Property Purchase Intentions

Nanyang Technological University
Nanyang Business School |

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AB103 Statistics and Quantitative Methods
Case Study: Property Purchase Strategy

Nupur Gupta

Table of Contents
No. Contents Page Number
1 Introduction 3 1.1 Problem Context 3 1.2 Reasons for choosing 21 Years for Analysis 3
1.3 Other Indicators of Aging 3
2 Data Analysis 4 2.1 Suitability of a Linear Model 4 2.2 Correlation Analysis 4 2.3 Regression Analysis 4 2.4 Hypothesis Testing 5 2.5 Linear Correlation Testing
2.6 Prediction 3 Recommendations and Insights 4 Appendix 8

1. Introduction

2.1. Problem Context

The age structure of a population affects a nation's key socioeconomic issues. Countries with young populations (high percentage under age 15) need to invest more in schools, while countries with older populations (high percentage ages 65 and over) need to invest more in the health sector. The age structure can also be used to help predict potential political issues. For example, the rapid growth of a young adult population unable to find employment can lead to unrest. The age structure also hints business opportunities. For example, an aging population requires more old folk home services.

In this case study, we are doing an analysis on Singapore’s population, from Year 1990 to Year 2010, to examine whether Singapore has symptoms of becoming an aging population. We will then proceed on with recommendations for the situation that Singapore is currently facing.

2.2. Reasons for choosing 21 Years for Analysis

The length of 21 years is suitable for carrying out the analysis because firstly it consists of 2 generations. Thereofre our model can be tested with the passing of 2 generations. Secondly withing the span of 21 years another generation can enter the data thus the model can be further tested. Moreover to get a good aproximate of the coefficient of correlation having data with n > 20 is better.

2.3. Other Indicators of Aging

* Old Age Support Ratio (Refer to Appendix A Fig. 1)

The graph shown indicates the number of residents aged 15-64, who are supporting an elderly resident aged 65 years and over. Over the decades, there is a decrease in the numbers, which actually indicates that there are lesser proportion of the working population and more of the elderly population which needs to be supported by them. Thus, this is another indicator of an aging population because there is an increasingly large number of the elderly.

* Low Birth Rate (Refer to Appendix A Fig. 2)

From the diagram, it is shown that Singapore has one of the lowest birth rates in the world, with 8.99 births per 1000 population. As such, the population growth is significantly small. The proportion of the elderly in the population increases at a faster rate than that of the population growth.

* Life expectancy (Refer to Appendix A Fig. 3)

Another indicator that shows that can possibly indicate aging would be the life expectancy of a country. When the life expectancy is higher, people will tend to live longer and thus there will be more elderly people in the population. Such a trend can effectively contribute to an aging population. From the diagram, Singapore is ranked 3rd with an average life expectancy at birth of 81.89. This would thus indicate that Singapore is likely to experience aging when more of its people can live up to an average age of 82 years old.

2. Data Analysis

3.4. Suitability of a Linear Model

Scattergrams are used to graphically describe a relationship between two variables, x and y. From the scatter plot above, we can see that as x increases, y also increases, so a linear model can be used to reflect the deterministic component of the relationship between x and y. 3.5. Correlation Analysis

The r value of 0.986 indicates a strong positive linear relation between the two variables.

3.6. Regression Analysis

The R2 value represents the proportion of the total sample variability around y that is explained by the linear relationship between y and x. Since the R2 value is 0.97281, it means that the sum of squares of deviations of the y values about the predicted value has been reduced by 97.281% by the use of least squares equation y, instead of y, to predict y.

The p-value is the probability of observing a value for the test statistic that is at least contradictory to the null hypothesis, and supportive of the alternative hypothesis assuming H0 is true. Since the p-value (2.44786E-16) is so small, we can conclude that there is a very small probability of observing the test statistic we obtained, given that H0 is true

3.7. Hypothesis Testing

H0: ϱ =0
Ha: ϱ ≠ 0

Test Statistic: t = r √ n-2 √1-r2
= 24.1155

Rejection region: t > tα or –t < -tα

At α= 0.05 level and df = 21-2=19, tα=1.729

Since the calculated t-value falls into the upper-tail rejection region, we reject the null hypothesis H0 and conclude that the two variables are at least linearly related.

H0: β 1 =0
Ha: β 1 ≠ 0

Test Statistic: t = β1 Sβ1 = β1 s/√SSxx
=26.074

Rejection region: t > tα or –t < -tα

At α= 0.05 level and df = 21-2=19, tα=1.729

Since the calculated t-value falls into the upper-tail rejection region, we reject the null hypothesis H0 and conclude that x does contribute information for the prediction of y using the straight line model.

3.8. Prediction

3. Recommendations

As can be seen by the strong positive correlation between x and y, as calculated in the earlier sections, there will be a larger proportion of the elderly (aged 65 and above) as the time goes by.

A recommended solution would be to increase the birth rate of Singapore so as to reduce the proportion of aged relative to the whole population. The Singapore government can provide more incentives for the married couples to give birth to more children. As compared to only focusing on giving one-off baby bonuses to the couples, the government can choose to adopt the strategies of providing subsidies to the necessities that the couples would require to raise a children. An example would be vouchers to purchase milk powder or diapers. This will help to reduce the cost of raising a child in Singapore generally, increasing the desire to have more children among Singaporeans. The government can also choose to instill the value of having large families into the younger generation through the education system, in hope that they will grow up with a want for more children. However, the effect of these solutions is limited. The past failures of the usage of monetary incentives in increasing the birth rate show that Singaporeans are not only just concerned about the money issue, but also the psychological responsibility that comes along with a child.

Another way to increase the birth rate of Singapore would be to encourage the couples who do not want to give birth (or singles who want children) to adopt children in foreign countries. These foreign-born children can apply for Singapore Citizenship, which will then add on to the proportion of the young in the society. However, this is not a long-term solution for Singapore.

While the above two solutions solve the problem of ageing population in Singapore, the time taken for them to produce significant result is very long. The Singapore government also needs to implement short-run strategies to solve the impeding need to take care of the growing population of elderly in Singapore. An example of a short-term strategy would be to renovate some of the child-care support facilities into elderly-support facilities. On one hand, this can help to provide more healthcare services to the elderly and on the other hand, when the birth rate increases in Singapore in the future, these facilities can conveniently be converted into child-care facilities to cope with the increase in the young.

4. Appendix A

Figure 1- Old Age Support Ratio taken from http://www.singstat.gov.sg/stats/charts/popn-area.html

Figure 2 - Low Birth Rate taken from http://www.aneki.com/lowest_birth.html

Figure 3 - High Life Expectancy taken from http://www.aneki.com/expectancy.html