Regression Project

REGRESSION ANALYSIS

1 . Econometric problem

Price of a hotel room can be based on the type of room and the added services and amenities of the establishment . All these parameters can be reduced to one indicator called star rating . Star rating is just like the countries growth rate , one figure that states the health of the country 's economy

How is a hotel given a star rating ? Ratings are weighted averages of independent ratings systems , customer surveys and media recognition ADDIN EN .CITE Expedia .com1161Expedia comLodging detailshttp /www

.expedia .com /pub /agent .dll ?qscr hgen h fnm H_VHW_detail .htx rhtx HTX_HOTVPAGE_LOCA class (Expedia .com . Hotels are given 1 to 5 stars as follows

One star (economy ) offers clean minimum accommodation for the budget traveler where cost is the primary concern . Amenities are bare minimum small room , no private bath or in-room telephone , no on-site dining

Two stars (Value ) in addition to one star features , these hotels offer some business services but no meeting rooms , baggage assistance and recreational facilities . Amenities are limited to private bathroom telephone , and TV

Three stars (quality ) emphasizes style , comfort and personalized service . There are more amenities like a pool or fitness center , a gift shop and on-site dining room service

Four stars (superior ) are upscale hotels with fine-dining restaurants lounge and room service . Designs are of high quality materials and more amenities

Five stars (exceptional ) are given to the world 's finest hotels featuring luxury appointments and superlative service of the highest standards

Among the amenities in the hotels surveyed include : internet-access , pay movies , cable /satellite TV , voice mail , multi-line telephones coffee /tea makers , refrigerators , crib for babies , wheel chair accessibility for the disabled , in-room safe , smoking and non-smoking areas , pool , guarded parking , physical fitness centers and many others

2 . Hypothesis

Hotel room price (Y ) is a function of hotel star rating

Complete regession model : Y bo b1X

Where : bo y-intercept b1 regression coefficient

Null hypothesis : bo 0 b1 0

If the null hypothesis is accepted , this means that price of the hotel room is independent of its star rating

Alternative hypothesis : the coefficient is not equal to zero

Expected problems : This project assumes that the hotel ratings are objective

Data came from internet search hotel rooms Honolulu (http /www .expedia .com /pub /agent .dll ?qscr dspv flag l itid itdx itty from f foop 0 hwrq htid 2796 spsh spsi crti 4 nfla 1 mdpcid 21187-1 ExpediaHotelImages hsp Synd_HSP ROW zz 12 . The raw data are found in the appendix . In addition to star rating and prices , other variables were also taken : the distance of the hotel from the airport (miles , number of amenities , customer evaluation (ratings of 1 to 5 from worst to best ) of the hotel in terms of hotel service , room condition , cleanliness of the establishment , comfort of guest rooms , and the overall average customer satisfaction . Information on fifteen hotels were downloaded although there were some information (missing data indicated by ) that were not obtained during the browsing

Descriptive statistics using Minitab statistical software

Variable N N Mean Median TrMean StDev

Stars 15 0 2 .833 3 .000 2 .731 0 .748

Price 15 0 131 .9 99 .0 111 .2 102 .0

Ameniti 13 2 19 .54 21 .00 19 .00 7 .36

Airport 12 2 10 .54 9 .00 9 .45 4 .36

Service 15 0 4 .033 4 .100 4 .038 0 .479

Conditio 15 0 3 .360 3 .200 3 .369 0 .495

Cleanlin 15 0 3 .840 3 .800 3 .869 0 .455

Comfort 15 0 3 .613 3 .700 3 .638 0 .536

Satisfac 15 0 3 .712 3 .750 3 .744 0 .428

Variable SE Mean Minimum Maximum Q1 Q3

Stars 0 .193 2 .000 5 .000 2 .500 3 .000

Price 26 .3 59 .0 475 .0 75 .0 158 .0

Ammeniti 2 .04 10 .00 35 .00 12 .50 24 .50

Airport 1 .26 8 .00 24 .00 9 .00 10 .00

Service 0 .124 3 .100 4 .900 3 .700 4 .500

Conditio 0 .128 2 .400 4 .200 3 .000 3 .700

Cleanlin 0 .117 2 .800 4 .500 3 .700 4 .300

Comfort 0 .138 2 .400 4 .500 3 .100 4 .000

Satisfac 0 .111 2 .675 4 .325 3 .500 4 .000

The hotels ranged in star rating from a minimum of 2 to a maximum of 5 with a mean of 2 .83 . The median hotel had 3 stars , half of the hotels were 3 or less stars and the other half more than 3 stars . The hotels had around 20 amenities . These amenities were not weighed , thus an internet access had the same weight as a refrigerator . Customers were moderately satisfied with the hotels they checked into (average of around 3 .7 ) although the highest was 4 .3 very near the maximum customer rating

Variance is the square of the standard deviation (StDev . The variance of price is 102 for a mean of 131 .90 per night

Correlations : Stars , Price , Amenities , Airport , Service , Condition Cleanliness

Stars Price Ameniti Airport Service Conditio Cleanlin Comfort

Price 0 .776

0 .001

Ameniti 0 .413 0 .509

0 .161 0 .076

Airport 0 .370 0 .087 -0 .348

0 .237 0 .788 0 .325

Service 0 .505 0 .500 0 .600 0 .073

0 .055 0 .058 0 .030 0 .822

Conditio 0 .087 0 .151 0 .222 -0 .161 0 .482

0 .759 0 .591 0 .465 0 .617 0 .069

Cleanlin 0 .262 0 .090 0 .291 -0 .125 0 .672 0 .749

0 .345 0 .749 0 .334 0 .698 0 .006 0 .001

Comfort 0 .051 -0 .126 0 .122 -0 .013 0 .491 0 .812 0 .863

0 .858 0 .655 0 .692 0 .967 0 .063 0 .000 0 .000

Satisfac 0 .252 0 .168 0 .357 -0 .066 0 .751 0 .877 0 .940 0 .914

0 .365 0 .549 0 .231 0 .838 0 .001 0 .000 0 .000 0 .000

Cell Contents : Pearson correlation

P-Value

The correlation (Pearson correlation ) between the two variables indicated by the row and column is given in the first line and the level of significance (p-value . For example the correlation between price and stars is 0 .776 and the level of significance is 0 .001 . The two variables are highly correlated . The correlation between number of amenities and the price of the hotel room is nearly significant (r 0 .509 ,

br 0 .076 . This simply means that the dearer hotel has more amenities than the cheaper ones . This is to be expected , the customer pays for the amenities . The distance of the hotel from the a airport is not a factor in the pricing of the hotel (r 0 .087 ,

0 .788 , or in the granting of stars (r 0 .37 ,

0 .237 . The number of amenities was slightly negatively correlated with airport distance (r -0 .348 ,p 0 .325

Customer satisfaction was most correlated with room cleanliness (r 0 .94 ,

0 .000 ) and comfort of the room (r 0 .914 ,

0 .000 . This was true regardless of the star rating . Customer satisfaction was slightly correlated with star rating (r 0 .252 ,

0 .365

5 . Simple linear regression between hotel room price and star ratings

Regression Analysis : Price versus Stars

The regression equation is

Price - 168 106 Stars

Predictor Coef SE Coef T

p Constant -167 .68 69 .80 -2 .40 0 .032

Stars 105 .74 23 .87 4 .43 0 .001

S 66 .81 R-Sq 60 .1 R-Sq (adj 57 .1

Analysis of Variance

Source DF SS MS F

p Regression 1 87592 87592 19 .62 0 .001

Residual Error 13 58031 4464Unusual Observations

Obs Stars Price Fit SE Fit Residual St Resid

3 5 .00 475 .0 361 .0 54 .5 114 .0 2 .95RX

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence

The linear regression model is highly significant (F 19 .62 ,

0 .001 It explains 57 .1 (R-sq (adj )of all the variations of the hotel room prices in Honolulu . This figure is an indication of the goodness of fit of the regression line to the plot of price by stars . Both the intercept (b0 Constant - 167 .68 ) and the slope (b1 stars 105 .74 ) are significant with t -2 .4 (p 0 .032 ) and t 4 .43 (p 0 .001 . This means that for every one star increase in hotel rating there is a corresponding increase of 105 .74 per night of stay

?2 . The possible violation could be that of the star rating which is not strictly a continuous variable although there were ratings of 2 .5 and 3 .5 . Another is the price which had a large range of values

6 . Conclusion

The hotel star rating is the main factor that determines hotel room price . After all this rating was computed based on all the factors that contribute to the overall character of the hotel from design , comfort amenities to luxuries . Each star level caters to a class of travelers from the economy travelers who consider price more than anything else to the middle class of tourists or travelers who opt for comfort , and to the high level executive who must carry the name of their companies in the 5-star hotel chains

The regression model could be improved if there were enough hotels in the range of 4-stars and 5-stars

Reference

ADDIN EN .REFLIST Expedia .com . Lodging Details . Available HYPERLINK "http /www .expedia .com /pub /agent .dll ?qscr hgen hfnm H_VHW_detail .htx rh tx HTX_HOTVPAGE_LOCA class http /www .expedia .com /pub /agent .dll ?qscr hgen hfnm H_VHW_detail .htx rht x HTX_HOTVPAGE_LOCA class

Appendix

Hotel rates in the Honolulu area

Stars Price Amenities Airport Service Condition Cleanliness Comfort Satisfaction

3 145 25 8 3 .8 4 .1 4 .3 4 .5 4 .175

2 .5 78 22 9 3 .7 3 .1 3 .7 3 .6 3 .525

5 475 35 12 4 .9 3 .2 3 .8 3 .1 3 .75

3 165 11 3 .5 3 .2 3 .8 3 .1 3 .4

3 175 9 4 .5 4 .2 4 .3 4 .3 4 .325

3 75 22 9 4 .1 3 .5 4 .2 3 .8 3 .9

2 .5 69 24 4 .1 3 .4 3 .8 3 .7 3 .75

3 83 9 4 .1 3 .4 3 .7 3 .5 3 .675

2 74 17 9 3 .1 2 .4 2 .8 2 .4 2 .675

3 .5 99 10 24 4 3 .1 3 .7 3 .8 3 .65

2 .5 99 12 10 3 .4 3 3 .2 3 .1 3 .175

2 .5 158 13 10 4 .3 4 .1 4 .3 4 .1 4 .2

3 59 21 8 .5 4 .5 3 4 .5 4 4

2 116 15 9 4 3 3 .5 3 .5 3 .5

2 109 27 4 .5 3 .7 4 3 .7 3 .975

- missing information ...