Inferential Analysis

For this section, we employ statistical techniques to perform inferential analysis. Inferential analysis aims to draw conclusions and make predictions about a population based on a sample of data taken from that population. It involves using statistical techniques to estimate population parameters, test hypotheses, and make predictions. Inferential analysis is used to infer qualities about a larger population based on a sample and to determine the probability of those inferences being accurate.

Significance: An important term to note in inferential statistics, "significance" typically refers to the likelihood that a result or relationship observed in a data sample is not due to random chance. Significance level (p-value) is usually <0.05 (5%).

Two-Way ANOVA: Basically, this technique examines how two different independent variables, individually or together, affect a dependent variable i.e., factors that result in an observation. These independent variables may moderate each others effect i.e., both factors may result in a more pronounced effect on the resultant observation as compared to examining each factor individually.

Example: To illustrate this, we can examine the popularity (dependent variable) of a student amongst his/her classmates according to whether he/she is cooperative (independent variable 1) and whether he/she is well-liked by teachers (independent variable 2). If we observe popularity just based on the student being cooperative, we will intuitively think that being cooperative will result in the student being more popular. On the other hand, if we observe popularity just based on the student being a teacher's pet, we will probably think that the student is not that popular amongst his/her classmates. Through two-way ANOVA, we can then compute the resultant popularity of the student by examining how these two factors interact with each other and probably the teacher's pet may not be as popular even if he/she is cooperative (oops!).

Tool: SPSS

New launch buyers earn MORE than re-sale buyers. Are there any factors that will further moderate the difference?

In the descriptive analysis section, we concluded that new launch buyers (transaction 2) earn more than re-sale buyers (transaction 3). Will other factors such as District and Level influence the price differences further? We have applied two-way ANOVA to test and explore the significance of the interactions between District x Transaction no., Level x Transaction no., and Tenure Category x Transaction no..

1. District x Transaction no. Analysis

Between-Subjects Effects

A two-way ANOVA was conducted to explore the impact of 'PostalDistrict' and 'Transactionnumber' on P/L (%). The analysis revealed significant main effects for both 'PostalDistrict' (F(26, 108433) = 54.928, p < .001) and 'Transactionnumber' (F(1, 108433) = 231.861, p < .001), indicating that the P/L (%) varies significantly across postal districts and between transaction numbers.

The interaction between 'PostalDistrict' and 'Transactionnumber' was also significant (F(26, 108433) = 8.849, p < .001), suggesting that the impact of 'Transactionnumber' on P/L (%) differs depending on the postal district.

Effect Size

The effect size for the model, indicated by the adjusted R-squared value, is 0.042. This means that approximately 4.2% of the variance in P/L (%) is accounted for by the combined effects of 'PostalDistrict' and 'Transactionnumber' and their interaction.

Estimated Marginal Means

The line plots for the estimated marginal means of P/L (%) indicate that there is a general trend for transaction number 2 to have higher P/L (%) across all postal districts, although there are variations in this pattern, as evidenced by the significant interaction. The interaction plot shows that the slopes of the lines representing each postal district are not parallel, confirming the presence of an interaction effect.

Inferences

The results suggest that both the postal district and the transaction number are significant predictors of P/L (%), with an additional significant interaction between these two factors. The variability in P/L (%) across different postal districts may reflect geographical differences that affect transactions. The significant interaction effect implies that the effect of the transaction number on P/L (%) is not uniform across postal districts, indicating that certain districts may perform differently as the transaction number changes.

Districts 6, 7, 8, 22 and 26 yielded the most differences between transaction 2 and 3, while Districts 13, 14 and 28 yielded the lowest differences.

In other words, second buyers for districts 13, 14 and 28 still retain similar profits to new launch buyers despite not buying the property at new launch. Conversely, properties in districts 6, 7, 8, 22 and 26 fall into the other extreme end.

2. Level x Transaction no. Analysis

Data

To segregate the levels into "Low", "Middle" and "High", a summary was derived before categorising the levels accordingly.

Summary:

count 107970.000000

mean 9.001334

std 7.663597

min 1.000000

25% 4.000000

50% 7.000000

75% 12.000000

max 71.000000

Name: Level, dtype: float64

Categorisation:

Low: Values from the minimum up to (but not including) the 25th percentile - 1 to 3 (since 4 is the start of the 25th percentile)
Middle: Values from the 25th percentile up to (but not including) the 75th percentile - 4 to 11 (since 12 is the start of the 75th percentile)
High: Values from the 75th percentile up to the maximum - 12 and above

Between-Subjects Effects

A two-way ANOVA was conducted to examine the effect of 'LevelCategorised' and 'Transactionnumber' on P/L (%). The analysis revealed a significant main effect of 'LevelCategorised' (F(2, 108486) = 13.330, p < .001), indicating that the mean P/L (%) significantly differs across the levels of categorization. There was also a significant main effect of 'Transactionnumber' (F(1, 108486) = 1772.078, p < .001), suggesting that the transaction number significantly affects the P/L (%).

However, the interaction effect between 'LevelCategorised' and 'Transactionnumber' was not statistically significant (F(2, 108486) = 1.406, p = .245). This suggests that the effect of 'LevelCategorised' on P/L (%) does not significantly differ across transaction numbers 2 and 3.

Effect Size

The effect size for the model, as indicated by the adjusted R-squared value, is 0.018. This suggests that approximately 1.8% of the variance in P/L (%) can be explained by the model, which includes 'LevelCategorised', 'Transactionnumber', and their interaction.

Estimated Marginal Means

The parallel lines in the interaction plot indicate a lack of interaction, consistent with the statistical test, implying that the trend of P/L (%) change between transactions 2 and 3 is similar across all levels.

Inferences

The results suggest that both the level and the transaction number independently affect the P/L (%), with higher P/L (%) associated with transaction number 2 across all levels.

For level, contrary to common belief that High levels will yield higher profits, it is the Low and Middle levels that yield better profits. This is especially so for the first buyers i.e., transaction 2.

The lack of a significant interaction indicates that the relationship between the level and P/L (%) is similar regardless of the transaction number.

So if you are focused on making better profits, regardless of whether new launch or second-hand, low and middle floors are more desirable.

3. Tenure Category x Transaction no. Analysis

Between-Subjects Effects

A two-way ANOVA was performed to determine the effects of tenure category and transaction number on P/L (%). There were significant main effects for tenure category (F(2, 108482) = 49.389, p < .001) and transaction number (F(1, 108482) = 1954.114, p < .001), indicating that both factors independently affect P/L (%).

The interaction effect between tenure category and transaction number approached significance (F(1, 108482) = 3.547, p = .060), suggesting a trend where the effect of tenure category on P/L (%) may differ between transaction numbers, although this trend did not reach conventional levels of statistical significance.

Effect Size

The adjusted R-squared value is 0.019, indicating that approximately 1.9% of the variance in P/L (%) is explained by the tenure category, transaction number, and their interaction.

Estimated Marginal Means

The interaction plot shows the estimated marginal means of P/L (%) for each combination of tenure category and transaction number. The plot indicates that for both Freehold and Leasehold categories, P/L (%) is higher for transaction number 2 compared to transaction number 3. The parallel lines in the interaction plot suggest that the trend is similar for both tenure categories, aligning with the statistical findings of a non-significant interaction effect.

Inferences

The results indicate that both the tenure category and the transaction number significantly influence P/L (%), with transaction number 2 associated with higher P/L (%) in both Freehold and Leasehold categories. The lack of a statistically significant interaction suggests that the relative difference in P/L (%) between transaction numbers 2 and 3 is consistent regardless of whether the property is Freehold or Leasehold.

Thus, regardless of new launch or second-hand sales, freehold properties are still more profitable as established in the descriptive analysis section.

* Caveat: Analysis does not consider factors such as holding period, unit layout, development size etc.