91Ó°ÊÓ

The first order model for the hotel image(Y) as a function of the six ambient conditions can be written as

$\left(\mathbf{y}\right)\mathbf{=}{\mathbf{β}}_{\mathbf{0}}\mathbf{+}{\mathbf{β}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}\mathbf{+}{\mathbf{β}}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}{\mathbf{β}}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{3}}\mathbf{+}{\mathbf{β}}_{\mathbf{4}}{\mathbf{x}}_{\mathbf{4}}\mathbf{+}{\mathbf{β}}_{\mathbf{5}}{\mathbf{x}}_{\mathbf{5}}\mathbf{+}{\mathbf{β}}_{\mathbf{6}}{\mathbf{x}}_{\mathbf{6}}\mathbf{+}\mathbf{Î\mu }$

Where,

${\mathbf{β}}_{\mathbf{1}}\mathbf{,}{\mathbf{β}}_{\mathbf{2}}\mathbf{,}{\mathbf{β}}_{\mathbf{3}}\mathbf{,}{\mathbf{β}}_{\mathbf{4}}\mathbf{,}{\mathbf{β}}_{\mathbf{5}}$are the model parameters

$X_1$is air quality

$X_2$is temperature

${\mathbf{x}}_3$is odor/aroma

${\mathbf{x}}_4$is music

${\mathbf{x}}_5$is noise level

${\mathbf{x}}_6$is overall image

Therefore, the equation for the hotel is$\mathbf{y}\mathbf{=}{\mathbf{β}}_{\mathbf{0}}\mathbf{+}{\mathbf{β}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}\mathbf{+}{\mathbf{β}}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}{\mathbf{β}}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{3}}\mathbf{+}{\mathbf{β}}_{\mathbf{4}}{\mathbf{x}}_{\mathbf{4}}\mathbf{+}{\mathbf{β}}_{\mathbf{5}}{\mathbf{x}}_{\mathbf{5}}\mathbf{+}{\mathbf{β}}_{\mathbf{6}}{\mathbf{x}}_{\mathbf{6}}\mathbf{+}\mathbf{Î\mu }$

The values for${\mathbf{x}}_{\mathbf{1}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{122}\mathbf{,}{\mathbf{x}}_{\mathbf{2}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{018}\mathbf{,}{\mathbf{x}}_{\mathbf{3}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{124}\mathbf{,}{\mathbf{x}}_{\mathbf{4}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{119}\mathbf{,}{\mathbf{x}}_{\mathbf{5}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{101}$and${\mathbf{x}}_6\mathbf{=}\mathbf{0}.463$which can be interpreted as

For$X_1$, the value 0.122 indicates that since it’s a positive value, the guests are satisfied with air quality however, a lower value indicates that there is a lot to improve in for the hotel.

Forlocalid="1651776167603" ${\mathbf{x}}_2$ , the value 0.018 indicates that since it’s a positive value, the guests are satisfied with temperature however, it’s a very low value indicates that there is a lot to improve in for the hotel.

Forlocalid="1651776182169">x3, the value 0.124 indicates that since it’s a positive value, the guests are satisfied with air odor/aroma around the hotel, however, a lower value indicates that there is a lot to improve in for the hotel.

Forlocalid="1651776192792" ${\mathbf{x}}_4$, the value 0.119 indicates that since it’s a positive value, the guests are satisfied with music however, a lower value indicates that there is a lot to improve in for the hotel.

Forlocalid="1651776110861" ${\mathbf{x}}_5$, the value 0.101 indicates that since it’s a positive value, the guests are satisfied with air noise level however, a lower value indicates that there is a lot to improve in for the hotel. The hotel can promote noise reducing events and activities around the hotel.

Forlocalid="1651776097046" ${\mathbf{x}}_{\mathbf{6}}$, the value 0.463 indicates that since it’s a positive value, the guests are satisfied with their overall stay at the hotel, a lower value indicates that there is a lot to improve in for the hotel.

Overall, all the beta values are positive indicating a positive impact on their overall stay at the hotel, however the beta values are very low meaning that the hotel has a lot to improve upon.

99% confidence interval for ${\mathbf{β}}_{\mathbf{6}}$ is (0.350, 0.576) meaning that we are sure to conclude that the value of ${\mathbf{β}}_{\mathbf{6}}$ lies within the interval (0.350, 0.576) with 99% accuracy. Even the value of ${\mathbf{x}}_6$ estimate calculated after the research is 0.463 which lies within the interval.

The value of ${\mathbf{R}}^{\mathbf{2}}$ is 0.508 which means that around 50.8% of the variation in the variables is explained by the model. The value of 50.8% is not very high indicating that the model might not be a good fit for the data.

The value of adjusted ${\mathbf{R}}^{\mathbf{2}}$ is 0.501 which means that around 50% variation in the variable is explained by the independent variables. The value indicates that the variables are not the best fit to the data.