1,22152

2 502942,4203 -173622,42 -1,22757

3 539320,8643 -159548,864 -1,12807

4 569176,277 -140991,277 -0,99686

5 641431,3934 -195776,393 -1,38421

6 682325,7822 -163625,782 -1,15689

7 726481,6866 -136284,687 -0,96358

8 770386,7053 -162339,705 -1,1478

9 663760,2314 -201049,231 -1,42149

10 643187,5941 -174628,594 -1,23469

11 562904,1315 -128582,131 -0,90912

12 502189,7628

19410,2371

6 0,137237

13 514232,2822 -174832,282 -1,23613

14 522009,7427 -161309,743 -1,14052

15 569427,1628 -92327,1628 -0,65279

16 609819,78 -73919,78 -0,52264


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17 705407,2777 -78607,2777 -0,55578

18 739276,8635 -74276,8635 -0,52516

19 780673,0239

182126,976

1 1,287704

20 810026,664

9

206773,335

1 1,4

61963

21 727234,3441

26365,6559

2 0,186415

22 670785,0344 33814,9656 0,239084

23 586989,1703

45210,8297

4 0,319657

24 505200,3927

141499,607

3 1,000454

25 528783,6598

7916,34015

5 0,055971

26 545593,0098

36806,9901

6 0,260239

27 583225,883

20774,1170

5 0,146881

28 617597,2404 28102,7596 0,198697

29 708919,6792

84680,3208

4 0,598721

30 696375,3881

93324,6118

8 0,659839

31 728488,7732

312811,226

8 2,21169

32 737018,8911

360381,108

9 2,548026

33 701894,8762

98705,1238

2 0,697881

34 649208,8538

95991,1461

8 0,678692

35 547850,9822

64649,0177

8 0,457092

36 484878,6412

128121,358

8 0,905865

37 490649,0151

4050,98491

3 0,028642

38 502942,4203 -43842,4203 -0,30998

39 540575,2934 -9375,29342 -0,06629

40 555377,5568

42222,4431

5 0,298528

41 708919,6792 -48619,6792 -0,34376

42 696375,3881

11324,6118

8 0,080069

43 729241,4306

118158,569

4 0,835424


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44 737018,8911

160381,108

9 1,133953

45 701894,8762 -56394,8762 -0,39873

46 649208,8538 -10808,8538 -0,07642

47 547850,9822 -20850,9822 -0,14742

48 484878,641283721,3587

9 0,591941

49 487638,3852 -17638,3852 -0,12471

50 494914,074 -67514,074 -0,47735

51 541327,9509 -11227,9509 -0,07939

52 558388,1867 28311,8133 0,200175

53 669781,4911 -36681,4911 -0,25935

54 1039085,419 -353585,419 -2,49998

55 682576,668 -49476,668 -0,34982

56 704403,7344

273296,265

6 1,932305

57 649961,5113 1638,48872 0,011585

58 638169,8777 -48669,8777 -0,34411

59 550761,2577

241477,742

3 1,707336

60 510315,9546

287125,045

4 2,030079

4. Characterization of the intensity of the relationship between Arrivals of foreign touristsregistered at Romanian borders and Arrivals of foreign tourists at turistical units.

We use the coefficient of linear correlation :

=

=multiple R= 0,602

We have a medium intensity correlation because the intensity correlation tends to 0.75

Then, we check if the linear model is appropriate, meaning if R=r:Ratio of determination

-500000

0

500000

0 100000 200000 300000 400000Residuals


Arrivals of foreign tourists at

turistical units Residual Plot


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R==0.602 => R=r=0.602So, we have a linear relation between variables.Consider that Arrivals of foreign tourists at turistical units as the only influence factor

and the other having a constant influence. 60.2% (R square) out of Arrivals of foreign touristsregistered at Ro borders in the sample of 60 is the explained by Arrivals of foreign tourists at

turistical units variable. When we measure considering other factors the regression is explainedonly 35.4% out of y variable.

5. Interpret the regression coefficient and the intercept for the sample.

= 321050,2002 ( no specific interpretation)

= 2,508858208 positive => direct relationshipRegression sample

=321050,2002+2,508858208x+

6. Is the model valid for the sample of 60 observations ?

Step 1 : We test the following hypothesis

: ===

:At least 2 predicted values are different=

We test if predicted values have similar values.

Step2 : overall variations

Explained variation = ESS= 6,73923E+11Unexplained variation=RSS=1,18023E+12

= 337703 => = 321050,2002+2,508858208*75500=510468,9949

If only would Arrivals of foreign tourists at turistical units influence Arrivals of foreign

tourists registered at Ro borders the first observation would have a bigger number of foreigntourists at the boarders.

Residuals - => = -=-172765,9949

So, we have a loss of 172765,9949.

= 0 = 1,18023E+12

Step 3 : average variation


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= ESR= 6,74E+11

= RMS = 2,03E+10

Step 4 : Fisher test

=

= 33,11847

> => > => 33,11847 > 3,15

The regression model is valid, the line is fitting the points in the scatter diagram and wecan use the regression model for predictions.

Step 5 :

Significance F probability is 3,44E-07(higher than =0,05) and is 33,11847 , theregression model is valid for a probability of at most 95% and it can be used to analyze thedependence between Arrivals of foreign tourists registered at Ro borders and Arrivals of foreigntourists at turistical units => the computed probability to make type II error

We can find at least 2 predicted y which are significantly different => the model is valid

Inference to the sample of observations to the population conducted only for the slope:For 95 % : One more tourist in the sample for Arrivals of foreign tourists at turistical

units induces a bigger Arrivals of foreign tourists registered at Ro borders with 2,508858208 orone tourist less in Arrivals of foreign tourists at turistical units induces a smaller Arrivals of

foreign tourists registered at Ro borders.

The extension of result :

One additional tourist in Arrivals of foreign tourists at turistical units can determine anincrease in Arrivals of foreign tourists registered at Ro borders with at least 1,636201 until at

most 3,381516. Because the confidence interval for the slope (1,636201; 3,381516) does notcomprise the value of 0, it means that in 95% of cases. The additional Arrivals of foreign tourists

registered at Ro borders for one additional Arrivals of foreign tourists at turistical units will notbe 0. We reject the null hypothesis up on the slope saying that it is 0 and accept it is significantly

differently than 0.

Problem nr.4

The Romanian Passport Service wants to see the relationship between Arrivals of foreign

tourists registered at Ro borders, Number of tourists that slept in RO and Arrivals of foreigntourists at turistical units, within 2006-2010, which was counted every month. The institution

wants to keep an evidence of the European travelers. Data is registered as follows in Table nr. 4 :

Year Months

Marca

timp

Arrivals of foreign

tourists registered

Arrivals of

foreign tourists

Number of

tourists that


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at Ro borders at turistical units slept in RO

2006 1 1 337703 75500 188700

2 2 329320 72500 161900

3 3 379772 87000 191400

4 4 428185 98900 204500

5 5 445655 127700 275100

6 6 518700 144000 353600

7 7 590197 161600 423000

8 8 608047 179100 489100

9 9 462711 136600 317200

10 10 468559 128400 272500

11 11 434322 96400 205000

12 12 521600 72200 160200

2007 1 13 339400 77000 339400

2 14 360700 80100 360700

3 15 477100 99000 2188004 16 535900 115100 255700

5 17 626800 153200 341100

6 18 665000 166700 394600

7 19 962800 183200 468800

8 20 1016800 194900 473000

9 21 753600 161900 364100

10 22 704600 139400 295500

11 23 632200 106000 233200

12 24 646700 73400 171300

2008 1 25 536700 82800 2024002 26 582400 89500 203900

3 27 604000 104500 233500

4 28 645700 118200 260700

5 29 793600 154600 343800

6 30 789700 149600 353400

7 31 1041300 162400 386600

8 32 1097400 165800 397700

9 33 800600 151800 339500

10 34 745200 130800 285600

11 35 612500 90400 207200

12 36 613000 65300 144200

2009 1 37 494700 67600 158400

2 38 459100 72500 151000

3 39 531200 87500 179100

4 40 597600 93400 193900

5 41 660300 154600 343800

6 42 707700 149600 353400


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7 43 847400 162700 387400

8 44 897400 165800 397700

9 45 645500 151800 339500

10 46 638400 130800 285600

11 47 527000 90400 207200

12 48 568600 65300 144200

2010 1 49 470000 66400 141200

2 50 427400 69300 137900

3 51 530100 87800 177800

4 52 586700 94600 191900

5 53 633100 139000 282500

6 54 685500 286200 138500

7 55 633100 144100 309200

8 56 977700 152800 326800

9 57 651600 131100 311300

10 58 589500 126400 25290011 59 792239 91560 257932

12 60 797441 75439 156980

Table nr.4

1.The variables are identified, meaningArrivals of foreign tourists registered at Ro borders,

Number of tourists that slept in ROArrivals of foreign tourists at turistical units

2.After, we specify the variables :

Arrivals of foreign tourists registered at Ro borders = y(dependent variable)Arrivals of foreign tourists at turistical units = (regressor)Number of tourists that slept in RO = (regressor)

3.General formula of regression model

The one corresponds to the multiple linear model, because we have two regressors.

=+++, where , , = parameters= Arrivals of foreign tourists at turistical units= Number of tourists that slept in RO

Using Data Analysis from MS Excel, I obtained the following results :

Regression Statistics

Multiple R 0,6354188

R Square 0,403757051

Adjusted R Square 0,382836246

Standard Error 139266,7856


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Observations 60

ANOVA

df SS MS F

Significance

F

Regression 2 7,48629E+11 3,7431E+11 19,299 3,98E-07

Residual 57 1,10553E+12 1,9395E+10

Total 59 1,85416E+12

Coefficie

nts

Standar

d Error t Stat

P-

value

Lower

95%

Upper

95%

Lower

95,0%

Upper

95,0%

Intercept

275769,

8

59178,3

02

4,659

98

2E-

05

15726

7

39427

2,3

15726

7,3

39427

2,3

Arrivals of foreign tourists

at turistical units

1,73476

8

0,58027

45

2,989

56

0,00

41

0,572

79

2,8967

48

0,5727

88

2,8967

48

Number of tourists that

slept in RO 0,50974

0,25972

8

1,962

59

0,05

46

-

0,010

4

1,0298

36

-

0,0103

6

1,0298

36

RESIDUAL OUTPUT

Observatio

n

Predicted Arrivals of foreign tourists registered at Ro

borders Residuals

Standard

Residuals

1 502932,6

-

165229,6

3 -1,2071

2 484067,3 -154747,3 -1,1305

3 524258,8

-

144486,7

6 -1,0555

4 551580,1

-

123395,0

9 -0,9014

5 637529

-

191874,0

4 -1,4017

6 705820,3

-

187120,32 -1,367

7 771728,2

-

181531,1

8 -1,3261

8 835780,4

-

227733,4

2 -1,6637


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21

9 674428,5

-

211717,5

1 -1,5467

10 637418

-

168859,0

5 -1,2336

11 547498

-

113176,0

4 -0,8268

12 482680,3

38919,68

6 0,28432

13 582352,6

-

242952,5

6 -1,7749

14 598587,8 -237887,8 -1,7379

15 559042,8

-

81942,84

6 -0,5986

16 605782

-

69882,00

7 -0,5105

17 715408,4

-

88608,44

3 -0,6473

18 766098,9

-

101098,8

9 -0,7386

19 832545,2

130254,7

5 0,95156

20 854982,9

161817,0

6 1,18213

21 742224,9

11375,06

1 0,0831

22 668224,5

36375,48

8 0,26574

23 578526,5

53673,52

6 0,3921

24 490420,1

156279,8

5 1,14168

25 522579,9

14120,12

8 0,10315

26 534967,4

47432,57

3 0,34651

27 576077,2

27922,75

6 0,20399

28 613708,5

31991,51

3 0,23371

29 719213,4 74386,58 0,54342


22/29

22

4

30 715433,1

74266,92

3 0,54255

31 754561,5

286738,5

3 2,09473

32 766117,8 331282,21 2,42013

33 712164,2

88435,81

6 0,64605

34 648259,1

96940,91

6 0,70819

35 538210,9 74289,14 0,54271

36 462554,6

150445,4

2 1,09906

37 473782,8

20917,15

1 0,15281

38 478511,1

-

19411,13

9 -0,1418

39 518856,3

12343,65

4 0,09017

40 536635,6

60964,37

5 0,44537

41 719213,4

-

58913,41

6 -0,4304

42 715433,1

-

7733,076

9 -0,0565

43 755489,7

91910,31

1 0,67144

44 766117,8

131282,2

1 0,95906

45 712164,2

-

66664,18

4 -0,487

46 648259,1

-

9859,083

8 -0,072

47

538210,9 -11210,86 -0,0819

48 462554,6

106045,4

2 0,7747

49 462933,6

7066,395

6 0,05162

50 466282,3

-

38882,29

1 -0,284


23/29

23

51 518714,1

11385,88

5 0,08318

52 537697,9

49002,13

2 0,35798

53 660904

-

27803,98

9 -0,2031

54 842859,3

-

157359,3

2 -1,1496

55 683361,4

-

50261,35

6 -0,3672

56 707425,3

270274,7

4 1,97445

57 661879,8

-

10279,82

5 -0,0751

58 623957,6

-

34457,61

5 -0,2517

59 566083,3

226155,6

9 1,65215

60 486657,9

310783,1

3 2,27038

PROBABILITY OUTPUT

Percentile

Arrivals of foreign tourists registered at Ro

borders

0,83333 329320

2,5 337703

4,16667 339400

5,83333 360700

7,5 379772

9,16667 427400

10,8333 428185

12,5 43432214,1667 445655

15,8333 459100

17,5 462711

19,1667 468559

20,8333 470000

22,5 477100


24/29

24

24,1667 494700

25,8333 518700

27,5 521600

29,1667 527000

30,8333 530100

32,5 531200

34,1667 535900

35,8333 536700

37,5 568600

39,1667 582400

40,8333 586700

42,5 589500

44,1667 590197

45,8333 597600

47,5 604000

49,1667 60804750,8333 612500

52,5 613000

54,1667 626800

55,8333 632200

57,5 633100

59,1667 633100

60,8333 638400

62,5 645500

64,1667 645700

65,8333 64670067,5 651600

69,1667 660300

70,8333 665000

72,5 685500

74,1667 704600

75,8333 707700

77,5 745200

79,1667 753600

80,8333 789700

82,5 792239

84,1667 793600

85,8333 797441

87,5 800600

89,1667 847400

90,8333 897400

92,5 962800

94,1667 977700


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25

95,8333 1016800

97,5 1041300

99,1667 1097400

4. Characterize the intensity of the relationship between Arrivals of foreign tourists registered atRo borders and Arrivals of foreign tourists at turistical units and Number of tourists that slept in

RO .We use the coefficient of linear correlation :

=

=multiple R= 0,635419

We have a medium intensity correlation because the intensity correlation tends to 0.75Then, we check if the linear model is appropriate, meaning if R=r:

Ratio of determination

R==0.635=> R=r=0.635

So, we have a linear multiple relation between variables.Consider that Arrivals of foreign tourists at turistical units and Number of tourists thatslept in RO as the only influence factors and the other having a constant influence. 0,403757 %

(R square) out of Arrivals of foreign tourists registered at Ro borders in the 60 observations isexplained by Arrivals of foreign tourists at turistical units and Number of tourists that slept in

RO variables. When we measure considering other factors the regression is explained only0,382836 % out of y variable.

-500000

0

500000

0 100000 200000 300000 400000Residuals


Arrivals of foreign tourists at

turistical units Residual Plot


26/29

26

5. Interpretation of the regression coefficient and the intercept for the multiple regression model.

= 275769,8 ( no specific interpretation)

= 1,734768 positive => direct relationship

= 0,50974 positive => direct relationship

Multiple regression model

=275769,8 +1,734768 +0,50974

6. Is the multiple model valid for 60 observations ?

Step 1 : We test the following hypothesis

: ===

:At least 2 predicted values are different=

0

500000

1000000

1500000

0.8

3333

10.8

333

20.8

333

30.8

333

40.8

333

50.8

333

60.8

333

70.8

333

80.8

333

90.8

333

rrivalsofforeign

tourists

registeredatRob

orders

Sample Percentile

Normal Probability Plot

Series1

-300000

-200000

-100000

0

100000

200000

300000

400000

0 10 20 30 40 50 60 70

Series1


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27

We test if predicted values have similar values.

Step2 : overall variations

Explained variation = ESS= 7,49E+11

Unexplained variation=RSS= 1,11E+12

= 337703 => =275769,8 +1,734768 *75500 + 0,50974* 188700 =502932,6309

If only Arrivals of foreign tourists at turistical units and Number of tourists that slept inRO would influence Arrivals of foreign tourists registered at Ro borders the first observation

would have a bigger number of tourists that registered at the border.

Residuals - => = -= -165229,6309So, we have a loss of 165229,6309.

= 0 = 1,10553E+12

Step 3 : Average variation

= ESR= 3,74315E+11

= RMS = 19395237567

Step 4 : Fisher test

=

= 19,29931

> => 19,29931> => 19,29931> 2,76 =>

The regression model is valid, the line is fitting the points in the scatter diagram and we

can use the regression model for predictions.

Step 5 : Durbin-Watson Test

DW =

=

= 0,704143

Where =estimator of the variable


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28

If 0 the model

is valid.


29/29

References

1. http://graphpad.com/curvefit/linear_regression.htm2. http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm3. http://www.economywatch.com/world-industries/tourism/4. http://ec.europa.eu/enterprise/sectors/tourism/index_en.htm

Documents

Foreigners in Romania