A researcher wants to investigate the influence of the average no. of nights spent per year by the tourists from Japan on the average amount spent by them. Table 3 shows the related data obtained from the Department of Statistics Malaysia website. Table 4 shows a portion of Microsoft Excel output for the regression analysis performed based on the data in Table 3. Table 3: Data on the nights spent by tourists from Japan and amount spent Year Average no. of nights spent Average amount spent (in RM billion) 2010 5.9 1.1 2011 6.1 1.1 2012 6.1 1.4 2013 6.3 1.5 2014 6.4 1.8 2015 6.1 1.6 2016 6.2 1.3 2017 6.3 1.2 2018 6.6 1.7 2019 6.9 2.3 Table 4: Regression analysis Coefficients Standard Error t Stat P-value Intercept B0 1.4555 -3.7583 0.0056 Average no. of nights spent B1 0.2312 4.7934 0.0014 a. Note that the value of B0 and B1 are missing from Table 4. Using the right formulas, calculate the value of B0 and B1. b. Build the regression equation based on the values calculated in 4(a). c. Interpret the value of B1. d. Based on the p-value in Table 4, at a 95% confidence level, can we conclude that the average no. of nights spent by the tourists from Japan significantly influence the average amount spent by them? e. Estimate the average amount possibly spent by the Japanese tourists in a particular year if an average of 10 nights was spent.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
A researcher wants to investigate the influence of the average no. of nights spent per year by the tourists from Japan on the average amount spent by them. Table 3 shows the related data obtained from the Department of Statistics Malaysia website. Table 4 shows a portion of Microsoft Excel output for the regression analysis performed based on the data in Table 3.
Table 3: Data on the nights spent by tourists from Japan and amount spent
|
Year |
Average no. of nights spent |
Average amount spent (in RM billion) |
|
2010 |
5.9 |
1.1 |
|
2011 |
6.1 |
1.1 |
|
2012 |
6.1 |
1.4 |
|
2013 |
6.3 |
1.5 |
|
2014 |
6.4 |
1.8 |
|
2015 |
6.1 |
1.6 |
|
2016 |
6.2 |
1.3 |
|
2017 |
6.3 |
1.2 |
|
2018 |
6.6 |
1.7 |
|
2019 |
6.9 |
2.3 |
Table 4: Regression analysis
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
|
Intercept |
B0 |
1.4555 |
-3.7583 |
0.0056 |
|
Average no. of nights spent |
B1 |
0.2312 |
4.7934 |
0.0014 |
a. Note that the value of B0 and B1 are missing from Table 4. Using the right formulas, calculate the value of B0 and B1.
b. Build the regression equation based on the values calculated in 4(a).
c. Interpret the value of B1.
d. Based on the p-value in Table 4, at a 95% confidence level, can we conclude that the average no. of nights spent by the tourists from Japan significantly influence the average amount spent by them?
e. Estimate the average amount possibly spent by the Japanese tourists in a particular year if an average of 10 nights was spent.
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