The influence of main quality factors on the evolution of tourists number--a study in a Romanian business hotel.

Stan, Elena Roxana ; Gabroveanu, Emilia ; Radneantu, Nicoleta 等

1. INTRODUCTION

Quality in hospitality industry is more difficult to achieve than in other sectors. Ensuring quality requires quality in three major chronological stages (before consumption, consumption, after consumption), each being required for obtaining customer satisfaction.

It is essential to know the degree of clients' satisfaction, their needs and expectations so that it can highlight the quality costs, considered an important tool of quality valorization.

Representing a potential source of maximizing the profit of organizations, the quality costs are used as a tool for optimization of processes and activities relevant to quality.

Due to changes taking place continuously, is necessary description and analysis of economic and social phenomena and processes and analyze the influence of factors which may change them. To highlight the degree of influence of different factors may apply multifactorial regression model, respectively dispersion analysis method Analysis of Variance--ANOVA.

ANOVA method implies defining a regression model, which involves: determining the regression equation, testing the validity of the regression model, establishment and testing correlation, and testing significance and estimation of linear regression model parameters on confidence intervals.

For a better understanding of issues relating to determination and analysis of dependency between the number of tourists, quality costs based on material and quality costs for human resources, it will be applied multiple regression method for the value registered in a Romanian 4 stars hotel--Alpha Hotel (to maintain confidentiality the hotel was renamed; the data provided and used for the research are real).

Here are the steps followed for dispersion analysis method ANOVA. To facilitate the calculations and problem solving it has been used Excel software.

2. DETERMINE THE REGRESSION EQUATION

Analyzing characteristics: number of tourists accommodated in Alpha Hotel, quality costs based on material and quality costs for human resources, we establish:

[y.sub.i]--number of tourists accommodated in Alpha Hotel

[x.sub.i1]--quality costs based on material (lei)

[x.sub.i2]--quality costs for human resources (lei)

Regression equation which model the link between the variables mentioned is:

[y.sub.i] = [b.sub.0] + [b.sub.1] x [x.sub.i1] + [b.sub.2] x [x.sub.i2]. (1)

In Table 1, are presented intermediate values necessary for apply the least squares method:

Least square minimizes the residual sum of squares (Baltagi, 2008). Knowing that n = 9, [SIGMA][x.sub.i1] = 7204.581, [SIGMA][x.sub.i2] = 7941.783 and [SIGMA][y.sub.i] = 155.905, the system equations become:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Where: [b.sub.0] = 4131.3959, [b.sub.1] = -0.0049 and [b.sub.2] = 0.0194.

Regression line is defined by the equation:

[y.sub.i] = 4131.3959 - 0.0049 x [x.sub.i1] + 0.0194 x [x.sub.i2]. (3)

3. TESTING THE VALIDITY OF THE REGRESSION MODEL

To confirm the model establishment and use the approach was to verify the validity of the method. This is achieved in the following stages of linear regression model analysis.

The established assumptions are:

* [H.sub.0]: the model is not valid (null hypothesis)

* [H.sub.1]: the model is valid (alternative hypothesis)

To use the F test, compared with the analyzed data was applied EXCEL software. The obtained values, necessary for analysis of the validity of regression model, are:

Knowing that the probability of occurrence of the results is 95% and the limit of significance [alpha] = 0.05 it was obtained the limit region of rejection: [F.sub.[alpha];k;n-k-1] = [F.sub.0.05;2;6] = 5.14 (4)

For analyzed characteristics (number of tourists accommodated at Alpha Hotel, quality costs based on material and quality costs for human resources), [F.sub.c] = 744.0433605 > [F.sub.[alpha];k;n-k-1] = 5.14. In this case H0 is rejected, the regression model being statistically valid.

Another element which reflects the validity of the model is Significance F. If the value obtained for this element is less than 0.05, [H.sub.0] is rejected. In Table 2 it is shown that Significance F = 6.47629E-08 < 0.05, and the regression model is statistically valid.

4. DETERMINING AND TESTING THE CORRELATION

For determining the correlation was used Excel software. The values obtained for the correlation (R), R Square ([R.sup.2]), the adjusted R Square ([R.sup.2]), and standard deviation of errors ([s.sub.e]), are presented in table 3:

The correlation value (Multiple R) is set to 0.997990065 and shows that between number of tourists, quality costs based on material and quality costs for human resources, registered in the period under review at Alpha Hotel, is a very strong connection, almost perfect.

[R.sup.2] is called the coefficient of determination (Kennedy, 2003). R Square is set to 0.995984169 and shows that the influence of the two factors (quality costs based on material and quality costs for human resources) on the number of tourists accommodated at Alpha Hotel is about 99.60%, the remaining 0.40% is due to other random factors.

Adjusted R Square value can increase or decrease along with the inclusion of new exogenous variables in the regression model (Andrei, 2003). The value of standard error shows that points are not placed near the regression right.

5. TESTING THE SIGNIFICANCE AND ESTIMATION OF PARAMETERS FOR LINEAR REGRESSION MODEL ON CONFIDENCE INTERVALS

Estimators for regression parameters are determined by least squares method.

Testing their significance has in view the size of the selected collectivity, so if n <30, it is applied Student test (Gogonea & Zaharia, 2008). In Table 4, an ANOVA table, are presented the necessary elements for testing parameters and establish confidence intervals.

From the table below we establish the linear adjusting equation of the connection between analyzed indicators:

[y.sub.i] = 4131.3959--0.0049 x [x.sub.i1] + 0.0194 x [x.sub.i2] (5)

The value of [b.sub.0] is 4131.3959 and shows that if quality costs based on material are remaining constant, respectively quality costs for human resources, the number of tourists accommodated in Alpha Hotel, was set to a value of approximately 4131. Analyzing the value resulted for t test, [t.sub.c] = 11.4933, and significance threshold P-value = 2.60589E-05 < 0.05, we see that free term is statistically significant. This is reflected also by the presence of the confidence interval, respectively 3251.8297 < [b.sub.0] < 5010.9621.

The value of [b.sub.1] coefficient is -0.0049 and shows that by decreasing Variable 1 with one leu per year, the Intercept will decrease with 0.0049. This means that the decrease of quality costs based on material with 204.08 lei will decrease the number of tourists accommodated in Alpha Hotel by one. Threshold of significance P-value is 0.012902631 < 0.05, and the result [t.sub.cb1] = [absolute value of -3.49511] > 2.365 = [t.sub.0.025;7], shows us that this coefficient is considered statistically significant. The limits of the confidence interval of this parameter are: -0.0084 < [b.sub.1] < - 0.0015.

The value of coefficient [b.sub.2] is approximately 0.0194 and it shows that by increasing Variable 2 with one leu per year, the Intercept will increase with the value of [b.sub.2]. This means that the increase of quality costs for human resources with approximately 51.55 lei will increase the number of tourists accommodated in Alpha Hotel by one. For this coefficient the threshold of significance P-value is 1.04885E-05 < 0.05, respectively [t.sub.cb2] = 13.4449 > 2.365 = [t.sub.0.025;7], the coefficient being statistically significant.

The lower limit of the confidence interval of this parameter is approximately 0.0159, and the upper limit reaches 0.0230.

6. CONCLUSION

After testing the validity of regression model was established that this model is statistically valid. Thus, it was observed that between the number of accommodated at Alpha Hotel and quality costs based on material costs, namely quality costs for human resources is a strong connection.

For the most part, service quality dimensions are determined by the activities of staff. Because the improvement of quality of service and productivity growth is found in an inverse relationship, requires the activity in a manner that ensures a balance between quality and quantity of services, that balance is a benchmark used to staff. Always investments in human resources and material basis will attract, through the quality of services, new tourists.

7. REFERENCES

Andrei, T. (2003). Statistica si econometrie, Publisher Economica, ISBN 973-590-764-X, Bucharest

Baltagi, B. H. (2008). Econometrics 4th edition, Publisher Springer, ISBN 978-3-540-76515-8, Berlin

Gogonea, R. M. & Zaharia, M. (2008). Econometrie cu aplicatii in comert-turism-servicii, Publisher Universitara, ISBN 978-973-749-496-2, Bucharest

Kennedy, P. (2003). A guide to Econometrics--fifth edition, Publisher MPG Books, Bodmin, Cornwall, ISBN 0-26211280-9, United Kingdom

*** Alpha Hotel--financial-accounting department

Tab. 1. Algorithm required for applying least squares method

 [x.sub.
Years [y.sub.i] [x.sub.i1] [x.sub.i2] i1.sup.2]

2000 13.924 590.477 650.234 348663.0875
2001 14.025 669.778 677.955 448602.5693
2002 14.458 671.452 710.437 450847.7883
2003 16.890 674.742 805.700 455276.7666
2004 17.258 681.152 853.544 463968.0471
2005 17.582 702.472 885.622 493466.9108
2006 17.869 852.524 915.487 726797.1706
2007 18.256 975.662 987.556 951916.3382
2008 25.643 1386.322 1455.248 1921888.688
[SIGMA] 155.905 7204.581 7941.783 6261427.366

 [x.sub.i2 [x.sub.i1] [y.sub.i] [y.sub.i]
Years sup.2] x [x.sub.i2] x [x.sub.i1] x [x.sub.i2]

2000 422804.2548 383948.2216 8221.801748 9053.858216
2001 459622.982 454079.344 9393.63645 9508.318875
2002 504720.731 477024.3445 9707.853016 10271.49815
2003 649152.49 543639.6294 11396.39238 13608.273
2004 72853.3599 581393.2027 11755.32122 14730.46235
2005 784326.3269 622124.6576 12350.8627 15571.006
2006 838116.4472 780474.6392 15233.75136 16358.8372
2007 975266.8531 963520.8621 17811.68547 18028.82234
2008 2117746.742 2 017442.318 35549.45505 37316.92446
[SIGMA] 7480294.186 6823647.219 131420.7594 144448.0006

Source: calculations made by the authors. To facilitate
calculations, values were expressed in thousands of tourists,
respectively lei

Tab. 2. ANOVA table with the necessary values for analysis the
regression model

ANOVA

 Regression Residual Total

Df 2 6 8
SS 100881273.9 406755.6246 101288029.6
MS 50440636.97 67792.60409
F 744.0433605
Significance F 6.47629E-08

Tab. 3. The values of parameters R, [R.sup.2], [[bar.R].sup.2] and
[s.sub.e]

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.997990065
R Square 0.995984169
Adjusted R Square 0.994645558
Standard Error 260.370129
Observations 9

Tab. 4. Elements necessary for testing parameters and establish
confidence intervals

 Intercept X Variable 1 X Variable 2

Coefficients 4131.3959 -0.0049 0.0194
Standard Error 359.4597 0.0014 0.0015
t Stat 11.4933 -3.4951 13.4449
P-value 2.60589E-05 0.012902631 1.04885E-05
Lower 95% 3251.8297 -0.0084 0.0159
Upper 95% 5010.9621 -0.0015 0.0230