| title: “BM Hotels Data Analysis” |
| output: html_notebook |
READING AND DESCRIBING DATA
Read the Data
BMHotelsData.df <- read.csv(paste("HotelsData34CitiesData.csv"))
colnames(BMHotelsData.df)## [1] "CityName" "Population"
## [3] "IsTourist" "Day"
## [5] "Date" "IsWeekend"
## [7] "HotelName" "Available"
## [9] "MaxRentUSD" "RentUSD"
## [11] "StarRating" "GuestRating"
## [13] "HotelAddress" "HotelPincode"
## [15] "HotelDescription" "FreeWifi"
## [17] "FreeBreakfast" "HotelCapacity"
## [19] "HasSwimmingPool" "IsMarriott"
## [21] "IsHilton" "IsMarriottOrHilton"
## [23] "MedianHomeValue" "MedianHouseHoldIncome"Conversion of dataframe
BMHotelsData.df$IsTourist <- as.factor(BMHotelsData.df$IsTourist)
BMHotelsData.df$IsWeekend <- as.factor(BMHotelsData.df$IsWeekend)
BMHotelsData.df$Available <- as.factor(BMHotelsData.df$Available)
BMHotelsData.df$StarRating <- as.factor(BMHotelsData.df$StarRating)
BMHotelsData.df$FreeWifi <- as.factor(BMHotelsData.df$FreeWifi)
BMHotelsData.df$FreeBreakfast <- as.factor(BMHotelsData.df$FreeBreakfast)
BMHotelsData.df$HasSwimmingPool <- as.factor(BMHotelsData.df$HasSwimmingPool)
BMHotelsData.df$IsMarriott <- as.factor(BMHotelsData.df$IsMarriott)
BMHotelsData.df$IsHilton <- as.factor(BMHotelsData.df$IsHilton)
BMHotelsData.df$IsMarriottOrHilton <- as.factor(BMHotelsData.df$IsMarriottOrHilton)
BMHotelsData.df$MedianHouseHoldIncome <- as.integer(BMHotelsData.df$MedianHouseHoldIncome)
BMHotelsData.df$CityName <- as.factor(BMHotelsData.df$CityName)
attach(BMHotelsData.df)
dim(BMHotelsData.df) ## 17030 rows, 24 columns## [1] 17030 24unique(BMHotelsData.df$CityName)## [1] Tampa New York City Cleveland Milwaukee Nashville
## [6] Jacksonville Louisville New Orleans Los Angeles Fresno
## [11] St. Louis Memphis Philadelphia Kansas City Niagara Falls
## [16] Las Vegas San Antonio Houston Tucson Buffalo
## [21] Boston Phoenix Seattle Albuquerque Asheville
## [26] San Francisco Arlington Baltimore Columbus San Jose
## [31] Chicago Lake Tahoe Anaheim Maui
## 34 Levels: Albuquerque Anaheim Arlington Asheville Baltimore ... TucsonUnique hotels Name and zipCodes
#### Group 1 -- Group 1
length(unique(BMHotelsData.df$HotelName)) # 1691 unique hotels ## [1] 1691length(unique(BMHotelsData.df$HotelPincode)) # 593 unique zip code## [1] 593Descriptive statistics
library(psych)
describe(BMHotelsData.df)[, c(1:9)]## vars n mean sd median
## CityName* 1 17030 17.38 9.73 17.0
## Population 2 17030 29404198.02 152326494.83 595047.0
## IsTourist* 3 17030 1.41 0.49 1.0
## Day* 4 17030 4.10 2.17 4.0
## Date* 5 17030 5.50 2.87 6.0
## IsWeekend* 6 17030 1.30 0.46 1.0
## HotelName* 7 17030 843.36 488.88 843.0
## Available* 8 17030 1.93 0.25 2.0
## MaxRentUSD 9 17030 200.41 290.38 153.0
## RentUSD 10 17030 156.81 265.78 119.0
## StarRating* 11 17030 5.33 1.92 5.0
## GuestRating 12 17030 5.16 2.03 4.4
## HotelAddress* 13 17030 1328.31 776.84 1326.0
## HotelPincode 14 17030 59675.59 30176.62 64150.0
## HotelDescription* 15 17030 744.70 423.69 761.0
## FreeWifi* 16 17030 1.93 0.25 2.0
## FreeBreakfast* 17 17030 1.47 0.50 1.0
## HotelCapacity 18 17030 177.28 268.87 118.0
## HasSwimmingPool* 19 17030 1.58 0.49 2.0
## IsMarriott* 20 17030 1.09 0.29 1.0
## IsHilton* 21 17030 1.06 0.24 1.0
## IsMarriottOrHilton* 22 17030 1.16 0.37 1.0
## MedianHomeValue 23 17030 320125.92 275396.36 219100.0
## MedianHouseHoldIncome 24 17030 54279.95 23455.73 51250.0
## trimmed mad min max
## CityName* 17.35 11.86 1 34
## Population 696034.82 392952.75 21717 840600000
## IsTourist* 1.39 0.00 1 2
## Day* 4.12 2.97 1 7
## Date* 5.50 2.97 1 10
## IsWeekend* 1.25 0.00 1 2
## HotelName* 843.03 628.62 1 1691
## Available* 2.00 0.00 1 2
## MaxRentUSD 164.20 87.47 1 9280
## RentUSD 128.77 63.75 4 9280
## StarRating* 5.18 1.48 1 10
## GuestRating 4.96 1.04 1 10
## HotelAddress* 1331.38 1037.08 1 2620
## HotelPincode 61360.03 38598.01 2108 98198
## HotelDescription* 747.01 538.18 1 1474
## FreeWifi* 2.00 0.00 1 2
## FreeBreakfast* 1.47 0.00 1 2
## HotelCapacity 134.40 85.99 1 4028
## HasSwimmingPool* 1.60 0.00 1 2
## IsMarriott* 1.00 0.00 1 2
## IsHilton* 1.00 0.00 1 2
## IsMarriottOrHilton* 1.07 0.00 1 2
## MedianHomeValue 268171.56 157896.90 2800 2308300
## MedianHouseHoldIncome 51929.32 20796.43 2930 168036str(BMHotelsData.df)## 'data.frame': 17030 obs. of 24 variables:
## $ CityName : Factor w/ 34 levels "Albuquerque",..: 33 33 33 33 33 33 33 33 33 33 ...
## $ Population : int 377165 377165 377165 377165 377165 377165 377165 377165 377165 377165 ...
## $ IsTourist : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ Day : Factor w/ 7 levels "Friday","Monday",..: 7 5 1 3 4 2 6 7 5 1 ...
## $ Date : Factor w/ 10 levels "Dec 1 2017","Dec 2 2017",..: 9 10 1 2 3 4 5 6 7 8 ...
## $ IsWeekend : Factor w/ 2 levels "0","1": 1 1 2 2 1 1 1 1 1 2 ...
## $ HotelName : Factor w/ 1691 levels "1840s Carrollton Inn, Baltimore",..: 705 705 705 705 705 705 705 705 705 705 ...
## $ Available : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ MaxRentUSD : num 244 244 244 244 244 244 244 244 244 244 ...
## $ RentUSD : num 119 119 153 244 119 102 139 119 123 157 ...
## $ StarRating : Factor w/ 10 levels "1","1.5","2",..: 4 4 4 4 4 4 4 4 4 4 ...
## $ GuestRating : num 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 4.2 ...
## $ HotelAddress : Factor w/ 2620 levels "0570 W 151st Street, Olathe, KS",..: 2452 2452 2452 2452 2452 2452 2452 2452 2452 2452 ...
## $ HotelPincode : int 33610 33610 33610 33610 33610 33610 33610 33610 33610 33610 ...
## $ HotelDescription : Factor w/ 1474 levels ""," Motel with outdoor pool, near Heavenly Ski Resort",..: 865 865 865 865 865 865 865 865 865 865 ...
## $ FreeWifi : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ FreeBreakfast : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ HotelCapacity : int 76 76 76 76 76 76 76 76 76 76 ...
## $ HasSwimmingPool : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ IsMarriott : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ IsHilton : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ IsMarriottOrHilton : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ MedianHomeValue : int 92300 92300 92300 92300 92300 92300 92300 92300 92300 92300 ...
## $ MedianHouseHoldIncome: int 2930 2930 2930 2930 2930 2930 2930 2930 2930 2930 ...summary(BMHotelsData.df
)## CityName Population IsTourist Day
## Kansas City : 720 Min. : 21717 0:10060 Friday :3408
## New York City: 580 1st Qu.: 377165 1: 6970 Monday :1703
## Buffalo : 550 Median : 595047 Saturday :1704
## Lake Tahoe : 540 Mean : 29404198 Sunday :1703
## Las Vegas : 540 3rd Qu.: 880619 Thursday :3406
## Boston : 510 Max. :840600000 Tuesday :1704
## (Other) :13590 Wednesday:3402
## Date IsWeekend HotelName
## Dec 8 2017:1708 0:11902 Americas Best Value Inn : 40
## Dec 2 2017:1703 1: 5128 Americas Best Value Inn & Suites: 20
## Dec 3 2017:1703 Clarion Hotel : 20
## Dec 4 2017:1703 Comfort Inn Downtown : 20
## Dec 5 2017:1703 Country Inn & Suites By Carlson : 20
## Dec 6 2017:1703 Days Inn : 20
## (Other) :6807 (Other) :16890
## Available MaxRentUSD RentUSD StarRating
## 0: 1170 Min. : 1.0 Min. : 4.0 3 :4064
## 1:15860 1st Qu.: 99.0 1st Qu.: 80.0 2.5 :4036
## Median : 153.0 Median : 119.0 3.5 :2578
## Mean : 200.4 Mean : 156.8 4 :2461
## 3rd Qu.: 229.0 3rd Qu.: 179.0 2 :2400
## Max. :9280.0 Max. :9280.0 4.5 : 712
## (Other): 779
## GuestRating
## Min. : 1.000
## 1st Qu.: 3.900
## Median : 4.400
## Mean : 5.163
## 3rd Qu.: 7.000
## Max. :10.000
##
## HotelAddress
## 111 West Adams Street, Chicago, IL, 60603, United States of America : 20
## 1230 N Old World Third St, Milwaukee, WI, 53212, United States of America : 20
## 145 E Harmon Ave : 20
## 210 Franklin St, Buffalo, NY, 14202, United States of America : 20
## 2575 S Kihei Rd, Kihei, HI, 96753, United States of America : 20
## 3110 N Blackstone Ave, Fresno, CA, 93703, United States of America, 866-925-8648: 20
## (Other) :16910
## HotelPincode
## Min. : 2108
## 1st Qu.:33612
## Median :64150
## Mean :59676
## 3rd Qu.:89109
## Max. :98198
##
## HotelDescription
## No-frills Fresno motel with outdoor pool : 71
## Motel with outdoor pool, near Disney California Adventure® Park : 70
## 4-star hotel with restaurant, near Westfield San Francisco Centre : 60
## No-frills Tampa hotel with outdoor pool : 60
## 3-star hotel with outdoor pool, near Disney California Adventure® Park: 50
## 4-star hotel with restaurant, near Millennium Park : 50
## (Other) :16669
## FreeWifi FreeBreakfast HotelCapacity HasSwimmingPool IsMarriott
## 0: 1121 0:8980 Min. : 1.0 0:7152 0:15480
## 1:15909 1:8050 1st Qu.: 69.0 1:9878 1: 1550
## Median : 118.0
## Mean : 177.3
## 3rd Qu.: 199.0
## Max. :4028.0
##
## IsHilton IsMarriottOrHilton MedianHomeValue MedianHouseHoldIncome
## 0:16022 0:14326 Min. : 2800 Min. : 2930
## 1: 1008 1: 2704 1st Qu.: 142400 1st Qu.: 37246
## Median : 219100 Median : 51250
## Mean : 320126 Mean : 54280
## 3rd Qu.: 406900 3rd Qu.: 65678
## Max. :2308300 Max. :168036
## table(BMHotelsData.df$IsTourist)##
## 0 1
## 10060 6970table(BMHotelsData.df$IsWeekend)##
## 0 1
## 11902 5128table(BMHotelsData.df$HasSwimmingPool)##
## 0 1
## 7152 9878table(BMHotelsData.df$FreeWifi)##
## 0 1
## 1121 15909table(BMHotelsData.df$FreeBreakfast)##
## 0 1
## 8980 8050Regression
OLS regression with INTERACTIONS
Model <- log(RentUSD) ~ HotelCapacity + MaxRentUSD + GuestRating + HasSwimmingPool + FreeBreakfast + IsTourist + IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome + CityName +IsMarriott*HotelCapacity+IsMarriott*HasSwimmingPool+IsMarriott*FreeBreakfast+IsMarriott*IsTourist+IsMarriott*IsWeekend+IsMarriott*MedianHomeValue+IsMarriott*MedianHouseHoldIncome + IsMarriott*MaxRentUSD + IsMarriott*GuestRating
fitOLS<- lm(Model, data = BMHotelsData.df)
summary(fitOLS)##
## Call:
## lm(formula = Model, data = BMHotelsData.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.7266 -0.1967 -0.0081 0.1977 4.7087
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.389e+00 2.008e-02 168.787 < 2e-16
## HotelCapacity 1.738e-04 1.085e-05 16.020 < 2e-16
## MaxRentUSD 1.541e-03 1.629e-05 94.631 < 2e-16
## GuestRating 2.089e-01 3.312e-03 63.077 < 2e-16
## HasSwimmingPool1 -1.366e-02 6.195e-03 -2.204 0.02751
## FreeBreakfast1 -4.667e-02 5.790e-03 -8.060 8.14e-16
## IsTourist1 2.593e-01 2.096e-02 12.371 < 2e-16
## IsWeekend1 6.853e-02 5.605e-03 12.226 < 2e-16
## IsMarriott1 6.837e-01 3.515e-02 19.453 < 2e-16
## MedianHomeValue 3.434e-07 2.329e-08 14.743 < 2e-16
## MedianHouseHoldIncome -1.335e-06 1.693e-07 -7.882 3.41e-15
## CityNameAnaheim -7.397e-01 2.369e-02 -31.217 < 2e-16
## CityNameArlington 1.700e-01 2.079e-02 8.173 3.22e-16
## CityNameAsheville 5.908e-02 2.099e-02 2.814 0.00490
## CityNameBaltimore -6.293e-01 2.459e-02 -25.593 < 2e-16
## CityNameBoston -7.836e-01 2.588e-02 -30.276 < 2e-16
## CityNameBuffalo 1.556e-01 2.014e-02 7.724 1.19e-14
## CityNameChicago -9.096e-01 2.565e-02 -35.469 < 2e-16
## CityNameCleveland 1.535e-01 2.061e-02 7.446 1.01e-13
## CityNameColumbus 6.535e-02 2.066e-02 3.163 0.00157
## CityNameFresno 8.524e-02 2.048e-02 4.162 3.16e-05
## CityNameHouston 1.962e-01 2.098e-02 9.351 < 2e-16
## CityNameJacksonville 3.417e-01 2.072e-02 16.491 < 2e-16
## CityNameKansas City 1.179e-01 1.905e-02 6.191 6.12e-10
## CityNameLake Tahoe -1.061e+00 2.372e-02 -44.743 < 2e-16
## CityNameLas Vegas -3.721e-01 2.188e-02 -17.006 < 2e-16
## CityNameLos Angeles -6.180e-01 2.504e-02 -24.684 < 2e-16
## CityNameLouisville -6.642e-01 2.405e-02 -27.617 < 2e-16
## CityNameMaui 3.387e-01 2.148e-02 15.770 < 2e-16
## CityNameMemphis -3.733e-02 2.101e-02 -1.777 0.07558
## CityNameMilwaukee 1.342e-01 2.081e-02 6.450 1.15e-10
## CityNameNashville 4.316e-01 2.042e-02 21.137 < 2e-16
## CityNameNew Orleans -1.613e-02 2.074e-02 -0.778 0.43685
## CityNameNew York City 1.514e-01 2.073e-02 7.304 2.92e-13
## CityNameNiagara Falls -3.276e-01 2.146e-02 -15.269 < 2e-16
## CityNamePhiladelphia -7.521e-01 2.592e-02 -29.018 < 2e-16
## CityNamePhoenix 4.339e-01 2.098e-02 20.680 < 2e-16
## CityNameSan Antonio 2.506e-01 2.047e-02 12.246 < 2e-16
## CityNameSan Francisco -1.012e+00 2.916e-02 -34.714 < 2e-16
## CityNameSan Jose 5.020e-01 2.153e-02 23.318 < 2e-16
## CityNameSeattle NA NA NA NA
## CityNameSt. Louis -5.572e-01 2.463e-02 -22.621 < 2e-16
## CityNameTampa 3.052e-01 2.038e-02 14.976 < 2e-16
## CityNameTucson -3.507e-03 2.085e-02 -0.168 0.86641
## HotelCapacity:IsMarriott1 3.272e-05 3.986e-05 0.821 0.41177
## HasSwimmingPool1:IsMarriott1 -9.049e-02 2.097e-02 -4.316 1.60e-05
## FreeBreakfast1:IsMarriott1 -6.302e-02 1.982e-02 -3.180 0.00148
## IsTourist1:IsMarriott1 -5.185e-02 2.447e-02 -2.119 0.03413
## IsWeekend1:IsMarriott1 -1.482e-01 1.859e-02 -7.974 1.64e-15
## IsMarriott1:MedianHomeValue 4.133e-07 6.448e-08 6.410 1.49e-10
## IsMarriott1:MedianHouseHoldIncome -9.505e-07 4.829e-07 -1.968 0.04905
## MaxRentUSD:IsMarriott1 -1.039e-03 1.971e-05 -52.681 < 2e-16
## GuestRating:IsMarriott1 -4.788e-02 5.092e-03 -9.403 < 2e-16
##
## (Intercept) ***
## HotelCapacity ***
## MaxRentUSD ***
## GuestRating ***
## HasSwimmingPool1 *
## FreeBreakfast1 ***
## IsTourist1 ***
## IsWeekend1 ***
## IsMarriott1 ***
## MedianHomeValue ***
## MedianHouseHoldIncome ***
## CityNameAnaheim ***
## CityNameArlington ***
## CityNameAsheville **
## CityNameBaltimore ***
## CityNameBoston ***
## CityNameBuffalo ***
## CityNameChicago ***
## CityNameCleveland ***
## CityNameColumbus **
## CityNameFresno ***
## CityNameHouston ***
## CityNameJacksonville ***
## CityNameKansas City ***
## CityNameLake Tahoe ***
## CityNameLas Vegas ***
## CityNameLos Angeles ***
## CityNameLouisville ***
## CityNameMaui ***
## CityNameMemphis .
## CityNameMilwaukee ***
## CityNameNashville ***
## CityNameNew Orleans
## CityNameNew York City ***
## CityNameNiagara Falls ***
## CityNamePhiladelphia ***
## CityNamePhoenix ***
## CityNameSan Antonio ***
## CityNameSan Francisco ***
## CityNameSan Jose ***
## CityNameSeattle
## CityNameSt. Louis ***
## CityNameTampa ***
## CityNameTucson
## HotelCapacity:IsMarriott1
## HasSwimmingPool1:IsMarriott1 ***
## FreeBreakfast1:IsMarriott1 **
## IsTourist1:IsMarriott1 *
## IsWeekend1:IsMarriott1 ***
## IsMarriott1:MedianHomeValue ***
## IsMarriott1:MedianHouseHoldIncome *
## MaxRentUSD:IsMarriott1 ***
## GuestRating:IsMarriott1 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3199 on 16978 degrees of freedom
## Multiple R-squared: 0.7203, Adjusted R-squared: 0.7195
## F-statistic: 857.4 on 51 and 16978 DF, p-value: < 2.2e-16coef(summary(fitOLS))[, "Std. Error"] ## (Intercept) HotelCapacity
## 2.008079e-02 1.085076e-05
## MaxRentUSD GuestRating
## 1.628825e-05 3.312455e-03
## HasSwimmingPool1 FreeBreakfast1
## 6.194945e-03 5.790386e-03
## IsTourist1 IsWeekend1
## 2.095693e-02 5.605224e-03
## IsMarriott1 MedianHomeValue
## 3.514599e-02 2.329296e-08
## MedianHouseHoldIncome CityNameAnaheim
## 1.693460e-07 2.369425e-02
## CityNameArlington CityNameAsheville
## 2.079468e-02 2.099244e-02
## CityNameBaltimore CityNameBoston
## 2.458944e-02 2.588201e-02
## CityNameBuffalo CityNameChicago
## 2.014414e-02 2.564559e-02
## CityNameCleveland CityNameColumbus
## 2.060980e-02 2.066200e-02
## CityNameFresno CityNameHouston
## 2.047783e-02 2.098448e-02
## CityNameJacksonville CityNameKansas City
## 2.072124e-02 1.904987e-02
## CityNameLake Tahoe CityNameLas Vegas
## 2.371979e-02 2.187812e-02
## CityNameLos Angeles CityNameLouisville
## 2.503592e-02 2.404999e-02
## CityNameMaui CityNameMemphis
## 2.148002e-02 2.100613e-02
## CityNameMilwaukee CityNameNashville
## 2.081428e-02 2.042087e-02
## CityNameNew Orleans CityNameNew York City
## 2.073896e-02 2.073453e-02
## CityNameNiagara Falls CityNamePhiladelphia
## 2.145722e-02 2.591934e-02
## CityNamePhoenix CityNameSan Antonio
## 2.098092e-02 2.046710e-02
## CityNameSan Francisco CityNameSan Jose
## 2.916033e-02 2.152747e-02
## CityNameSt. Louis CityNameTampa
## 2.463017e-02 2.037933e-02
## CityNameTucson HotelCapacity:IsMarriott1
## 2.084938e-02 3.986195e-05
## HasSwimmingPool1:IsMarriott1 FreeBreakfast1:IsMarriott1
## 2.096834e-02 1.982006e-02
## IsTourist1:IsMarriott1 IsWeekend1:IsMarriott1
## 2.447333e-02 1.858502e-02
## IsMarriott1:MedianHomeValue IsMarriott1:MedianHouseHoldIncome
## 6.447718e-08 4.829222e-07
## MaxRentUSD:IsMarriott1 GuestRating:IsMarriott1
## 1.971395e-05 5.092125e-03EstandSE = coef(summary(fitOLS))[, c("Estimate","Std. Error","Pr(>|t|)")]
library(data.table)
dt <- data.table(EstandSE)
write.csv(dt, file = "OLSEstimates.csv")Fgls Regression with all Interactions(IsMariott)
# Step 1: Find lnOLSressq i.e. the Log of the Square of the OLS Residuals
OLSres <- resid(fitOLS)
OLSressq <- OLSres^2 # Square residuals
lnOLSressq <- log(OLSressq) # Take natural log of squared residuals
MOdel1<-lnOLSressq ~ HotelCapacity + MaxRentUSD + GuestRating + HasSwimmingPool + FreeBreakfast + IsTourist + IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome + CityName +IsMarriott*HotelCapacity+IsMarriott*HasSwimmingPool+IsMarriott*FreeBreakfast+IsMarriott*IsTourist+IsMarriott*IsWeekend+IsMarriott*MedianHomeValue+IsMarriott*MedianHouseHoldIncome + IsMarriott*MaxRentUSD + IsMarriott*GuestRating
#Auxillary Model
# Step 2: Auxillary Model -- Regress lnOLSressq on the x variables
aux <- lm(MOdel1 , data = BMHotelsData.df) # Run auxillary model
# Step 3a: Calculate ghat i.e. the fitted values of the Auxillary Model
ghat <- fitted(aux) # Predict g^
# Step 3b: Calculate hhat = exp(ghat)
hhat <- exp(ghat) # Create h^
# Step 4: Implement FGLS by running the regression with weights equal to 1/hhat
fGLS <- lm(Model , weights = 1/hhat,data = BMHotelsData.df) # Weight is 1/h^
summary(fGLS)##
## Call:
## lm(formula = Model, data = BMHotelsData.df, weights = 1/hhat)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -14.191 -1.102 0.038 1.163 38.580
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.438e+00 1.845e-02 186.384 < 2e-16
## HotelCapacity 8.338e-05 1.160e-05 7.191 6.72e-13
## MaxRentUSD 2.905e-03 2.511e-05 115.653 < 2e-16
## GuestRating 1.525e-01 2.634e-03 57.906 < 2e-16
## HasSwimmingPool1 -9.354e-03 4.885e-03 -1.915 0.055510
## FreeBreakfast1 -1.819e-02 4.599e-03 -3.956 7.65e-05
## IsTourist1 2.226e-01 1.808e-02 12.311 < 2e-16
## IsWeekend1 4.813e-02 4.395e-03 10.950 < 2e-16
## IsMarriott1 7.932e-01 2.950e-02 26.888 < 2e-16
## MedianHomeValue 1.987e-07 1.724e-08 11.526 < 2e-16
## MedianHouseHoldIncome -1.138e-06 1.306e-07 -8.713 < 2e-16
## CityNameAnaheim -5.070e-01 1.858e-02 -27.295 < 2e-16
## CityNameArlington 1.176e-01 2.028e-02 5.797 6.86e-09
## CityNameAsheville 1.763e-02 1.521e-02 1.159 0.246324
## CityNameBaltimore -4.148e-01 2.002e-02 -20.716 < 2e-16
## CityNameBoston -5.703e-01 1.784e-02 -31.967 < 2e-16
## CityNameBuffalo 1.668e-01 1.878e-02 8.882 < 2e-16
## CityNameChicago -6.929e-01 2.054e-02 -33.733 < 2e-16
## CityNameCleveland 1.673e-01 1.771e-02 9.448 < 2e-16
## CityNameColumbus 1.074e-01 1.785e-02 6.013 1.86e-09
## CityNameFresno 9.982e-02 1.752e-02 5.699 1.22e-08
## CityNameHouston 2.075e-01 2.038e-02 10.184 < 2e-16
## CityNameJacksonville 3.149e-01 1.826e-02 17.249 < 2e-16
## CityNameKansas City 1.228e-01 1.792e-02 6.855 7.37e-12
## CityNameLake Tahoe -8.067e-01 1.908e-02 -42.268 < 2e-16
## CityNameLas Vegas -2.846e-01 2.077e-02 -13.704 < 2e-16
## CityNameLos Angeles -4.283e-01 1.764e-02 -24.279 < 2e-16
## CityNameLouisville -4.665e-01 1.971e-02 -23.664 < 2e-16
## CityNameMaui 2.410e-01 1.431e-02 16.842 < 2e-16
## CityNameMemphis 2.006e-03 2.110e-02 0.095 0.924257
## CityNameMilwaukee 1.442e-01 1.839e-02 7.843 4.67e-15
## CityNameNashville 3.273e-01 1.936e-02 16.905 < 2e-16
## CityNameNew Orleans 3.229e-04 1.704e-02 0.019 0.984880
## CityNameNew York City 1.397e-01 1.397e-02 9.996 < 2e-16
## CityNameNiagara Falls -2.800e-01 1.833e-02 -15.278 < 2e-16
## CityNamePhiladelphia -5.258e-01 1.851e-02 -28.415 < 2e-16
## CityNamePhoenix 3.300e-01 2.074e-02 15.913 < 2e-16
## CityNameSan Antonio 1.494e-01 2.405e-02 6.211 5.39e-10
## CityNameSan Francisco -7.376e-01 2.166e-02 -34.058 < 2e-16
## CityNameSan Jose 4.405e-01 2.035e-02 21.645 < 2e-16
## CityNameSeattle NA NA NA NA
## CityNameSt. Louis -3.267e-01 2.175e-02 -15.024 < 2e-16
## CityNameTampa 2.646e-01 1.865e-02 14.186 < 2e-16
## CityNameTucson 2.261e-02 2.029e-02 1.114 0.265267
## HotelCapacity:IsMarriott1 1.604e-04 4.459e-05 3.598 0.000321
## HasSwimmingPool1:IsMarriott1 -6.893e-02 1.765e-02 -3.906 9.41e-05
## FreeBreakfast1:IsMarriott1 -7.542e-02 1.578e-02 -4.778 1.78e-06
## IsTourist1:IsMarriott1 -6.232e-02 2.402e-02 -2.595 0.009480
## IsWeekend1:IsMarriott1 -1.289e-01 1.553e-02 -8.295 < 2e-16
## IsMarriott1:MedianHomeValue 6.201e-07 6.016e-08 10.306 < 2e-16
## IsMarriott1:MedianHouseHoldIncome -1.558e-06 3.949e-07 -3.946 7.99e-05
## MaxRentUSD:IsMarriott1 -2.221e-03 3.366e-05 -65.975 < 2e-16
## GuestRating:IsMarriott1 -4.087e-02 3.911e-03 -10.451 < 2e-16
##
## (Intercept) ***
## HotelCapacity ***
## MaxRentUSD ***
## GuestRating ***
## HasSwimmingPool1 .
## FreeBreakfast1 ***
## IsTourist1 ***
## IsWeekend1 ***
## IsMarriott1 ***
## MedianHomeValue ***
## MedianHouseHoldIncome ***
## CityNameAnaheim ***
## CityNameArlington ***
## CityNameAsheville
## CityNameBaltimore ***
## CityNameBoston ***
## CityNameBuffalo ***
## CityNameChicago ***
## CityNameCleveland ***
## CityNameColumbus ***
## CityNameFresno ***
## CityNameHouston ***
## CityNameJacksonville ***
## CityNameKansas City ***
## CityNameLake Tahoe ***
## CityNameLas Vegas ***
## CityNameLos Angeles ***
## CityNameLouisville ***
## CityNameMaui ***
## CityNameMemphis
## CityNameMilwaukee ***
## CityNameNashville ***
## CityNameNew Orleans
## CityNameNew York City ***
## CityNameNiagara Falls ***
## CityNamePhiladelphia ***
## CityNamePhoenix ***
## CityNameSan Antonio ***
## CityNameSan Francisco ***
## CityNameSan Jose ***
## CityNameSeattle
## CityNameSt. Louis ***
## CityNameTampa ***
## CityNameTucson
## HotelCapacity:IsMarriott1 ***
## HasSwimmingPool1:IsMarriott1 ***
## FreeBreakfast1:IsMarriott1 ***
## IsTourist1:IsMarriott1 **
## IsWeekend1:IsMarriott1 ***
## IsMarriott1:MedianHomeValue ***
## IsMarriott1:MedianHouseHoldIncome ***
## MaxRentUSD:IsMarriott1 ***
## GuestRating:IsMarriott1 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.705 on 16978 degrees of freedom
## Multiple R-squared: 0.7786, Adjusted R-squared: 0.7779
## F-statistic: 1171 on 51 and 16978 DF, p-value: < 2.2e-16#FGLSEstandSE = coef(summary(fGLS))[, c("Estimate","Std. Error","Pr(>|t|)")]
#library(data.table)
#dt <- data.table(FGLSEstandSE)
#write.csv(dt, file = "FGLSEstimatesAllcities.csv")Step wise Regression(Backward Regression)
log-linear (without interactions)
library(MASS)
Model1 <- log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast + IsTourist + Available + IsMarriott+ MedianHomeValue + MedianHouseHoldIncome + CityName + IsMarriottOrHilton + GuestRating + MaxRentUSD
fit1<- lm(Model1, data = BMHotelsData.df)
summary(fit1)##
## Call:
## lm(formula = Model1, data = BMHotelsData.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2389 -0.2187 -0.0136 0.2030 4.6902
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.671e+00 2.384e-02 153.977 < 2e-16 ***
## HotelCapacity 2.001e-04 1.099e-05 18.206 < 2e-16 ***
## HasSwimmingPool1 -2.446e-02 6.442e-03 -3.797 0.000147 ***
## FreeBreakfast1 -7.082e-02 5.904e-03 -11.995 < 2e-16 ***
## IsTourist1 2.667e-01 2.228e-02 11.974 < 2e-16 ***
## Available1 -3.017e-01 1.100e-02 -27.423 < 2e-16 ***
## IsMarriott1 9.424e-03 1.342e-02 0.702 0.482550
## MedianHomeValue 5.770e-07 2.413e-08 23.907 < 2e-16 ***
## MedianHouseHoldIncome -2.296e-06 1.724e-07 -13.320 < 2e-16 ***
## CityNameAnaheim -8.675e-01 2.510e-02 -34.563 < 2e-16 ***
## CityNameArlington 2.086e-01 2.206e-02 9.456 < 2e-16 ***
## CityNameAsheville -3.032e-02 2.280e-02 -1.330 0.183577
## CityNameBaltimore -7.713e-01 2.595e-02 -29.721 < 2e-16 ***
## CityNameBoston -9.113e-01 2.730e-02 -33.387 < 2e-16 ***
## CityNameBuffalo 1.797e-01 2.140e-02 8.394 < 2e-16 ***
## CityNameChicago -1.008e+00 2.717e-02 -37.123 < 2e-16 ***
## CityNameCleveland 1.911e-01 2.186e-02 8.742 < 2e-16 ***
## CityNameColumbus 1.036e-01 2.196e-02 4.717 2.41e-06 ***
## CityNameFresno 1.148e-01 2.177e-02 5.273 1.36e-07 ***
## CityNameHouston 2.398e-01 2.225e-02 10.781 < 2e-16 ***
## CityNameJacksonville 3.758e-01 2.205e-02 17.044 < 2e-16 ***
## CityNameKansas City 1.640e-01 2.018e-02 8.128 4.67e-16 ***
## CityNameLake Tahoe -1.160e+00 2.511e-02 -46.191 < 2e-16 ***
## CityNameLas Vegas -3.672e-01 2.319e-02 -15.832 < 2e-16 ***
## CityNameLos Angeles -7.535e-01 2.625e-02 -28.699 < 2e-16 ***
## CityNameLouisville -7.665e-01 2.539e-02 -30.188 < 2e-16 ***
## CityNameMaui 4.461e-01 2.263e-02 19.716 < 2e-16 ***
## CityNameMemphis -4.515e-02 2.233e-02 -2.022 0.043240 *
## CityNameMilwaukee 1.678e-01 2.210e-02 7.594 3.27e-14 ***
## CityNameNashville 5.039e-01 2.168e-02 23.240 < 2e-16 ***
## CityNameNew Orleans -3.116e-02 2.197e-02 -1.418 0.156207
## CityNameNew York City 3.041e-01 2.176e-02 13.975 < 2e-16 ***
## CityNameNiagara Falls -3.119e-01 2.279e-02 -13.685 < 2e-16 ***
## CityNamePhiladelphia -8.657e-01 2.746e-02 -31.531 < 2e-16 ***
## CityNamePhoenix 5.146e-01 2.203e-02 23.361 < 2e-16 ***
## CityNameSan Antonio 3.049e-01 2.174e-02 14.026 < 2e-16 ***
## CityNameSan Francisco -1.239e+00 3.057e-02 -40.518 < 2e-16 ***
## CityNameSan Jose 5.321e-01 2.284e-02 23.301 < 2e-16 ***
## CityNameSeattle NA NA NA NA
## CityNameSt. Louis -7.524e-01 2.719e-02 -27.666 < 2e-16 ***
## CityNameTampa 3.608e-01 2.175e-02 16.592 < 2e-16 ***
## CityNameTucson 1.173e-02 2.218e-02 0.529 0.596864
## IsMarriottOrHilton1 1.092e-01 1.189e-02 9.185 < 2e-16 ***
## GuestRating 2.384e-01 3.441e-03 69.294 < 2e-16 ***
## MaxRentUSD 8.164e-04 9.832e-06 83.030 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3403 on 16986 degrees of freedom
## Multiple R-squared: 0.6834, Adjusted R-squared: 0.6826
## F-statistic: 852.6 on 43 and 16986 DF, p-value: < 2.2e-16stepAIC(fit1,direction="backward")## Start: AIC=-36673.35
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## IsTourist + Available + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + IsMarriottOrHilton + GuestRating + MaxRentUSD
##
##
## Step: AIC=-36673.35
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## Available + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + IsMarriottOrHilton + GuestRating + MaxRentUSD
##
## Df Sum of Sq RSS AIC
## - IsMarriott 1 0.06 1966.8 -36675
## <none> 1966.7 -36673
## - HasSwimmingPool 1 1.67 1968.4 -36661
## - IsMarriottOrHilton 1 9.77 1976.5 -36591
## - FreeBreakfast 1 16.66 1983.3 -36532
## - MedianHouseHoldIncome 1 20.54 1987.2 -36498
## - HotelCapacity 1 38.38 2005.1 -36346
## - MedianHomeValue 1 66.17 2032.9 -36112
## - Available 1 87.07 2053.8 -35938
## - GuestRating 1 555.95 2522.6 -32436
## - MaxRentUSD 1 798.20 2764.9 -30874
## - CityName 33 1052.08 3018.8 -29442
##
## Step: AIC=-36674.85
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## Available + MedianHomeValue + MedianHouseHoldIncome + CityName +
## IsMarriottOrHilton + GuestRating + MaxRentUSD
##
## Df Sum of Sq RSS AIC
## <none> 1966.8 -36675
## - HasSwimmingPool 1 1.70 1968.5 -36662
## - FreeBreakfast 1 16.73 1983.5 -36533
## - MedianHouseHoldIncome 1 20.50 1987.2 -36500
## - IsMarriottOrHilton 1 21.43 1988.2 -36492
## - HotelCapacity 1 38.48 2005.2 -36347
## - MedianHomeValue 1 66.15 2032.9 -36114
## - Available 1 87.17 2053.9 -35938
## - GuestRating 1 555.92 2522.7 -32438
## - MaxRentUSD 1 802.58 2769.3 -30849
## - CityName 33 1056.74 3023.5 -29417##
## Call:
## lm(formula = log(RentUSD) ~ HotelCapacity + HasSwimmingPool +
## FreeBreakfast + Available + MedianHomeValue + MedianHouseHoldIncome +
## CityName + IsMarriottOrHilton + GuestRating + MaxRentUSD,
## data = BMHotelsData.df)
##
## Coefficients:
## (Intercept) HotelCapacity HasSwimmingPool1
## 3.671e+00 2.003e-04 -2.466e-02
## FreeBreakfast1 Available1 MedianHomeValue
## -7.095e-02 -3.018e-01 5.768e-07
## MedianHouseHoldIncome CityNameAnaheim CityNameArlington
## -2.292e-06 -6.005e-01 2.088e-01
## CityNameAsheville CityNameBaltimore CityNameBoston
## 2.363e-01 -7.712e-01 -6.446e-01
## CityNameBuffalo CityNameChicago CityNameCleveland
## 1.794e-01 -7.418e-01 1.912e-01
## CityNameColumbus CityNameFresno CityNameHouston
## 1.039e-01 1.148e-01 2.403e-01
## CityNameJacksonville CityNameKansas City CityNameLake Tahoe
## 3.755e-01 1.644e-01 -8.928e-01
## CityNameLas Vegas CityNameLos Angeles CityNameLouisville
## -1.006e-01 -4.864e-01 -7.666e-01
## CityNameMaui CityNameMemphis CityNameMilwaukee
## 7.133e-01 -4.522e-02 1.682e-01
## CityNameNashville CityNameNew Orleans CityNameNew York City
## 5.039e-01 2.360e-01 5.706e-01
## CityNameNiagara Falls CityNamePhiladelphia CityNamePhoenix
## -4.486e-02 -5.989e-01 5.152e-01
## CityNameSan Antonio CityNameSan Francisco CityNameSan Jose
## 3.050e-01 -9.717e-01 5.323e-01
## CityNameSeattle CityNameSt. Louis CityNameTampa
## 2.668e-01 -7.564e-01 3.625e-01
## CityNameTucson IsMarriottOrHilton1 GuestRating
## 1.197e-02 1.150e-01 2.384e-01
## MaxRentUSD
## 8.168e-04Model with lower AIC - log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast + Available + MedianHomeValue + MedianHouseHoldIncome + CityName + IsMarriottOrHilton + GuestRating + MaxRentUSD
fgls of above
# Step 1: Find lnOLSressq i.e. the Log of the Square of the OLS Residuals
OLSres <- resid(fit1)
OLSressq <- OLSres^2 # Square residuals
lnOLSressq <- log(OLSressq) # Take natural log of squared residuals
MOdela<-lnOLSressq ~ HotelCapacity + HasSwimmingPool + FreeBreakfast + IsTourist + Available + IsMarriott+ MedianHomeValue + MedianHouseHoldIncome + CityName + IsMarriottOrHilton + GuestRating + MaxRentUSD
#Auxillary Model
# Step 2: Auxillary Model -- Regress lnOLSressq on the x variables
aux <- lm(MOdela, data = BMHotelsData.df) # Run auxillary model
# Step 3a: Calculate ghat i.e. the fitted values of the Auxillary Model
ghat <- fitted(aux) # Predict g^
# Step 3b: Calculate hhat = exp(ghat)
hhat <- exp(ghat) # Create h^
# Step 4: Implement FGLS by running the regression with weights equal to 1/hhat
fGLS1 <- lm(Model1 , weights = 1/hhat,data = BMHotelsData.df) # Weight is 1/h^
summary(fGLS1)##
## Call:
## lm(formula = Model1, data = BMHotelsData.df, weights = 1/hhat)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -14.234 -1.018 0.051 1.088 33.636
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.712e+00 2.068e-02 179.475 < 2e-16 ***
## HotelCapacity 9.379e-05 1.137e-05 8.248 < 2e-16 ***
## HasSwimmingPool1 -1.815e-02 4.958e-03 -3.661 0.000252 ***
## FreeBreakfast1 -2.375e-02 4.556e-03 -5.212 1.89e-07 ***
## IsTourist1 2.332e-01 1.898e-02 12.284 < 2e-16 ***
## Available1 -2.443e-01 9.213e-03 -26.517 < 2e-16 ***
## IsMarriott1 -2.127e-02 8.978e-03 -2.369 0.017830 *
## MedianHomeValue 2.745e-07 1.873e-08 14.661 < 2e-16 ***
## MedianHouseHoldIncome -1.466e-06 1.307e-07 -11.215 < 2e-16 ***
## CityNameAnaheim -5.707e-01 1.835e-02 -31.092 < 2e-16 ***
## CityNameArlington 1.169e-01 1.988e-02 5.882 4.13e-09 ***
## CityNameAsheville -9.119e-02 1.689e-02 -5.399 6.78e-08 ***
## CityNameBaltimore -4.383e-01 1.989e-02 -22.037 < 2e-16 ***
## CityNameBoston -6.154e-01 1.867e-02 -32.971 < 2e-16 ***
## CityNameBuffalo 1.703e-01 1.891e-02 9.007 < 2e-16 ***
## CityNameChicago -7.387e-01 2.215e-02 -33.349 < 2e-16 ***
## CityNameCleveland 1.763e-01 1.768e-02 9.970 < 2e-16 ***
## CityNameColumbus 1.173e-01 1.763e-02 6.650 3.01e-11 ***
## CityNameFresno 1.065e-01 1.810e-02 5.882 4.14e-09 ***
## CityNameHouston 2.342e-01 2.035e-02 11.508 < 2e-16 ***
## CityNameJacksonville 3.182e-01 1.802e-02 17.661 < 2e-16 ***
## CityNameKansas City 1.527e-01 1.829e-02 8.346 < 2e-16 ***
## CityNameLake Tahoe -8.556e-01 1.956e-02 -43.750 < 2e-16 ***
## CityNameLas Vegas -3.174e-01 1.959e-02 -16.201 < 2e-16 ***
## CityNameLos Angeles -4.940e-01 1.876e-02 -26.335 < 2e-16 ***
## CityNameLouisville -5.312e-01 2.054e-02 -25.857 < 2e-16 ***
## CityNameMaui 2.409e-01 1.713e-02 14.065 < 2e-16 ***
## CityNameMemphis 3.860e-02 2.167e-02 1.781 0.074911 .
## CityNameMilwaukee 1.600e-01 1.818e-02 8.799 < 2e-16 ***
## CityNameNashville 3.731e-01 2.175e-02 17.154 < 2e-16 ***
## CityNameNew Orleans -2.158e-02 1.734e-02 -1.244 0.213367
## CityNameNew York City 1.111e-01 1.823e-02 6.095 1.12e-09 ***
## CityNameNiagara Falls -2.699e-01 1.876e-02 -14.384 < 2e-16 ***
## CityNamePhiladelphia -5.765e-01 2.024e-02 -28.476 < 2e-16 ***
## CityNamePhoenix 3.629e-01 2.066e-02 17.562 < 2e-16 ***
## CityNameSan Antonio 1.682e-01 2.411e-02 6.978 3.11e-12 ***
## CityNameSan Francisco -8.245e-01 2.341e-02 -35.221 < 2e-16 ***
## CityNameSan Jose 4.471e-01 2.073e-02 21.565 < 2e-16 ***
## CityNameSeattle NA NA NA NA
## CityNameSt. Louis -4.652e-01 2.144e-02 -21.700 < 2e-16 ***
## CityNameTampa 2.768e-01 1.854e-02 14.929 < 2e-16 ***
## CityNameTucson 2.852e-02 2.182e-02 1.307 0.191156
## IsMarriottOrHilton1 1.049e-01 7.630e-03 13.744 < 2e-16 ***
## GuestRating 1.636e-01 2.623e-03 62.360 < 2e-16 ***
## MaxRentUSD 2.405e-03 2.201e-05 109.231 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.645 on 16986 degrees of freedom
## Multiple R-squared: 0.7629, Adjusted R-squared: 0.7623
## F-statistic: 1271 on 43 and 16986 DF, p-value: < 2.2e-16#FGLSEstandSE = coef(summary(fGLS))[, c("Estimate","Std. Error","Pr(>|t|)")]
#library(data.table)
#dt <- data.table(FGLSEstandSE)
#write.csv(dt, file = "FGLSEstimatesAllcities.csv")
stepAIC(fGLS1,direction="backward")## Start: AIC=17005.44
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## IsTourist + Available + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + IsMarriottOrHilton + GuestRating + MaxRentUSD
##
##
## Step: AIC=17005.44
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## Available + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + IsMarriottOrHilton + GuestRating + MaxRentUSD
##
## Df Sum of Sq RSS AIC
## <none> 45987 17005
## - IsMarriott 1 15 46003 17009
## - HasSwimmingPool 1 36 46024 17017
## - FreeBreakfast 1 74 46061 17031
## - HotelCapacity 1 184 46172 17072
## - MedianHouseHoldIncome 1 341 46328 17129
## - IsMarriottOrHilton 1 511 46499 17192
## - MedianHomeValue 1 582 46569 17218
## - Available 1 1904 47891 17694
## - GuestRating 1 10528 56516 20514
## - CityName 33 17387 63374 22401
## - MaxRentUSD 1 32303 78290 26064##
## Call:
## lm(formula = log(RentUSD) ~ HotelCapacity + HasSwimmingPool +
## FreeBreakfast + Available + IsMarriott + MedianHomeValue +
## MedianHouseHoldIncome + CityName + IsMarriottOrHilton + GuestRating +
## MaxRentUSD, data = BMHotelsData.df, weights = 1/hhat)
##
## Coefficients:
## (Intercept) HotelCapacity HasSwimmingPool1
## 3.712e+00 9.379e-05 -1.815e-02
## FreeBreakfast1 Available1 IsMarriott1
## -2.375e-02 -2.443e-01 -2.127e-02
## MedianHomeValue MedianHouseHoldIncome CityNameAnaheim
## 2.745e-07 -1.466e-06 -3.375e-01
## CityNameArlington CityNameAsheville CityNameBaltimore
## 1.169e-01 1.420e-01 -4.383e-01
## CityNameBoston CityNameBuffalo CityNameChicago
## -3.823e-01 1.703e-01 -5.056e-01
## CityNameCleveland CityNameColumbus CityNameFresno
## 1.763e-01 1.173e-01 1.065e-01
## CityNameHouston CityNameJacksonville CityNameKansas City
## 2.342e-01 3.182e-01 1.527e-01
## CityNameLake Tahoe CityNameLas Vegas CityNameLos Angeles
## -6.224e-01 -8.427e-02 -2.609e-01
## CityNameLouisville CityNameMaui CityNameMemphis
## -5.312e-01 4.740e-01 3.860e-02
## CityNameMilwaukee CityNameNashville CityNameNew Orleans
## 1.600e-01 3.731e-01 2.116e-01
## CityNameNew York City CityNameNiagara Falls CityNamePhiladelphia
## 3.442e-01 -3.672e-02 -3.433e-01
## CityNamePhoenix CityNameSan Antonio CityNameSan Francisco
## 3.629e-01 1.682e-01 -5.913e-01
## CityNameSan Jose CityNameSeattle CityNameSt. Louis
## 4.471e-01 2.332e-01 -4.652e-01
## CityNameTampa CityNameTucson IsMarriottOrHilton1
## 2.768e-01 2.852e-02 1.049e-01
## GuestRating MaxRentUSD
## 1.636e-01 2.405e-03Model with lower AIC - log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast + Available + IsMarriott + MedianHomeValue + MedianHouseHoldIncome + CityName + IsMarriottOrHilton + GuestRating + MaxRentUSD
log linear (With Interaction- IsMariott)
Model2<-log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast + IsTourist + IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome + CityName + MaxRentUSD + GuestRating + IsMarriott*HotelCapacity + IsMarriott*HasSwimmingPool + IsMarriott*FreeBreakfast + IsMarriott*IsTourist + IsMarriott*IsWeekend + IsMarriott*MedianHomeValue + IsMarriott*MedianHouseHoldIncome + IsMarriott*CityName + IsMarriott*MaxRentUSD + IsMarriott*GuestRating
fit2<- lm(Model2, data = BMHotelsData.df)
stepAIC(fit2,direction="backward")## Start: AIC=-38867.95
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## IsTourist + IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + MaxRentUSD + GuestRating + IsMarriott * HotelCapacity +
## IsMarriott * HasSwimmingPool + IsMarriott * FreeBreakfast +
## IsMarriott * IsTourist + IsMarriott * IsWeekend + IsMarriott *
## MedianHomeValue + IsMarriott * MedianHouseHoldIncome + IsMarriott *
## CityName + IsMarriott * MaxRentUSD + IsMarriott * GuestRating
##
##
## Step: AIC=-38867.95
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## IsTourist + IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + MaxRentUSD + GuestRating + HotelCapacity:IsMarriott +
## HasSwimmingPool:IsMarriott + FreeBreakfast:IsMarriott + IsWeekend:IsMarriott +
## IsMarriott:MedianHomeValue + IsMarriott:MedianHouseHoldIncome +
## IsMarriott:CityName + IsMarriott:MaxRentUSD + IsMarriott:GuestRating
##
##
## Step: AIC=-38867.95
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + MaxRentUSD + GuestRating + HotelCapacity:IsMarriott +
## HasSwimmingPool:IsMarriott + FreeBreakfast:IsMarriott + IsWeekend:IsMarriott +
## IsMarriott:MedianHomeValue + IsMarriott:MedianHouseHoldIncome +
## IsMarriott:CityName + IsMarriott:MaxRentUSD + IsMarriott:GuestRating
##
## Df Sum of Sq RSS AIC
## - HotelCapacity:IsMarriott 1 0.040 1721.5 -38870
## <none> 1721.4 -38868
## - IsMarriott:GuestRating 1 0.559 1722.0 -38864
## - FreeBreakfast:IsMarriott 1 0.657 1722.1 -38863
## - IsMarriott:MedianHouseHoldIncome 1 0.771 1722.2 -38862
## - HasSwimmingPool:IsMarriott 1 0.879 1722.3 -38861
## - IsMarriott:MedianHomeValue 1 3.261 1724.7 -38838
## - IsWeekend:IsMarriott 1 6.492 1727.9 -38806
## - IsMarriott:CityName 30 16.334 1737.7 -38767
## - IsMarriott:MaxRentUSD 1 258.622 1980.0 -36486
##
## Step: AIC=-38869.56
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + MaxRentUSD + GuestRating + HasSwimmingPool:IsMarriott +
## FreeBreakfast:IsMarriott + IsWeekend:IsMarriott + IsMarriott:MedianHomeValue +
## IsMarriott:MedianHouseHoldIncome + IsMarriott:CityName +
## IsMarriott:MaxRentUSD + IsMarriott:GuestRating
##
## Df Sum of Sq RSS AIC
## <none> 1721.5 -38870
## - IsMarriott:GuestRating 1 0.547 1722.0 -38866
## - IsMarriott:MedianHouseHoldIncome 1 0.776 1722.2 -38864
## - FreeBreakfast:IsMarriott 1 0.815 1722.3 -38863
## - HasSwimmingPool:IsMarriott 1 0.897 1722.3 -38863
## - IsMarriott:MedianHomeValue 1 3.339 1724.8 -38839
## - IsWeekend:IsMarriott 1 6.493 1727.9 -38807
## - IsMarriott:CityName 30 16.404 1737.8 -38768
## - HotelCapacity 1 30.073 1751.5 -38577
## - IsMarriott:MaxRentUSD 1 258.638 1980.1 -36488##
## Call:
## lm(formula = log(RentUSD) ~ HotelCapacity + HasSwimmingPool +
## FreeBreakfast + IsWeekend + IsMarriott + MedianHomeValue +
## MedianHouseHoldIncome + CityName + MaxRentUSD + GuestRating +
## HasSwimmingPool:IsMarriott + FreeBreakfast:IsMarriott + IsWeekend:IsMarriott +
## IsMarriott:MedianHomeValue + IsMarriott:MedianHouseHoldIncome +
## IsMarriott:CityName + IsMarriott:MaxRentUSD + IsMarriott:GuestRating,
## data = BMHotelsData.df)
##
## Coefficients:
## (Intercept) HotelCapacity
## 3.397e+00 1.809e-04
## HasSwimmingPool1 FreeBreakfast1
## -1.238e-02 -4.764e-02
## IsWeekend1 IsMarriott1
## 6.851e-02 7.491e-01
## MedianHomeValue MedianHouseHoldIncome
## 3.391e-07 -1.341e-06
## CityNameAnaheim CityNameArlington
## -4.742e-01 1.556e-01
## CityNameAsheville CityNameBaltimore
## 3.233e-01 -6.092e-01
## CityNameBoston CityNameBuffalo
## -5.160e-01 1.571e-01
## CityNameChicago CityNameCleveland
## -6.403e-01 1.587e-01
## CityNameColumbus CityNameFresno
## 6.956e-02 8.135e-02
## CityNameHouston CityNameJacksonville
## 2.160e-01 3.499e-01
## CityNameKansas City CityNameLake Tahoe
## 1.262e-01 -7.914e-01
## CityNameLas Vegas CityNameLos Angeles
## -1.351e-01 -3.388e-01
## CityNameLouisville CityNameMaui
## -6.559e-01 5.844e-01
## CityNameMemphis CityNameMilwaukee
## -3.481e-02 1.360e-01
## CityNameNashville CityNameNew Orleans
## 4.230e-01 2.718e-01
## CityNameNew York City CityNameNiagara Falls
## 4.126e-01 -6.313e-02
## CityNamePhiladelphia CityNamePhoenix
## -4.787e-01 4.665e-01
## CityNameSan Antonio CityNameSan Francisco
## 2.485e-01 -7.389e-01
## CityNameSan Jose CityNameSeattle
## 5.030e-01 2.617e-01
## CityNameSt. Louis CityNameTampa
## -5.542e-01 2.740e-01
## CityNameTucson MaxRentUSD
## -8.130e-03 1.545e-03
## GuestRating HasSwimmingPool1:IsMarriott1
## 2.067e-01 -8.421e-02
## FreeBreakfast1:IsMarriott1 IsWeekend1:IsMarriott1
## -6.566e-02 -1.481e-01
## IsMarriott1:MedianHomeValue IsMarriott1:MedianHouseHoldIncome
## 5.682e-07 -1.804e-06
## IsMarriott1:CityNameAnaheim IsMarriott1:CityNameArlington
## 2.482e-02 5.305e-02
## IsMarriott1:CityNameAsheville IsMarriott1:CityNameBaltimore
## -1.676e-01 -1.670e-01
## IsMarriott1:CityNameBoston IsMarriott1:CityNameBuffalo
## -8.843e-02 NA
## IsMarriott1:CityNameChicago IsMarriott1:CityNameCleveland
## -8.976e-02 -7.071e-02
## IsMarriott1:CityNameColumbus IsMarriott1:CityNameFresno
## -1.161e-01 1.273e-01
## IsMarriott1:CityNameHouston IsMarriott1:CityNameJacksonville
## -2.008e-01 -8.441e-02
## IsMarriott1:CityNameKansas City IsMarriott1:CityNameLake Tahoe
## -9.893e-02 NA
## IsMarriott1:CityNameLas Vegas IsMarriott1:CityNameLos Angeles
## 1.332e-01 -2.265e-01
## IsMarriott1:CityNameLouisville IsMarriott1:CityNameMaui
## -6.302e-02 -3.831e-02
## IsMarriott1:CityNameMemphis IsMarriott1:CityNameMilwaukee
## -4.405e-02 -6.387e-02
## IsMarriott1:CityNameNashville IsMarriott1:CityNameNew Orleans
## 1.897e-01 -3.583e-01
## IsMarriott1:CityNameNew York City IsMarriott1:CityNameNiagara Falls
## -1.608e-01 -1.707e-01
## IsMarriott1:CityNamePhiladelphia IsMarriott1:CityNamePhoenix
## -2.255e-01 -2.173e-01
## IsMarriott1:CityNameSan Antonio IsMarriott1:CityNameSan Francisco
## 8.221e-02 -2.187e-01
## IsMarriott1:CityNameSan Jose IsMarriott1:CityNameSeattle
## -7.678e-02 NA
## IsMarriott1:CityNameSt. Louis IsMarriott1:CityNameTampa
## -1.404e-02 1.461e-01
## IsMarriott1:CityNameTucson IsMarriott1:MaxRentUSD
## 9.418e-02 -1.033e-03
## IsMarriott1:GuestRating
## -4.649e-02** MODEL with lower AIC**- log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast + IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome + CityName + MaxRentUSD + GuestRating + HasSwimmingPool:IsMarriott + FreeBreakfast:IsMarriott + IsWeekend:IsMarriott + IsMarriott:MedianHomeValue + IsMarriott:MedianHouseHoldIncome + IsMarriott:CityName + IsMarriott:MaxRentUSD + IsMarriott:GuestRating
FGLS
# Step 1: Find lnOLSressq i.e. the Log of the Square of the OLS Residuals
OLSres <- resid(fit2)
OLSressq <- OLSres^2 # Square residuals
lnOLSressq <- log(OLSressq) # Take natural log of squared residuals
MOdelB<-lnOLSressq ~ HotelCapacity + HasSwimmingPool + FreeBreakfast + IsTourist + IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome + CityName + MaxRentUSD + GuestRating + IsMarriott*HotelCapacity + IsMarriott*HasSwimmingPool + IsMarriott*FreeBreakfast + IsMarriott*IsTourist + IsMarriott*IsWeekend + IsMarriott*MedianHomeValue + IsMarriott*MedianHouseHoldIncome + IsMarriott*CityName + IsMarriott*MaxRentUSD + IsMarriott*GuestRating
#Auxillary Model
# Step 2: Auxillary Model -- Regress lnOLSressq on the x variables
aux <- lm(MOdelB, data = BMHotelsData.df) # Run auxillary model
# Step 3a: Calculate ghat i.e. the fitted values of the Auxillary Model
ghat <- fitted(aux) # Predict g^
# Step 3b: Calculate hhat = exp(ghat)
hhat <- exp(ghat) # Create h^
# Step 4: Implement FGLS by running the regression with weights equal to 1/hhat
fGLS2 <- lm(Model2 , weights = 1/hhat,data = BMHotelsData.df) # Weight is 1/h^
summary(fGLS2)##
## Call:
## lm(formula = Model2, data = BMHotelsData.df, weights = 1/hhat)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -14.213 -1.094 0.039 1.174 35.336
##
## Coefficients: (5 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.443e+00 1.869e-02 184.229 < 2e-16
## HotelCapacity 9.394e-05 1.163e-05 8.078 7.01e-16
## HasSwimmingPool1 -4.466e-03 4.842e-03 -0.922 0.356330
## FreeBreakfast1 -1.989e-02 4.540e-03 -4.381 1.19e-05
## IsTourist1 2.233e-01 1.829e-02 12.212 < 2e-16
## IsWeekend1 4.708e-02 4.308e-03 10.930 < 2e-16
## IsMarriott1 7.526e-01 7.489e-02 10.048 < 2e-16
## MedianHomeValue 1.987e-07 1.739e-08 11.428 < 2e-16
## MedianHouseHoldIncome -1.177e-06 1.289e-07 -9.129 < 2e-16
## CityNameAnaheim -5.002e-01 1.850e-02 -27.036 < 2e-16
## CityNameArlington 1.043e-01 2.102e-02 4.963 7.00e-07
## CityNameAsheville 1.532e-02 1.548e-02 0.990 0.322415
## CityNameBaltimore -4.005e-01 2.039e-02 -19.643 < 2e-16
## CityNameBoston -5.628e-01 1.756e-02 -32.043 < 2e-16
## CityNameBuffalo 1.690e-01 1.910e-02 8.846 < 2e-16
## CityNameChicago -6.833e-01 2.051e-02 -33.317 < 2e-16
## CityNameCleveland 1.756e-01 1.812e-02 9.688 < 2e-16
## CityNameColumbus 1.106e-01 1.803e-02 6.135 8.68e-10
## CityNameFresno 9.632e-02 1.793e-02 5.372 7.90e-08
## CityNameHouston 2.227e-01 2.126e-02 10.474 < 2e-16
## CityNameJacksonville 3.128e-01 1.919e-02 16.297 < 2e-16
## CityNameKansas City 1.284e-01 1.902e-02 6.749 1.54e-11
## CityNameLake Tahoe -8.009e-01 1.891e-02 -42.359 < 2e-16
## CityNameLas Vegas -3.061e-01 2.234e-02 -13.703 < 2e-16
## CityNameLos Angeles -4.188e-01 1.749e-02 -23.945 < 2e-16
## CityNameLouisville -4.558e-01 2.022e-02 -22.540 < 2e-16
## CityNameMaui 2.178e-01 1.488e-02 14.643 < 2e-16
## CityNameMemphis 2.640e-03 2.181e-02 0.121 0.903662
## CityNameMilwaukee 1.478e-01 1.888e-02 7.827 5.27e-15
## CityNameNashville 3.189e-01 1.995e-02 15.983 < 2e-16
## CityNameNew Orleans 2.087e-02 1.650e-02 1.265 0.205883
## CityNameNew York City 1.565e-01 1.363e-02 11.482 < 2e-16
## CityNameNiagara Falls -2.766e-01 1.867e-02 -14.813 < 2e-16
## CityNamePhiladelphia -5.140e-01 1.852e-02 -27.748 < 2e-16
## CityNamePhoenix 3.489e-01 2.102e-02 16.602 < 2e-16
## CityNameSan Antonio 1.436e-01 2.422e-02 5.929 3.11e-09
## CityNameSan Francisco -7.249e-01 2.153e-02 -33.671 < 2e-16
## CityNameSan Jose 4.382e-01 2.044e-02 21.445 < 2e-16
## CityNameSeattle NA NA NA NA
## CityNameSt. Louis -3.272e-01 2.190e-02 -14.940 < 2e-16
## CityNameTampa 2.454e-01 1.844e-02 13.309 < 2e-16
## CityNameTucson 2.186e-02 2.065e-02 1.059 0.289771
## MaxRentUSD 2.917e-03 2.494e-05 116.962 < 2e-16
## GuestRating 1.504e-01 2.639e-03 56.992 < 2e-16
## HotelCapacity:IsMarriott1 2.683e-04 4.350e-05 6.168 7.08e-10
## HasSwimmingPool1:IsMarriott1 -2.096e-02 1.954e-02 -1.073 0.283455
## FreeBreakfast1:IsMarriott1 -2.717e-02 1.727e-02 -1.573 0.115768
## IsTourist1:IsMarriott1 -3.562e-01 1.257e-01 -2.834 0.004602
## IsWeekend1:IsMarriott1 -9.635e-02 1.300e-02 -7.411 1.31e-13
## IsMarriott1:MedianHomeValue 7.208e-07 7.634e-08 9.441 < 2e-16
## IsMarriott1:MedianHouseHoldIncome -3.628e-06 4.495e-07 -8.072 7.39e-16
## IsMarriott1:CityNameAnaheim 2.091e-01 1.447e-01 1.445 0.148507
## IsMarriott1:CityNameArlington 4.235e-02 6.212e-02 0.682 0.495464
## IsMarriott1:CityNameAsheville 2.724e-01 1.293e-01 2.107 0.035131
## IsMarriott1:CityNameBaltimore -1.831e-01 7.532e-02 -2.431 0.015080
## IsMarriott1:CityNameBoston 3.261e-01 1.169e-01 2.790 0.005276
## IsMarriott1:CityNameBuffalo NA NA NA NA
## IsMarriott1:CityNameChicago 2.842e-01 1.274e-01 2.230 0.025754
## IsMarriott1:CityNameCleveland -1.024e-01 3.851e-02 -2.660 0.007810
## IsMarriott1:CityNameColumbus -3.116e-02 9.088e-02 -0.343 0.731701
## IsMarriott1:CityNameFresno 7.040e-02 7.020e-02 1.003 0.315929
## IsMarriott1:CityNameHouston -2.082e-01 4.721e-02 -4.409 1.05e-05
## IsMarriott1:CityNameJacksonville -4.216e-02 3.967e-02 -1.063 0.287889
## IsMarriott1:CityNameKansas City -7.562e-02 3.886e-02 -1.946 0.051683
## IsMarriott1:CityNameLake Tahoe NA NA NA NA
## IsMarriott1:CityNameLas Vegas 4.402e-01 1.287e-01 3.420 0.000627
## IsMarriott1:CityNameLos Angeles 4.384e-02 9.889e-02 0.443 0.657554
## IsMarriott1:CityNameLouisville -2.028e-01 7.469e-02 -2.714 0.006644
## IsMarriott1:CityNameMaui 4.544e-01 1.168e-01 3.889 0.000101
## IsMarriott1:CityNameMemphis 4.674e-03 6.015e-02 0.078 0.938063
## IsMarriott1:CityNameMilwaukee -5.079e-02 4.560e-02 -1.114 0.265434
## IsMarriott1:CityNameNashville 2.491e-01 5.280e-02 4.717 2.41e-06
## IsMarriott1:CityNameNew Orleans 4.043e-02 1.254e-01 0.322 0.747209
## IsMarriott1:CityNameNew York City 1.829e-01 1.249e-01 1.465 0.143062
## IsMarriott1:CityNameNiagara Falls 1.389e-01 1.347e-01 1.031 0.302638
## IsMarriott1:CityNamePhiladelphia 9.806e-02 1.089e-01 0.901 0.367860
## IsMarriott1:CityNamePhoenix -1.741e-01 4.859e-02 -3.583 0.000340
## IsMarriott1:CityNameSan Antonio 1.136e-01 1.141e-01 0.996 0.319071
## IsMarriott1:CityNameSan Francisco NA NA NA NA
## IsMarriott1:CityNameSan Jose 4.594e-03 1.129e-01 0.041 0.967532
## IsMarriott1:CityNameSeattle NA NA NA NA
## IsMarriott1:CityNameSt. Louis -7.452e-02 8.506e-02 -0.876 0.381028
## IsMarriott1:CityNameTampa 1.016e-01 5.509e-02 1.844 0.065242
## IsMarriott1:CityNameTucson 8.702e-02 8.928e-02 0.975 0.329734
## IsMarriott1:MaxRentUSD -2.341e-03 3.113e-05 -75.211 < 2e-16
## IsMarriott1:GuestRating -1.565e-02 1.530e-02 -1.023 0.306268
##
## (Intercept) ***
## HotelCapacity ***
## HasSwimmingPool1
## FreeBreakfast1 ***
## IsTourist1 ***
## IsWeekend1 ***
## IsMarriott1 ***
## MedianHomeValue ***
## MedianHouseHoldIncome ***
## CityNameAnaheim ***
## CityNameArlington ***
## CityNameAsheville
## CityNameBaltimore ***
## CityNameBoston ***
## CityNameBuffalo ***
## CityNameChicago ***
## CityNameCleveland ***
## CityNameColumbus ***
## CityNameFresno ***
## CityNameHouston ***
## CityNameJacksonville ***
## CityNameKansas City ***
## CityNameLake Tahoe ***
## CityNameLas Vegas ***
## CityNameLos Angeles ***
## CityNameLouisville ***
## CityNameMaui ***
## CityNameMemphis
## CityNameMilwaukee ***
## CityNameNashville ***
## CityNameNew Orleans
## CityNameNew York City ***
## CityNameNiagara Falls ***
## CityNamePhiladelphia ***
## CityNamePhoenix ***
## CityNameSan Antonio ***
## CityNameSan Francisco ***
## CityNameSan Jose ***
## CityNameSeattle
## CityNameSt. Louis ***
## CityNameTampa ***
## CityNameTucson
## MaxRentUSD ***
## GuestRating ***
## HotelCapacity:IsMarriott1 ***
## HasSwimmingPool1:IsMarriott1
## FreeBreakfast1:IsMarriott1
## IsTourist1:IsMarriott1 **
## IsWeekend1:IsMarriott1 ***
## IsMarriott1:MedianHomeValue ***
## IsMarriott1:MedianHouseHoldIncome ***
## IsMarriott1:CityNameAnaheim
## IsMarriott1:CityNameArlington
## IsMarriott1:CityNameAsheville *
## IsMarriott1:CityNameBaltimore *
## IsMarriott1:CityNameBoston **
## IsMarriott1:CityNameBuffalo
## IsMarriott1:CityNameChicago *
## IsMarriott1:CityNameCleveland **
## IsMarriott1:CityNameColumbus
## IsMarriott1:CityNameFresno
## IsMarriott1:CityNameHouston ***
## IsMarriott1:CityNameJacksonville
## IsMarriott1:CityNameKansas City .
## IsMarriott1:CityNameLake Tahoe
## IsMarriott1:CityNameLas Vegas ***
## IsMarriott1:CityNameLos Angeles
## IsMarriott1:CityNameLouisville **
## IsMarriott1:CityNameMaui ***
## IsMarriott1:CityNameMemphis
## IsMarriott1:CityNameMilwaukee
## IsMarriott1:CityNameNashville ***
## IsMarriott1:CityNameNew Orleans
## IsMarriott1:CityNameNew York City
## IsMarriott1:CityNameNiagara Falls
## IsMarriott1:CityNamePhiladelphia
## IsMarriott1:CityNamePhoenix ***
## IsMarriott1:CityNameSan Antonio
## IsMarriott1:CityNameSan Francisco
## IsMarriott1:CityNameSan Jose
## IsMarriott1:CityNameSeattle
## IsMarriott1:CityNameSt. Louis
## IsMarriott1:CityNameTampa .
## IsMarriott1:CityNameTucson
## IsMarriott1:MaxRentUSD ***
## IsMarriott1:GuestRating
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.696 on 16949 degrees of freedom
## Multiple R-squared: 0.7849, Adjusted R-squared: 0.7839
## F-statistic: 773.2 on 80 and 16949 DF, p-value: < 2.2e-16#FGLSEstandSE = coef(summary(fGLS))[, c("Estimate","Std. Error","Pr(>|t|)")]
#library(data.table)
#dt <- data.table(FGLSEstandSE)
#write.csv(dt, file = "FGLSEstimatesAllcities.csv")
stepAIC(fGLS2,direction="backward")## Start: AIC=18064.93
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## IsTourist + IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + MaxRentUSD + GuestRating + IsMarriott * HotelCapacity +
## IsMarriott * HasSwimmingPool + IsMarriott * FreeBreakfast +
## IsMarriott * IsTourist + IsMarriott * IsWeekend + IsMarriott *
## MedianHomeValue + IsMarriott * MedianHouseHoldIncome + IsMarriott *
## CityName + IsMarriott * MaxRentUSD + IsMarriott * GuestRating
##
##
## Step: AIC=18064.93
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## IsTourist + IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + MaxRentUSD + GuestRating + HotelCapacity:IsMarriott +
## HasSwimmingPool:IsMarriott + FreeBreakfast:IsMarriott + IsWeekend:IsMarriott +
## IsMarriott:MedianHomeValue + IsMarriott:MedianHouseHoldIncome +
## IsMarriott:CityName + IsMarriott:MaxRentUSD + IsMarriott:GuestRating
##
##
## Step: AIC=18064.93
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + MaxRentUSD + GuestRating + HotelCapacity:IsMarriott +
## HasSwimmingPool:IsMarriott + FreeBreakfast:IsMarriott + IsWeekend:IsMarriott +
## IsMarriott:MedianHomeValue + IsMarriott:MedianHouseHoldIncome +
## IsMarriott:CityName + IsMarriott:MaxRentUSD + IsMarriott:GuestRating
##
## Df Sum of Sq RSS AIC
## - IsMarriott:GuestRating 1 3.0 48730 18064
## - HasSwimmingPool:IsMarriott 1 3.3 48730 18064
## <none> 48727 18065
## - FreeBreakfast:IsMarriott 1 7.1 48734 18065
## - HotelCapacity:IsMarriott 1 109.4 48836 18101
## - IsWeekend:IsMarriott 1 157.9 48885 18118
## - IsMarriott:MedianHouseHoldIncome 1 187.3 48914 18128
## - IsMarriott:MedianHomeValue 1 256.3 48983 18152
## - IsMarriott:CityName 30 760.1 49487 18269
## - IsMarriott:MaxRentUSD 1 16262.4 64990 22967
##
## Step: AIC=18063.98
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + MaxRentUSD + GuestRating + HotelCapacity:IsMarriott +
## HasSwimmingPool:IsMarriott + FreeBreakfast:IsMarriott + IsWeekend:IsMarriott +
## IsMarriott:MedianHomeValue + IsMarriott:MedianHouseHoldIncome +
## IsMarriott:CityName + IsMarriott:MaxRentUSD
##
## Df Sum of Sq RSS AIC
## - HasSwimmingPool:IsMarriott 1 3.4 48733 18063
## <none> 48730 18064
## - FreeBreakfast:IsMarriott 1 12.1 48742 18066
## - HotelCapacity:IsMarriott 1 108.6 48839 18100
## - IsWeekend:IsMarriott 1 157.9 48888 18117
## - IsMarriott:MedianHouseHoldIncome 1 185.4 48916 18127
## - IsMarriott:MedianHomeValue 1 253.3 48983 18150
## - IsMarriott:CityName 30 1586.7 50317 18550
## - GuestRating 1 9564.9 58295 21114
## - IsMarriott:MaxRentUSD 1 16498.4 65228 23028
##
## Step: AIC=18063.17
## log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast +
## IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome +
## CityName + MaxRentUSD + GuestRating + HotelCapacity:IsMarriott +
## FreeBreakfast:IsMarriott + IsWeekend:IsMarriott + IsMarriott:MedianHomeValue +
## IsMarriott:MedianHouseHoldIncome + IsMarriott:CityName +
## IsMarriott:MaxRentUSD
##
## Df Sum of Sq RSS AIC
## - HasSwimmingPool 1 4.2 48738 18063
## <none> 48733 18063
## - FreeBreakfast:IsMarriott 1 11.1 48745 18065
## - HotelCapacity:IsMarriott 1 109.1 48843 18099
## - IsWeekend:IsMarriott 1 157.9 48891 18116
## - IsMarriott:MedianHouseHoldIncome 1 232.8 48966 18142
## - IsMarriott:MedianHomeValue 1 272.0 49006 18156
## - IsMarriott:CityName 30 1612.2 50346 18557
## - GuestRating 1 9581.9 58315 21118
## - IsMarriott:MaxRentUSD 1 16503.7 65237 23028
##
## Step: AIC=18062.64
## log(RentUSD) ~ HotelCapacity + FreeBreakfast + IsWeekend + IsMarriott +
## MedianHomeValue + MedianHouseHoldIncome + CityName + MaxRentUSD +
## GuestRating + HotelCapacity:IsMarriott + FreeBreakfast:IsMarriott +
## IsWeekend:IsMarriott + IsMarriott:MedianHomeValue + IsMarriott:MedianHouseHoldIncome +
## IsMarriott:CityName + IsMarriott:MaxRentUSD
##
## Df Sum of Sq RSS AIC
## <none> 48738 18063
## - FreeBreakfast:IsMarriott 1 10.1 48748 18064
## - HotelCapacity:IsMarriott 1 111.8 48850 18100
## - IsWeekend:IsMarriott 1 157.9 48896 18116
## - IsMarriott:MedianHouseHoldIncome 1 238.2 48976 18144
## - IsMarriott:MedianHomeValue 1 273.7 49011 18156
## - IsMarriott:CityName 30 1643.8 50381 18568
## - GuestRating 1 9662.8 58400 21141
## - IsMarriott:MaxRentUSD 1 16522.4 65260 23032##
## Call:
## lm(formula = log(RentUSD) ~ HotelCapacity + FreeBreakfast + IsWeekend +
## IsMarriott + MedianHomeValue + MedianHouseHoldIncome + CityName +
## MaxRentUSD + GuestRating + HotelCapacity:IsMarriott + FreeBreakfast:IsMarriott +
## IsWeekend:IsMarriott + IsMarriott:MedianHomeValue + IsMarriott:MedianHouseHoldIncome +
## IsMarriott:CityName + IsMarriott:MaxRentUSD, data = BMHotelsData.df,
## weights = 1/hhat)
##
## Coefficients:
## (Intercept) HotelCapacity
## 3.442e+00 9.200e-05
## FreeBreakfast1 IsWeekend1
## -2.049e-02 4.708e-02
## IsMarriott1 MedianHomeValue
## 6.726e-01 2.005e-07
## MedianHouseHoldIncome CityNameAnaheim
## -1.188e-06 -2.750e-01
## CityNameArlington CityNameAsheville
## 1.037e-01 2.390e-01
## CityNameBaltimore CityNameBoston
## -3.966e-01 -3.354e-01
## CityNameBuffalo CityNameChicago
## 1.705e-01 -4.539e-01
## CityNameCleveland CityNameColumbus
## 1.769e-01 1.113e-01
## CityNameFresno CityNameHouston
## 9.538e-02 2.235e-01
## CityNameJacksonville CityNameKansas City
## 3.127e-01 1.288e-01
## CityNameLake Tahoe CityNameLas Vegas
## -5.750e-01 -8.276e-02
## CityNameLos Angeles CityNameLouisville
## -1.932e-01 -4.521e-01
## CityNameMaui CityNameMemphis
## 4.399e-01 4.953e-03
## CityNameMilwaukee CityNameNashville
## 1.486e-01 3.189e-01
## CityNameNew Orleans CityNameNew York City
## 2.448e-01 3.821e-01
## CityNameNiagara Falls CityNamePhiladelphia
## -5.236e-02 -2.856e-01
## CityNamePhoenix CityNameSan Antonio
## 3.485e-01 1.436e-01
## CityNameSan Francisco CityNameSan Jose
## -4.978e-01 4.385e-01
## CityNameSeattle CityNameSt. Louis
## 2.246e-01 -3.236e-01
## CityNameTampa CityNameTucson
## 2.455e-01 2.452e-02
## MaxRentUSD GuestRating
## 2.919e-03 1.496e-01
## HotelCapacity:IsMarriott1 FreeBreakfast1:IsMarriott1
## 2.708e-04 -3.023e-02
## IsWeekend1:IsMarriott1 IsMarriott1:MedianHomeValue
## -9.635e-02 7.300e-07
## IsMarriott1:MedianHouseHoldIncome IsMarriott1:CityNameAnaheim
## -3.814e-06 -2.123e-01
## IsMarriott1:CityNameArlington IsMarriott1:CityNameAsheville
## 4.462e-02 -8.192e-02
## IsMarriott1:CityNameBaltimore IsMarriott1:CityNameBoston
## -2.450e-01 -8.548e-02
## IsMarriott1:CityNameBuffalo IsMarriott1:CityNameChicago
## NA -1.251e-01
## IsMarriott1:CityNameCleveland IsMarriott1:CityNameColumbus
## -9.386e-02 -6.188e-03
## IsMarriott1:CityNameFresno IsMarriott1:CityNameHouston
## 7.357e-02 -2.056e-01
## IsMarriott1:CityNameJacksonville IsMarriott1:CityNameKansas City
## -3.986e-02 -7.163e-02
## IsMarriott1:CityNameLake Tahoe IsMarriott1:CityNameLas Vegas
## NA 8.603e-02
## IsMarriott1:CityNameLos Angeles IsMarriott1:CityNameLouisville
## -3.734e-01 -2.721e-01
## IsMarriott1:CityNameMaui IsMarriott1:CityNameMemphis
## 1.066e-01 8.482e-03
## IsMarriott1:CityNameMilwaukee IsMarriott1:CityNameNashville
## -4.543e-02 2.641e-01
## IsMarriott1:CityNameNew Orleans IsMarriott1:CityNameNew York City
## -3.022e-01 -1.502e-01
## IsMarriott1:CityNameNiagara Falls IsMarriott1:CityNamePhiladelphia
## -2.198e-01 -3.153e-01
## IsMarriott1:CityNamePhoenix IsMarriott1:CityNameSan Antonio
## -1.711e-01 1.142e-01
## IsMarriott1:CityNameSan Francisco IsMarriott1:CityNameSan Jose
## -4.095e-01 3.544e-03
## IsMarriott1:CityNameSeattle IsMarriott1:CityNameSt. Louis
## NA -1.344e-01
## IsMarriott1:CityNameTampa IsMarriott1:CityNameTucson
## 1.070e-01 1.060e-01
## IsMarriott1:MaxRentUSD
## -2.346e-03MOdel with lower AIC
log(RentUSD) ~ log(RentUSD) ~ HotelCapacity + FreeBreakfast + IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome + CityName + MaxRentUSD + GuestRating + HotelCapacity:IsMarriott + FreeBreakfast:IsMarriott + IsWeekend:IsMarriott + IsMarriott:MedianHomeValue + IsMarriott:MedianHouseHoldIncome + IsMarriott:CityName + IsMarriott:MaxRentUSD
All Subsets regression
(without interactions)
library(leaps)## Warning: package 'leaps' was built under R version 3.4.2leaps<-regsubsets(log(RentUSD) ~ HasSwimmingPool + FreeBreakfast + IsTourist + HotelCapacity+ IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome + MaxRentUSD + GuestRating ,really.big=T,data=BMHotelsData.df,nbest=4)
summary(leaps)## Subset selection object
## Call: regsubsets.formula(log(RentUSD) ~ HasSwimmingPool + FreeBreakfast +
## IsTourist + HotelCapacity + IsWeekend + IsMarriott + MedianHomeValue +
## MedianHouseHoldIncome + MaxRentUSD + GuestRating, really.big = T,
## data = BMHotelsData.df, nbest = 4)
## 10 Variables (and intercept)
## Forced in Forced out
## HasSwimmingPool1 FALSE FALSE
## FreeBreakfast1 FALSE FALSE
## IsTourist1 FALSE FALSE
## HotelCapacity FALSE FALSE
## IsWeekend1 FALSE FALSE
## IsMarriott1 FALSE FALSE
## MedianHomeValue FALSE FALSE
## MedianHouseHoldIncome FALSE FALSE
## MaxRentUSD FALSE FALSE
## GuestRating FALSE FALSE
## 4 subsets of each size up to 8
## Selection Algorithm: exhaustive
## HasSwimmingPool1 FreeBreakfast1 IsTourist1 HotelCapacity
## 1 ( 1 ) " " " " " " " "
## 1 ( 2 ) " " " " " " " "
## 1 ( 3 ) " " " " " " " "
## 1 ( 4 ) " " " " "*" " "
## 2 ( 1 ) " " " " " " " "
## 2 ( 2 ) " " " " " " " "
## 2 ( 3 ) " " " " "*" " "
## 2 ( 4 ) " " " " " " " "
## 3 ( 1 ) " " " " " " "*"
## 3 ( 2 ) " " " " " " " "
## 3 ( 3 ) " " " " " " " "
## 3 ( 4 ) " " "*" " " " "
## 4 ( 1 ) " " " " " " "*"
## 4 ( 2 ) " " " " " " " "
## 4 ( 3 ) " " " " " " "*"
## 4 ( 4 ) " " "*" " " " "
## 5 ( 1 ) " " " " " " "*"
## 5 ( 2 ) " " " " " " "*"
## 5 ( 3 ) " " "*" " " "*"
## 5 ( 4 ) " " "*" " " " "
## 6 ( 1 ) " " " " " " "*"
## 6 ( 2 ) " " "*" " " "*"
## 6 ( 3 ) " " " " " " "*"
## 6 ( 4 ) "*" " " " " "*"
## 7 ( 1 ) " " "*" " " "*"
## 7 ( 2 ) " " " " " " "*"
## 7 ( 3 ) " " "*" " " "*"
## 7 ( 4 ) "*" " " " " "*"
## 8 ( 1 ) " " "*" " " "*"
## 8 ( 2 ) "*" "*" " " "*"
## 8 ( 3 ) "*" " " " " "*"
## 8 ( 4 ) " " "*" "*" "*"
## IsWeekend1 IsMarriott1 MedianHomeValue MedianHouseHoldIncome
## 1 ( 1 ) " " " " " " " "
## 1 ( 2 ) " " " " "*" " "
## 1 ( 3 ) " " " " " " " "
## 1 ( 4 ) " " " " " " " "
## 2 ( 1 ) " " " " "*" " "
## 2 ( 2 ) " " " " " " " "
## 2 ( 3 ) " " " " " " " "
## 2 ( 4 ) " " " " " " "*"
## 3 ( 1 ) " " " " "*" " "
## 3 ( 2 ) " " " " "*" " "
## 3 ( 3 ) " " "*" "*" " "
## 3 ( 4 ) " " " " "*" " "
## 4 ( 1 ) " " " " "*" " "
## 4 ( 2 ) " " "*" "*" " "
## 4 ( 3 ) " " "*" "*" " "
## 4 ( 4 ) " " " " "*" " "
## 5 ( 1 ) " " "*" "*" " "
## 5 ( 2 ) "*" " " "*" " "
## 5 ( 3 ) " " " " "*" " "
## 5 ( 4 ) " " "*" "*" " "
## 6 ( 1 ) "*" "*" "*" " "
## 6 ( 2 ) " " "*" "*" " "
## 6 ( 3 ) " " "*" "*" "*"
## 6 ( 4 ) " " "*" "*" " "
## 7 ( 1 ) "*" "*" "*" " "
## 7 ( 2 ) "*" "*" "*" "*"
## 7 ( 3 ) " " "*" "*" "*"
## 7 ( 4 ) "*" "*" "*" " "
## 8 ( 1 ) "*" "*" "*" "*"
## 8 ( 2 ) "*" "*" "*" " "
## 8 ( 3 ) "*" "*" "*" "*"
## 8 ( 4 ) "*" "*" "*" " "
## MaxRentUSD GuestRating
## 1 ( 1 ) "*" " "
## 1 ( 2 ) " " " "
## 1 ( 3 ) " " "*"
## 1 ( 4 ) " " " "
## 2 ( 1 ) "*" " "
## 2 ( 2 ) "*" "*"
## 2 ( 3 ) "*" " "
## 2 ( 4 ) "*" " "
## 3 ( 1 ) "*" " "
## 3 ( 2 ) "*" "*"
## 3 ( 3 ) "*" " "
## 3 ( 4 ) "*" " "
## 4 ( 1 ) "*" "*"
## 4 ( 2 ) "*" "*"
## 4 ( 3 ) "*" " "
## 4 ( 4 ) "*" "*"
## 5 ( 1 ) "*" "*"
## 5 ( 2 ) "*" "*"
## 5 ( 3 ) "*" "*"
## 5 ( 4 ) "*" "*"
## 6 ( 1 ) "*" "*"
## 6 ( 2 ) "*" "*"
## 6 ( 3 ) "*" "*"
## 6 ( 4 ) "*" "*"
## 7 ( 1 ) "*" "*"
## 7 ( 2 ) "*" "*"
## 7 ( 3 ) "*" "*"
## 7 ( 4 ) "*" "*"
## 8 ( 1 ) "*" "*"
## 8 ( 2 ) "*" "*"
## 8 ( 3 ) "*" "*"
## 8 ( 4 ) "*" "*"plot(leaps,scales="adjr2")
#library(car)
#subsets(leaps, statistic="cp",main="Cp Plot for All Substs Regresion")
#abline(1,1,lty=2,col="red")** Result**
Here,the model with predictors- Intercept + FreeBreakfast + HotelCapacity + IsWeekend + IsMarriot + MedianHomeVaue + HouseHoldIncome + MAaxRentUsd + GuestRating has Highest adjr2.
(without interactions) Variable CityName included-
library(leaps)
leaps<-regsubsets(log(RentUSD) ~ HasSwimmingPool + FreeBreakfast + IsTourist + HotelCapacity+ IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome + MaxRentUSD + GuestRating + CityName ,really.big=T,data=BMHotelsData.df,nbest=4)## Warning in leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax,
## force.in = force.in, : 1 linear dependencies found## Reordering variables and trying again:summary(leaps)## Subset selection object
## Call: regsubsets.formula(log(RentUSD) ~ HasSwimmingPool + FreeBreakfast +
## IsTourist + HotelCapacity + IsWeekend + IsMarriott + MedianHomeValue +
## MedianHouseHoldIncome + MaxRentUSD + GuestRating + CityName,
## really.big = T, data = BMHotelsData.df, nbest = 4)
## 43 Variables (and intercept)
## Forced in Forced out
## HasSwimmingPool1 FALSE FALSE
## FreeBreakfast1 FALSE FALSE
## IsTourist1 FALSE FALSE
## HotelCapacity FALSE FALSE
## IsWeekend1 FALSE FALSE
## IsMarriott1 FALSE FALSE
## MedianHomeValue FALSE FALSE
## MedianHouseHoldIncome FALSE FALSE
## MaxRentUSD FALSE FALSE
## GuestRating FALSE FALSE
## CityNameAnaheim FALSE FALSE
## CityNameArlington FALSE FALSE
## CityNameAsheville FALSE FALSE
## CityNameBaltimore FALSE FALSE
## CityNameBoston FALSE FALSE
## CityNameBuffalo FALSE FALSE
## CityNameChicago FALSE FALSE
## CityNameCleveland FALSE FALSE
## CityNameColumbus FALSE FALSE
## CityNameFresno FALSE FALSE
## CityNameHouston FALSE FALSE
## CityNameJacksonville FALSE FALSE
## CityNameKansas City FALSE FALSE
## CityNameLake Tahoe FALSE FALSE
## CityNameLas Vegas FALSE FALSE
## CityNameLos Angeles FALSE FALSE
## CityNameLouisville FALSE FALSE
## CityNameMaui FALSE FALSE
## CityNameMemphis FALSE FALSE
## CityNameMilwaukee FALSE FALSE
## CityNameNashville FALSE FALSE
## CityNameNew Orleans FALSE FALSE
## CityNameNew York City FALSE FALSE
## CityNameNiagara Falls FALSE FALSE
## CityNamePhiladelphia FALSE FALSE
## CityNamePhoenix FALSE FALSE
## CityNameSan Antonio FALSE FALSE
## CityNameSan Francisco FALSE FALSE
## CityNameSan Jose FALSE FALSE
## CityNameSt. Louis FALSE FALSE
## CityNameTampa FALSE FALSE
## CityNameTucson FALSE FALSE
## CityNameSeattle FALSE FALSE
## 4 subsets of each size up to 9
## Selection Algorithm: exhaustive
## HasSwimmingPool1 FreeBreakfast1 IsTourist1 HotelCapacity
## 1 ( 1 ) " " " " " " " "
## 1 ( 2 ) " " " " " " " "
## 1 ( 3 ) " " " " " " " "
## 1 ( 4 ) " " " " "*" " "
## 2 ( 1 ) " " " " " " " "
## 2 ( 2 ) " " " " " " " "
## 2 ( 3 ) " " " " "*" " "
## 2 ( 4 ) " " " " " " " "
## 3 ( 1 ) " " " " " " " "
## 3 ( 2 ) " " " " " " "*"
## 3 ( 3 ) " " " " " " " "
## 3 ( 4 ) " " " " " " " "
## 4 ( 1 ) " " " " " " " "
## 4 ( 2 ) " " " " " " " "
## 4 ( 3 ) " " " " " " "*"
## 4 ( 4 ) " " " " " " " "
## 5 ( 1 ) " " " " " " " "
## 5 ( 2 ) " " " " " " " "
## 5 ( 3 ) " " " " " " "*"
## 5 ( 4 ) " " " " " " " "
## 6 ( 1 ) " " " " " " " "
## 6 ( 2 ) " " " " " " " "
## 6 ( 3 ) " " " " " " "*"
## 6 ( 4 ) " " " " " " "*"
## 7 ( 1 ) " " " " " " "*"
## 7 ( 2 ) " " " " " " " "
## 7 ( 3 ) " " " " " " " "
## 7 ( 4 ) " " " " " " " "
## 8 ( 1 ) " " " " " " " "
## 8 ( 2 ) " " " " " " "*"
## 8 ( 3 ) " " " " " " " "
## 8 ( 4 ) " " " " " " " "
## 9 ( 1 ) " " " " " " "*"
## 9 ( 2 ) " " " " " " " "
## 9 ( 3 ) " " " " " " " "
## 9 ( 4 ) " " " " " " " "
## IsWeekend1 IsMarriott1 MedianHomeValue MedianHouseHoldIncome
## 1 ( 1 ) " " " " " " " "
## 1 ( 2 ) " " " " "*" " "
## 1 ( 3 ) " " " " " " " "
## 1 ( 4 ) " " " " " " " "
## 2 ( 1 ) " " " " "*" " "
## 2 ( 2 ) " " " " " " " "
## 2 ( 3 ) " " " " " " " "
## 2 ( 4 ) " " " " " " " "
## 3 ( 1 ) " " " " "*" " "
## 3 ( 2 ) " " " " "*" " "
## 3 ( 3 ) " " " " "*" " "
## 3 ( 4 ) " " " " "*" " "
## 4 ( 1 ) " " " " "*" " "
## 4 ( 2 ) " " " " "*" " "
## 4 ( 3 ) " " " " "*" " "
## 4 ( 4 ) " " "*" "*" " "
## 5 ( 1 ) " " " " "*" " "
## 5 ( 2 ) " " " " "*" " "
## 5 ( 3 ) " " " " "*" " "
## 5 ( 4 ) " " " " "*" " "
## 6 ( 1 ) " " " " "*" " "
## 6 ( 2 ) " " " " "*" " "
## 6 ( 3 ) " " " " "*" " "
## 6 ( 4 ) " " " " "*" " "
## 7 ( 1 ) " " " " "*" " "
## 7 ( 2 ) " " " " "*" " "
## 7 ( 3 ) " " "*" "*" " "
## 7 ( 4 ) " " " " "*" " "
## 8 ( 1 ) " " " " "*" " "
## 8 ( 2 ) " " " " "*" " "
## 8 ( 3 ) " " "*" "*" " "
## 8 ( 4 ) " " "*" "*" "*"
## 9 ( 1 ) " " " " "*" " "
## 9 ( 2 ) " " "*" "*" " "
## 9 ( 3 ) " " " " " " " "
## 9 ( 4 ) " " " " "*" " "
## MaxRentUSD GuestRating CityNameAnaheim CityNameArlington
## 1 ( 1 ) "*" " " " " " "
## 1 ( 2 ) " " " " " " " "
## 1 ( 3 ) " " "*" " " " "
## 1 ( 4 ) " " " " " " " "
## 2 ( 1 ) "*" " " " " " "
## 2 ( 2 ) "*" "*" " " " "
## 2 ( 3 ) "*" " " " " " "
## 2 ( 4 ) "*" " " " " " "
## 3 ( 1 ) "*" " " " " " "
## 3 ( 2 ) "*" " " " " " "
## 3 ( 3 ) "*" " " " " " "
## 3 ( 4 ) "*" "*" " " " "
## 4 ( 1 ) "*" "*" " " " "
## 4 ( 2 ) "*" "*" " " " "
## 4 ( 3 ) "*" " " " " " "
## 4 ( 4 ) "*" " " " " " "
## 5 ( 1 ) "*" "*" " " " "
## 5 ( 2 ) "*" "*" " " " "
## 5 ( 3 ) "*" "*" " " " "
## 5 ( 4 ) "*" "*" " " " "
## 6 ( 1 ) "*" "*" " " " "
## 6 ( 2 ) "*" "*" " " " "
## 6 ( 3 ) "*" "*" " " " "
## 6 ( 4 ) "*" "*" " " " "
## 7 ( 1 ) "*" "*" " " " "
## 7 ( 2 ) "*" "*" " " " "
## 7 ( 3 ) "*" "*" " " " "
## 7 ( 4 ) "*" "*" " " " "
## 8 ( 1 ) "*" "*" " " " "
## 8 ( 2 ) "*" "*" " " " "
## 8 ( 3 ) "*" "*" " " " "
## 8 ( 4 ) "*" "*" " " " "
## 9 ( 1 ) "*" "*" " " " "
## 9 ( 2 ) "*" "*" " " " "
## 9 ( 3 ) "*" "*" " " " "
## 9 ( 4 ) "*" "*" " " " "
## CityNameAsheville CityNameBaltimore CityNameBoston
## 1 ( 1 ) " " " " " "
## 1 ( 2 ) " " " " " "
## 1 ( 3 ) " " " " " "
## 1 ( 4 ) " " " " " "
## 2 ( 1 ) " " " " " "
## 2 ( 2 ) " " " " " "
## 2 ( 3 ) " " " " " "
## 2 ( 4 ) " " " " " "
## 3 ( 1 ) " " " " " "
## 3 ( 2 ) " " " " " "
## 3 ( 3 ) " " " " " "
## 3 ( 4 ) " " " " " "
## 4 ( 1 ) " " " " " "
## 4 ( 2 ) " " " " " "
## 4 ( 3 ) " " " " " "
## 4 ( 4 ) " " " " " "
## 5 ( 1 ) " " " " " "
## 5 ( 2 ) " " " " " "
## 5 ( 3 ) " " " " " "
## 5 ( 4 ) " " " " " "
## 6 ( 1 ) " " " " " "
## 6 ( 2 ) " " " " " "
## 6 ( 3 ) " " " " " "
## 6 ( 4 ) " " " " " "
## 7 ( 1 ) " " " " " "
## 7 ( 2 ) " " " " " "
## 7 ( 3 ) " " " " " "
## 7 ( 4 ) " " " " " "
## 8 ( 1 ) " " " " " "
## 8 ( 2 ) " " " " " "
## 8 ( 3 ) " " " " " "
## 8 ( 4 ) " " " " " "
## 9 ( 1 ) " " " " " "
## 9 ( 2 ) " " " " " "
## 9 ( 3 ) " " "*" " "
## 9 ( 4 ) " " " " " "
## CityNameBuffalo CityNameChicago CityNameCleveland
## 1 ( 1 ) " " " " " "
## 1 ( 2 ) " " " " " "
## 1 ( 3 ) " " " " " "
## 1 ( 4 ) " " " " " "
## 2 ( 1 ) " " " " " "
## 2 ( 2 ) " " " " " "
## 2 ( 3 ) " " " " " "
## 2 ( 4 ) " " " " " "
## 3 ( 1 ) " " " " " "
## 3 ( 2 ) " " " " " "
## 3 ( 3 ) " " " " " "
## 3 ( 4 ) " " " " " "
## 4 ( 1 ) " " " " " "
## 4 ( 2 ) " " " " " "
## 4 ( 3 ) " " " " " "
## 4 ( 4 ) " " " " " "
## 5 ( 1 ) " " " " " "
## 5 ( 2 ) " " " " " "
## 5 ( 3 ) " " " " " "
## 5 ( 4 ) " " " " " "
## 6 ( 1 ) " " " " " "
## 6 ( 2 ) " " " " " "
## 6 ( 3 ) " " " " " "
## 6 ( 4 ) " " " " " "
## 7 ( 1 ) " " " " " "
## 7 ( 2 ) " " " " " "
## 7 ( 3 ) " " " " " "
## 7 ( 4 ) " " " " " "
## 8 ( 1 ) " " " " " "
## 8 ( 2 ) " " " " " "
## 8 ( 3 ) " " " " " "
## 8 ( 4 ) " " " " " "
## 9 ( 1 ) " " " " " "
## 9 ( 2 ) " " " " " "
## 9 ( 3 ) " " " " " "
## 9 ( 4 ) " " " " " "
## CityNameColumbus CityNameFresno CityNameHouston
## 1 ( 1 ) " " " " " "
## 1 ( 2 ) " " " " " "
## 1 ( 3 ) " " " " " "
## 1 ( 4 ) " " " " " "
## 2 ( 1 ) " " " " " "
## 2 ( 2 ) " " " " " "
## 2 ( 3 ) " " " " " "
## 2 ( 4 ) " " " " " "
## 3 ( 1 ) " " " " " "
## 3 ( 2 ) " " " " " "
## 3 ( 3 ) " " " " " "
## 3 ( 4 ) " " " " " "
## 4 ( 1 ) " " " " " "
## 4 ( 2 ) " " " " " "
## 4 ( 3 ) " " " " " "
## 4 ( 4 ) " " " " " "
## 5 ( 1 ) " " " " " "
## 5 ( 2 ) " " " " " "
## 5 ( 3 ) " " " " " "
## 5 ( 4 ) " " " " " "
## 6 ( 1 ) " " " " " "
## 6 ( 2 ) " " " " " "
## 6 ( 3 ) " " " " " "
## 6 ( 4 ) " " " " " "
## 7 ( 1 ) " " " " " "
## 7 ( 2 ) " " " " " "
## 7 ( 3 ) " " " " " "
## 7 ( 4 ) " " " " " "
## 8 ( 1 ) " " " " " "
## 8 ( 2 ) " " " " " "
## 8 ( 3 ) " " " " " "
## 8 ( 4 ) " " " " " "
## 9 ( 1 ) " " " " " "
## 9 ( 2 ) " " " " " "
## 9 ( 3 ) " " " " " "
## 9 ( 4 ) " " " " " "
## CityNameJacksonville CityNameKansas City CityNameLake Tahoe
## 1 ( 1 ) " " " " " "
## 1 ( 2 ) " " " " " "
## 1 ( 3 ) " " " " " "
## 1 ( 4 ) " " " " " "
## 2 ( 1 ) " " " " " "
## 2 ( 2 ) " " " " " "
## 2 ( 3 ) " " " " " "
## 2 ( 4 ) " " " " " "
## 3 ( 1 ) " " " " " "
## 3 ( 2 ) " " " " " "
## 3 ( 3 ) " " " " " "
## 3 ( 4 ) " " " " " "
## 4 ( 1 ) " " " " " "
## 4 ( 2 ) " " " " " "
## 4 ( 3 ) " " " " " "
## 4 ( 4 ) " " " " " "
## 5 ( 1 ) " " " " " "
## 5 ( 2 ) " " " " " "
## 5 ( 3 ) " " " " " "
## 5 ( 4 ) " " " " "*"
## 6 ( 1 ) " " " " "*"
## 6 ( 2 ) " " " " " "
## 6 ( 3 ) " " " " " "
## 6 ( 4 ) " " " " " "
## 7 ( 1 ) " " " " "*"
## 7 ( 2 ) " " " " "*"
## 7 ( 3 ) " " " " "*"
## 7 ( 4 ) " " " " "*"
## 8 ( 1 ) " " " " "*"
## 8 ( 2 ) " " " " "*"
## 8 ( 3 ) " " " " "*"
## 8 ( 4 ) " " " " "*"
## 9 ( 1 ) " " " " "*"
## 9 ( 2 ) " " " " "*"
## 9 ( 3 ) " " " " "*"
## 9 ( 4 ) " " " " "*"
## CityNameLas Vegas CityNameLos Angeles CityNameLouisville
## 1 ( 1 ) " " " " " "
## 1 ( 2 ) " " " " " "
## 1 ( 3 ) " " " " " "
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## 5 ( 2 ) " " " " " "
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## 6 ( 1 ) " " " " " "
## 6 ( 2 ) " " " " " "
## 6 ( 3 ) " " " " " "
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## 7 ( 2 ) " " " " " "
## 7 ( 3 ) " " " " " "
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## 8 ( 3 ) " " " " " "
## 8 ( 4 ) " " " " " "
## 9 ( 1 ) " " " " " "
## 9 ( 2 ) " " " " " "
## 9 ( 3 ) " " " " "*"
## 9 ( 4 ) " " " " " "
## CityNameMaui CityNameMemphis CityNameMilwaukee CityNameNashville
## 1 ( 1 ) " " " " " " " "
## 1 ( 2 ) " " " " " " " "
## 1 ( 3 ) " " " " " " " "
## 1 ( 4 ) " " " " " " " "
## 2 ( 1 ) " " " " " " " "
## 2 ( 2 ) " " " " " " " "
## 2 ( 3 ) " " " " " " " "
## 2 ( 4 ) "*" " " " " " "
## 3 ( 1 ) " " " " " " " "
## 3 ( 2 ) " " " " " " " "
## 3 ( 3 ) "*" " " " " " "
## 3 ( 4 ) " " " " " " " "
## 4 ( 1 ) "*" " " " " " "
## 4 ( 2 ) " " " " " " " "
## 4 ( 3 ) " " " " " " " "
## 4 ( 4 ) " " " " " " " "
## 5 ( 1 ) "*" " " " " " "
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## 6 ( 1 ) "*" " " " " " "
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## 7 ( 1 ) "*" " " " " " "
## 7 ( 2 ) "*" " " " " " "
## 7 ( 3 ) "*" " " " " " "
## 7 ( 4 ) "*" " " " " " "
## 8 ( 1 ) "*" " " " " " "
## 8 ( 2 ) "*" " " " " " "
## 8 ( 3 ) "*" " " " " " "
## 8 ( 4 ) "*" " " " " " "
## 9 ( 1 ) "*" " " " " " "
## 9 ( 2 ) "*" " " " " " "
## 9 ( 3 ) "*" " " " " " "
## 9 ( 4 ) "*" " " " " "*"
## CityNameNew Orleans CityNameNew York City CityNameNiagara Falls
## 1 ( 1 ) " " " " " "
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## 5 ( 1 ) " " "*" " "
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## 5 ( 3 ) " " " " " "
## 5 ( 4 ) " " " " " "
## 6 ( 1 ) " " " " " "
## 6 ( 2 ) " " "*" " "
## 6 ( 3 ) " " " " " "
## 6 ( 4 ) " " "*" " "
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## 7 ( 2 ) " " "*" " "
## 7 ( 3 ) " " " " " "
## 7 ( 4 ) " " "*" " "
## 8 ( 1 ) " " "*" " "
## 8 ( 2 ) " " "*" " "
## 8 ( 3 ) " " "*" " "
## 8 ( 4 ) " " " " " "
## 9 ( 1 ) " " "*" " "
## 9 ( 2 ) " " "*" " "
## 9 ( 3 ) " " "*" " "
## 9 ( 4 ) " " "*" " "
## CityNamePhiladelphia CityNamePhoenix CityNameSan Antonio
## 1 ( 1 ) " " " " " "
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## 5 ( 2 ) " " " " " "
## 5 ( 3 ) " " " " " "
## 5 ( 4 ) " " " " " "
## 6 ( 1 ) " " " " " "
## 6 ( 2 ) " " "*" " "
## 6 ( 3 ) " " " " " "
## 6 ( 4 ) " " " " " "
## 7 ( 1 ) " " " " " "
## 7 ( 2 ) " " " " " "
## 7 ( 3 ) " " " " " "
## 7 ( 4 ) " " "*" " "
## 8 ( 1 ) " " "*" " "
## 8 ( 2 ) " " " " " "
## 8 ( 3 ) " " " " " "
## 8 ( 4 ) " " " " " "
## 9 ( 1 ) " " "*" " "
## 9 ( 2 ) " " "*" " "
## 9 ( 3 ) " " "*" " "
## 9 ( 4 ) " " "*" " "
## CityNameSan Francisco CityNameSan Jose CityNameSeattle
## 1 ( 1 ) " " " " " "
## 1 ( 2 ) " " " " " "
## 1 ( 3 ) " " " " " "
## 1 ( 4 ) " " " " " "
## 2 ( 1 ) " " " " " "
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## 2 ( 3 ) " " " " " "
## 2 ( 4 ) " " " " " "
## 3 ( 1 ) "*" " " " "
## 3 ( 2 ) " " " " " "
## 3 ( 3 ) " " " " " "
## 3 ( 4 ) " " " " " "
## 4 ( 1 ) " " " " " "
## 4 ( 2 ) "*" " " " "
## 4 ( 3 ) "*" " " " "
## 4 ( 4 ) "*" " " " "
## 5 ( 1 ) " " " " " "
## 5 ( 2 ) "*" " " " "
## 5 ( 3 ) " " " " " "
## 5 ( 4 ) "*" " " " "
## 6 ( 1 ) "*" " " " "
## 6 ( 2 ) " " " " " "
## 6 ( 3 ) "*" " " " "
## 6 ( 4 ) " " " " " "
## 7 ( 1 ) "*" " " " "
## 7 ( 2 ) "*" " " " "
## 7 ( 3 ) "*" " " " "
## 7 ( 4 ) " " " " " "
## 8 ( 1 ) "*" " " " "
## 8 ( 2 ) "*" " " " "
## 8 ( 3 ) "*" " " " "
## 8 ( 4 ) "*" " " " "
## 9 ( 1 ) "*" " " " "
## 9 ( 2 ) "*" " " " "
## 9 ( 3 ) " " "*" " "
## 9 ( 4 ) "*" " " " "
## CityNameSt. Louis CityNameTampa CityNameTucson
## 1 ( 1 ) " " " " " "
## 1 ( 2 ) " " " " " "
## 1 ( 3 ) " " " " " "
## 1 ( 4 ) " " " " " "
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## 9 ( 1 ) " " " " " "
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## 9 ( 4 ) " " " " " "plot(leaps,scales="adjr2")
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logit#subsets(leaps, statistic="cp",main="Cp Plot for All Substs Regresion")
#abline(1,1,lty=2,col="red")Result- Here the model with predictors - Intercept + HotelCapacity + MaxrentUSD + GuestRating + MedianHomeValue + CityName (of some cities) has highest adjr2
regsubsets function
(with interactions- IsMarriott)
library(leaps)
leaps<-regsubsets(log(RentUSD) ~ HotelCapacity + HasSwimmingPool + FreeBreakfast + IsTourist + IsWeekend + IsMarriott + MedianHomeValue + MedianHouseHoldIncome + GuestRating +MaxRentUSD + IsMarriott*HotelCapacity + IsMarriott*HasSwimmingPool + IsMarriott*FreeBreakfast + IsMarriott*IsTourist + IsMarriott*IsWeekend + + IsMarriott*MedianHomeValue + IsMarriott*MedianHouseHoldIncome + IsMarriott*MedianHouseHoldIncome ,really.big=T,data=BMHotelsData.df,nbest=4)
summary(leaps)## Subset selection object
## Call: regsubsets.formula(log(RentUSD) ~ HotelCapacity + HasSwimmingPool +
## FreeBreakfast + IsTourist + IsWeekend + IsMarriott + MedianHomeValue +
## MedianHouseHoldIncome + GuestRating + MaxRentUSD + IsMarriott *
## HotelCapacity + IsMarriott * HasSwimmingPool + IsMarriott *
## FreeBreakfast + IsMarriott * IsTourist + IsMarriott * IsWeekend +
## +IsMarriott * MedianHomeValue + IsMarriott * MedianHouseHoldIncome +
## IsMarriott * MedianHouseHoldIncome, really.big = T, data = BMHotelsData.df,
## nbest = 4)
## 17 Variables (and intercept)
## Forced in Forced out
## HotelCapacity FALSE FALSE
## HasSwimmingPool1 FALSE FALSE
## FreeBreakfast1 FALSE FALSE
## IsTourist1 FALSE FALSE
## IsWeekend1 FALSE FALSE
## IsMarriott1 FALSE FALSE
## MedianHomeValue FALSE FALSE
## MedianHouseHoldIncome FALSE FALSE
## GuestRating FALSE FALSE
## MaxRentUSD FALSE FALSE
## HotelCapacity:IsMarriott1 FALSE FALSE
## HasSwimmingPool1:IsMarriott1 FALSE FALSE
## FreeBreakfast1:IsMarriott1 FALSE FALSE
## IsTourist1:IsMarriott1 FALSE FALSE
## IsWeekend1:IsMarriott1 FALSE FALSE
## IsMarriott1:MedianHomeValue FALSE FALSE
## IsMarriott1:MedianHouseHoldIncome FALSE FALSE
## 4 subsets of each size up to 8
## Selection Algorithm: exhaustive
## HotelCapacity HasSwimmingPool1 FreeBreakfast1 IsTourist1
## 1 ( 1 ) " " " " " " " "
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## 1 ( 4 ) " " " " " " "*"
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## 2 ( 2 ) " " " " " " " "
## 2 ( 3 ) " " " " " " "*"
## 2 ( 4 ) " " " " " " " "
## 3 ( 1 ) "*" " " " " " "
## 3 ( 2 ) " " " " " " " "
## 3 ( 3 ) " " " " " " " "
## 3 ( 4 ) " " " " " " " "
## 4 ( 1 ) "*" " " " " " "
## 4 ( 2 ) " " " " " " " "
## 4 ( 3 ) "*" " " " " " "
## 4 ( 4 ) " " " " " " " "
## 5 ( 1 ) "*" " " " " " "
## 5 ( 2 ) "*" " " " " " "
## 5 ( 3 ) "*" " " " " " "
## 5 ( 4 ) "*" " " " " " "
## 6 ( 1 ) "*" " " " " " "
## 6 ( 2 ) "*" " " " " " "
## 6 ( 3 ) "*" " " "*" " "
## 6 ( 4 ) "*" " " " " " "
## 7 ( 1 ) "*" " " " " " "
## 7 ( 2 ) "*" " " "*" " "
## 7 ( 3 ) "*" " " " " " "
## 7 ( 4 ) "*" " " "*" " "
## 8 ( 1 ) "*" " " "*" " "
## 8 ( 2 ) "*" " " " " " "
## 8 ( 3 ) "*" " " " " " "
## 8 ( 4 ) "*" " " " " " "
## IsWeekend1 IsMarriott1 MedianHomeValue MedianHouseHoldIncome
## 1 ( 1 ) " " " " " " " "
## 1 ( 2 ) " " " " "*" " "
## 1 ( 3 ) " " " " " " " "
## 1 ( 4 ) " " " " " " " "
## 2 ( 1 ) " " " " "*" " "
## 2 ( 2 ) " " " " " " " "
## 2 ( 3 ) " " " " " " " "
## 2 ( 4 ) " " " " " " "*"
## 3 ( 1 ) " " " " "*" " "
## 3 ( 2 ) " " " " "*" " "
## 3 ( 3 ) " " "*" "*" " "
## 3 ( 4 ) " " " " "*" " "
## 4 ( 1 ) " " " " "*" " "
## 4 ( 2 ) " " "*" "*" " "
## 4 ( 3 ) " " "*" "*" " "
## 4 ( 4 ) " " " " "*" " "
## 5 ( 1 ) " " "*" "*" " "
## 5 ( 2 ) " " " " "*" " "
## 5 ( 3 ) " " " " "*" " "
## 5 ( 4 ) " " " " "*" " "
## 6 ( 1 ) " " "*" "*" " "
## 6 ( 2 ) "*" "*" "*" " "
## 6 ( 3 ) " " "*" "*" " "
## 6 ( 4 ) " " "*" "*" " "
## 7 ( 1 ) "*" "*" "*" " "
## 7 ( 2 ) " " "*" "*" " "
## 7 ( 3 ) " " "*" "*" " "
## 7 ( 4 ) "*" "*" "*" " "
## 8 ( 1 ) "*" "*" "*" " "
## 8 ( 2 ) "*" "*" "*" " "
## 8 ( 3 ) "*" "*" "*" " "
## 8 ( 4 ) "*" "*" "*" " "
## GuestRating MaxRentUSD HotelCapacity:IsMarriott1
## 1 ( 1 ) " " "*" " "
## 1 ( 2 ) " " " " " "
## 1 ( 3 ) "*" " " " "
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## 2 ( 1 ) " " "*" " "
## 2 ( 2 ) "*" "*" " "
## 2 ( 3 ) " " "*" " "
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## 3 ( 1 ) " " "*" " "
## 3 ( 2 ) "*" "*" " "
## 3 ( 3 ) " " "*" " "
## 3 ( 4 ) " " "*" "*"
## 4 ( 1 ) "*" "*" " "
## 4 ( 2 ) "*" "*" " "
## 4 ( 3 ) " " "*" " "
## 4 ( 4 ) "*" "*" "*"
## 5 ( 1 ) "*" "*" " "
## 5 ( 2 ) "*" "*" " "
## 5 ( 3 ) "*" "*" " "
## 5 ( 4 ) "*" "*" " "
## 6 ( 1 ) "*" "*" " "
## 6 ( 2 ) "*" "*" " "
## 6 ( 3 ) "*" "*" " "
## 6 ( 4 ) "*" "*" " "
## 7 ( 1 ) "*" "*" " "
## 7 ( 2 ) "*" "*" " "
## 7 ( 3 ) "*" "*" " "
## 7 ( 4 ) "*" "*" " "
## 8 ( 1 ) "*" "*" " "
## 8 ( 2 ) "*" "*" " "
## 8 ( 3 ) "*" "*" " "
## 8 ( 4 ) "*" "*" " "
## HasSwimmingPool1:IsMarriott1 FreeBreakfast1:IsMarriott1
## 1 ( 1 ) " " " "
## 1 ( 2 ) " " " "
## 1 ( 3 ) " " " "
## 1 ( 4 ) " " " "
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## 3 ( 3 ) " " " "
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## 4 ( 3 ) " " " "
## 4 ( 4 ) " " " "
## 5 ( 1 ) " " " "
## 5 ( 2 ) " " " "
## 5 ( 3 ) " " " "
## 5 ( 4 ) "*" " "
## 6 ( 1 ) " " " "
## 6 ( 2 ) " " " "
## 6 ( 3 ) " " " "
## 6 ( 4 ) "*" " "
## 7 ( 1 ) " " " "
## 7 ( 2 ) " " " "
## 7 ( 3 ) "*" " "
## 7 ( 4 ) " " " "
## 8 ( 1 ) " " " "
## 8 ( 2 ) " " " "
## 8 ( 3 ) "*" " "
## 8 ( 4 ) " " " "
## IsTourist1:IsMarriott1 IsWeekend1:IsMarriott1
## 1 ( 1 ) " " " "
## 1 ( 2 ) " " " "
## 1 ( 3 ) " " " "
## 1 ( 4 ) " " " "
## 2 ( 1 ) " " " "
## 2 ( 2 ) " " " "
## 2 ( 3 ) " " " "
## 2 ( 4 ) " " " "
## 3 ( 1 ) " " " "
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## 3 ( 3 ) " " " "
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## 4 ( 2 ) " " " "
## 4 ( 3 ) " " " "
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## 5 ( 2 ) " " " "
## 5 ( 3 ) " " " "
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## 6 ( 1 ) " " " "
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## 6 ( 3 ) " " " "
## 6 ( 4 ) " " " "
## 7 ( 1 ) " " " "
## 7 ( 2 ) " " " "
## 7 ( 3 ) " " " "
## 7 ( 4 ) " " " "
## 8 ( 1 ) " " " "
## 8 ( 2 ) " " "*"
## 8 ( 3 ) " " " "
## 8 ( 4 ) " " " "
## IsMarriott1:MedianHomeValue IsMarriott1:MedianHouseHoldIncome
## 1 ( 1 ) " " " "
## 1 ( 2 ) " " " "
## 1 ( 3 ) " " " "
## 1 ( 4 ) " " " "
## 2 ( 1 ) " " " "
## 2 ( 2 ) " " " "
## 2 ( 3 ) " " " "
## 2 ( 4 ) " " " "
## 3 ( 1 ) " " " "
## 3 ( 2 ) " " " "
## 3 ( 3 ) " " " "
## 3 ( 4 ) " " " "
## 4 ( 1 ) " " " "
## 4 ( 2 ) " " " "
## 4 ( 3 ) " " " "
## 4 ( 4 ) " " " "
## 5 ( 1 ) " " " "
## 5 ( 2 ) "*" " "
## 5 ( 3 ) " " "*"
## 5 ( 4 ) " " " "
## 6 ( 1 ) " " "*"
## 6 ( 2 ) " " " "
## 6 ( 3 ) " " " "
## 6 ( 4 ) " " " "
## 7 ( 1 ) " " "*"
## 7 ( 2 ) " " "*"
## 7 ( 3 ) " " "*"
## 7 ( 4 ) " " " "
## 8 ( 1 ) " " "*"
## 8 ( 2 ) " " "*"
## 8 ( 3 ) " " "*"
## 8 ( 4 ) "*" "*"plot(leaps,scales="adjr2")
library(car)
#subsets(leaps, statistic="cp",main="Cp Plot for All Substs Regresion")
#abline(1,1,lty=2,col="red")Result Here best predictors are- Intercept + Available + MedianHomeValue + SatrRating