Question

The weekly Hotel bill (HB) per traveller for COVID-19 mandatory quarantine accommodation 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?

Answer 1

Note : Allowed to only 4 questions per post.

a) Identify the dependent and independent variables of the study. (2 marks)

Dependent variable : Hotel Bill (HB)

Independent varibles :
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).

b) Explain why each of the variables you have identified in 3a above is either an independent or dependent variable. (4 marks)

Hotel Bill (HB) is a dependent variables, since we are trying to run a regression and predict the varibles using the other variables. THe value of this variable is an output of a linear equation obtain from the independent variable. Hence any change in any of the independent variables will impact the Hotel Bill

Independent varibles : as the name suggest are not dependent on other variables. Hence they are used to predict the dependent variables. Each of these variables are components of the facilities provided at the hotel. Hence the cost of the room would depend on the facilities provided.

c) To what extent does this study reflect a case study? (2 marks)
In this study,we want to check if the government may withdraw from taking care of the costs that the COVID-19 has come to stay with us similar to other diseases.

Hence to understand this better we are using past data of hotel bills and its components and able to predict the cost. Hence this study reflect a case study as we investigating a conclusion using past data.

d) Identify the variables that were significant at 1% significant level.

For this we check the regression results on Hotel Bill.

We check the Probability column for each variable.

The hypothesis to be tested:

For each variable, we take beta coefficient do test the following hypothesis.

$\\H_0 : \beta_i = 0\\ H_1 : \beta_i \ne 0\\$

We check the pvalue associated with that variable,
if the pvalue is less than 0.01(level of significance specified), then we reject the null hypothesis and conclude that the variable is significant or is statistically different from zero. Hence it is significant predictor of y.

if the pvalue is greater than 0.01(level of significance specified), then we fail to reject the null hypothesis and conclude that the variable is not significant or is not statistically different from zero. Hence it is not significant predictor of y and can be dropped from the regression.

Note : Pvalue is the probability.

In this case we find the probability for Availability of washroom in a room (AF) is significant at 1% significant level

e) From the correlation matrix which variable had the weakest correlation? (2 marks)

For this we check the correlation table and check the correlation values

We see thatn AB and AH has correlation of 0.004 which is the weakest correlation.

f) Was the model fit to achieve the objective of the study?
Model fit is give by the value of rsquare = 38%

g) How would you interpret the adjusted R-square and R-square
values of 31.4 and 38 respectively. (4 marks)

Coefficient of determination(rsqaure) = 38%
It is the measure of the amount of variability in y explained by x. Its value lies between 0 and 1. Greater the value, better is the model. In this case, it 38%, hence the model is bad, as only 38% of the variation in the Hotel bill is explained by all the independent variables collectively.

Adjusted R2 is an improved version of R2, which increases only if a significant variable is added to the model. It penalize the model for every junk or non significant variable that is added to the model.

Hence Adjusted R2 gives the true fit of the model after adjusting for the unwanted variables or non significant variables.