Question

and centres are in high demand in Accra due to the limited accommodation facilities for these persons. Government may withdraw from taking care of the costs as expert say that the COVID-19 has come to stay with us similar to other diseases. For this reason, it has become imperative for travellers to carefully plan for their accommodation. Information has been gathered to help travellers predict hotel bill based on the following elements: number of people in a hotel (AA), number of rooms in a hotel (AB), Hotel age (AC), number of beds in a room (AD), Internet connection (AE), Availability of washroom in a room (AF), Distance from hotel to airport (AG) and Traveller type (AH). The study primarily used primary data obtained from 84 travellers sampled for the process. Data was analysed using the correlation and regression analysis. The results from the correlation and regressions analysis are displayed in tables 1 and 2 respectively.
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Table 1: Correlation Analysis of Variables
HB AA AB AC AD AE AF AG AH HB 1 AA .009 1 AB .351” -.069 1 AC -.411” .036 .249” 1 AD .398” .062 .492” .634” 1 AE -.374” .052 .533” .566” .611” 1 AF .021 .035 -.189‟ .141 -.161 -.293” 1 AG .159 .047 .078 .241‟ .559” .329” -.154 1 AH -.071 -.643” -.004 -.185 -.083 -.203‟ .009 .140 1
„Correlation is significant at the 0.05 level
“Correlation is significant at the 0.01 level
Table 2: Regression Result on Hotel Bill (HB)
HB
Variables
Coefficient
Prob.
AA
0.248
0.889
AB
1.936
0.787
AC
-1.696*
0.088
AD
2.629*
0.081
AE
-8.09**
0.046
AF
23.27***
0.000
AG
1.42*
0.086
AH
3.056
0.338
N
84
R-Squared
38
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Adj R-squared
31.4
F-Stats
5.75***
0.000
*, ** and *** indicate significance levels of 0.10, 0.05, 0.01 respectively
Required: Use the information above and the results from tables 1 and 2 to answer the following questions.
a) Identify the dependent and independent variables of the study. (2 marks)
b) Explain why each of the variables you have identified in 3a above is either an independent or dependent variable. (4 marks)
c) To what extent does this study reflect a case study? (2 marks)
d) Identify the variables that were significant at 1% significant level.
e) From the correlation matrix which variable had the weakest correlation? (2 marks)
f) Was the model fit to achieve the objective of the study?
g) How would you interpret the adjusted R-square and R-square values of 31.4 and 38 respectively. (4 marks)
h) Which statistical technique will you advice the travellers to use to achieve the research objective. (4 marks)
i) Propose a suitable title for the study. (2 marks)
j) Formulate the null and alternate hypotheses for this study. (4 marks)
k) Was your hypothesis directional or non-directional? Justify. (2 marks)
l) Draw a conclusion for the study based on your null and alternate hypotheses? (2 marks)
m) What basis did you draw the conclusion in (l) above? (2 marks

Answer 1

Solution: Given is the correlation matrix and the regression analysis

Information has been gathered to help travellers predict hotel bill based on the following elements:

number of people in a hotel (AA),

number of rooms in a hotel (AB),

Hotel age (AC),

number of beds in a room (AD),

Internet connection (AE),

Availability of washroom in a room (AF),

Distance from hotel to airport (AG)

Traveller type (AH).

The study primarily used primary data obtained from 84 travellers sampled for the process. Data was analysed using the correlation and regression analysis.

The results from the correlation is displayed in table below.

variables	HB	AA	AB	AC	AD	AE	AF	AE	AH
HB	1
AA	0.09	1
AB	0.315	-0.069	1
AC	-0.411	0.36	0.249	1
AD	0.398	0.62	0.492	0.634	1
AE	-0.374	0.52	0.533	0.566	0.611	1
AF	0.21	0.35	-0.189	0.141	-0.161	-0.293	1
AG	0.159	0.047	0.078	0.241	0.559	0.329	-0.154	1
AH	-0.71	-0.643	-0.004	-0.185	-0.083	-0.203	0.009	0.14	1

regressions analysis are displayed in table below.

variables	coefficients	probability
AA	0.248	0.889
AB	1.936	0.787
AC	-1.936	0.088
AD	2.629	0.081
AE	-8.09	0.046
AF	23.27***	0
AG	1.42	0.086
AH	3.0156	0.338
N	84
R square	38
Adj r square	31.4
F stat	5.75**
p value	0.0001

a) Identify the dependent and independent variables of the study.

The variables are given as,we have to predict hotel bill based on the following variables. This clearly means that the hotel bil is dependant on multiple variables. Those variables are  number of people in a hotel (AA), number of rooms in a hotel (AB), Hotel age (AC), number of beds in a room (AD), Internet connection (AE), Availability of washroom in a room (AF), Distance from hotel to airport (AG) and Traveller type (AH).

Thus the independant variables are number of people in a hotel (AA), number of rooms in a hotel (AB), Hotel age (AC), number of beds in a room (AD), Internet connection (AE), Availability of washroom in a room (AF), Distance from hotel to airport (AG) and Traveller type (AH).

The dependent variable is hotel bill (HB)
b) Explain why each of the variables you have identified in 3a above is either an independent or dependent variable.

We know that the hotel bill (HB) is reponse variable becouse it is dependant quantity. As the independent veriable changes response variable will change according to the regression coefficient.

The hotel bill depend on how many number of people in a hotel (AA) ,the number of rooms in a hotel (AB), the popularity of  Hotel (AC), how many number of beds in a room (AD), is there an Internet connection (AE), how is the availability of washroom in a room (AF), what is the distance of hotel from airport (AG) and what kind of traveller type (AH) it is.

This is why the independent variales are number of people in a hotel (AA), number of rooms in a hotel (AB), Hotel age (AC), number of beds in a room (AD), Internet connection (AE), Availability of washroom in a room (AF), Distance from hotel to airport (AG) and Traveller type (AH).
c) To what extent does this study reflect a case study?

The sample size is 84 which is enough to assume the asymptotic behaviour of the study. We know that the covid19 is spreding day by day. It may not be sufficient data if the population is tremendous.
d) Identify the variables that were significant at 1% significant level.

We have given a table of regression analysis where *** represents the significance of the variable at 1% los.

The variable Availability of washroom in a room (AF) is significant at 1% significant level.

e) From the correlation matrix which variable had the weakest correlation?

From the correlation matrix AH and AB had the weakest correlation between them which is good.

The weakest correlation with the response variable HB is with AA i.e. number of people in the hotel which is 0.09
f) Was the model fit to achieve the objective of the study?

The F-Stats value is 5.75*** and it is significant at 1% los. Thus the model is fit to achieve the objective of the study.

and the p value = 0.001 < 0.01 = alpha or los also tend to reject H0 (model is not significant)
g) How would you interpret the adjusted R-square and R-square values of 31.4 and 38 respectively.

The R-Squared value is 38 i.e 38% of the variation is explained by the model
Adj R-squared value is 31.4  i.e 38% of the variation is explained by the model.

Usually we prefer Adj R-squared value which is not much good. The value that tend to 1 gives a best model.