Question

Hotel	Overall	Comfort	Amenities	In-House Dining
Muri Beach Odyssey	94.3	94.5	90.8	97.7
Pattaya Resort	92.9	96.6	84.1	96.6
Sojourner’s Respite	92.8	99.9	100.0	88.4
Spa Carribe	91.2	88.5	94.7	97.0
Penang Resort and Spa	90.4	95.0	87.8	91.1
Mokihana Hōkele	90.2	92.4	82.0	98.7
Theo’s of Cape Town	90.1	95.9	86.2	91.9
Cap d’Agde Resort	89.8	92.5	92.5	88.8
Spirit of Mykonos	89.3	94.6	85.8	90.7
Turismo del Mar	89.1	90.5	83.2	90.4
Hotel Iguana	89.1	90.8	81.9	88.5
Sidi Abdel Rahman Palace	89.0	93.0	93.0	89.6
Sainte-Maxime Quarters	88.6	92.5	78.2	91.2
Rotorua Inn	87.1	93.0	91.6	73.5
Club Lapu-Lapu	87.1	90.9	74.9	89.6
Terracina Retreat	86.5	94.3	78.0	91.5
Hacienda Punta Barco	86.1	95.4	77.3	90.8
Rendezvous Kolocep	86.0	94.8	76.4	91.4
Cabo de Gata Vista	86.0	92.0	72.2	89.2
Sanya Deluxe	85.1	93.4	77.3	91.8

The attached file shows the top 20 independent beachfront boutique hotels in the world as rated by the readers of Resorts & Spas. The hotels have an overall rating and ratings for comfort, amenities and in-house dining. Build an estimated regression model to predict the overall rating using the ratings for comfort, amenities and in-house dining. Next remove any variable that is not significant at a .05 level. What is the R Square of your new model? Round your answer to three decimal place.

Answer 1

I used R software to solve this problem:

R codes:

> overall=scan('clipboard')
Read 20 items
> overall
[1] 94.3 92.9 92.8 91.2 90.4 90.2 90.1 89.8 89.3 89.1 89.1 89.0 88.6 87.1 87.1
[16] 86.5 86.1 86.0 86.0 85.1
> comfort=scan('clipboard')
Read 20 items
> comfort
[1] 94.5 96.6 99.9 88.5 95.0 92.4 95.9 92.5 94.6 90.5 90.8 93.0 92.5 93.0 90.9
[16] 94.3 95.4 94.8 92.0 93.4
> amenity=scan('clipboard')
Read 20 items
> amenity
[1] 90.8 84.1 100.0 94.7 87.8 82.0 86.2 92.5 85.8 83.2 81.9 93.0
[13] 78.2 91.6 74.9 78.0 77.3 76.4 72.2 77.3
> dining=scan('clipboard')
Read 20 items
> dining
[1] 97.7 96.6 88.4 97.0 91.1 98.7 91.9 88.8 90.7 90.4 88.5 89.6 91.2 73.5 89.6
[16] 91.5 90.8 91.4 89.2 91.8
> fit=lm(overall~comfort+amenity+dining)
> summary(fit)

Call:
lm(formula = overall ~ comfort + amenity + dining)

Residuals:
Min 1Q Median 3Q Max
-2.40599 -1.22764 0.03497 0.86175 2.19540

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 35.69674 13.21538 2.701 0.01573 *
comfort 0.10935 0.12972 0.843 0.41167
amenity 0.24427 0.04332 5.639 3.69e-05 ***
dining 0.24743 0.06212 3.983 0.00107 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.388 on 16 degrees of freedom
Multiple R-squared: 0.7498, Adjusted R-squared: 0.7029
F-statistic: 15.98 on 3 and 16 DF, p-value: 4.524e-05

Estimated regression equation is,

overall = 35.69674 + 0.10935 comfort + 0.24427 amenities +  0.24743 in house dining

From summary table we see that comfort is not statistically significant. because its p value is greater than alpha=0.05.

So we remove this variable.

Summary table for new model:

> fit=lm(overall~amenity+dining)
> summary(fit)

Call:
lm(formula = overall ~ amenity + dining)

Residuals:
Min 1Q Median 3Q Max
-2.3614 -1.0761 0.4074 0.6252 2.5294

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 45.14615 6.93935 6.506 5.38e-06 ***
amenity 0.25258 0.04182 6.040 1.33e-05 ***
dining 0.24827 0.06158 4.031 0.000866 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.376 on 17 degrees of freedom
Multiple R-squared: 0.7387, Adjusted R-squared: 0.7079
F-statistic: 24.02 on 2 and 17 DF, p-value: 1.112e-05

R² for new model is 0.739.