Learning outcomes

Real estate industry has become a new economic development point and primary industry in England GDP in the recent past. This paper breaks down the pattern of England real estate series. This report seeks to analyze data on the real estate for different states in England. We look at different measures to try and understand the price of the real estate in England. Among the analysis we looked at include the measures of central tendency, measures of dispersion and the percentiles.

Measures of central tendency include the mean, median and the mode (Benzi & Klymko, 2013). This section seeks to identify the measures of central tendency for the real estate prices for the different series. The measures of central tendency help to see the centrality of the data and to see how the distribution compares (Brandes, 2001).

The table below (table 1) gives the measures of centrality which includes the mean, median and the mode. As can be seen in the table, the average prices ranges from £98,162.69 to £248,259.5. London has the highest average price (M = 248259.5) while North East had the lowest average median prices (M = 98162.69). Also, from the table (table 1), we can see that the median for all the states is greater than the mean. This shows that the datasets are skewed to the left (having longer tail to the left that has low scores pulling the mean down more than the median). The mode as can be seen is also either greater or equal to the media for the series that were found to have a value of the mode.

Table 1: Measures of centrality

In this section we sought to check the dispersion in the dataset, that is, how spread out the data is from the mean (Cho, Cho, & Eltinge, 2005). In terms of measures of dispersion, we observe that London still leads in disparity of the dataset. The standard deviation of the London was 105601.3 with a range of 376500. North East was found to have the least dispersed data having a range of 88500 with a standard deviation of 33317.99.

Table 2: Measures of dispersion

A percentile (or a centile) refers to a measure utilized in insights demonstrating the incentive beneath which a given level of perceptions in a gathering of perceptions falls (Langford, 2006).

Lastly, we also computed the percentiles. The percentile values are given in table 3 below where we can see that there are a lot of disparity from the 0% to 100% percentile for the different states.

• The median was greater than the mean for the all the series. Also the mode was either greater or equal to the median for all the series.
• London has the highest average price (M = 5)while North East had the lowest average median prices (M = 98162.69).
• Dataset for all the series are skewed to the left
• London still leads in disparity of the dataset while North East has the lowest disparity in terms of the dataset.

Measures of centrality

The second part of the question seeks to analyze the graph provided. The information represented in the graph is on the symmetry and skewness of the data. Basically, the plot presents the distribution of the data. We can also tell from the graph that London has the highest average prices for the real estates while North East has the lowest average prices. However, from the graph we cannot tell what the average values are. The reasons why a professional would use this format to present similar data to an audience include the following;

• It is a decent method to abridge a lot of information; Due to the five-number information rundown, a case plot can deal with and present an outline of a lot of information. A box plot comprises of the middle, which is the midpoint of the scope of information; the upper and lower quartiles, which speak to the numbers above and beneath the most noteworthy and lower quarters of the information and the base and greatest information esteems. Sorting out information in a crate plot by utilizing five key ideas is an effective method for managing expansive information unreasonably unmanageable for different diagrams, for example, line plots or stem and leaf plots.
• Displays Outliers; A box plot is one of not very many factual diagram techniques that indicate exceptions. There may be one exception or various anomalies inside a lot of information, which happens both underneath or more the base and most extreme information esteems. By broadening the lesser and more prominent information esteems to a maximum of 1.5 occasions the between quartile run, the crate plot conveys exceptions or cloud results. Any consequences of information that fall outside of the base and most extreme qualities known as anomalies are anything but difficult to decide on a box plot chart.

The limitation of this plot is that original data is not clearly shown in the box plot; also, mean and mode cannot be identified in a box plot. The limitation of not showing original data in the box plot can be overcome by having a histogram that shows the distribution of original data from the lowest data point to the highest data point. The limitation of not able to show the mean and the mode (most frequent) can be overcome by having the bar chart.

The next section which is question 3 seeks to analyze the regression equation. We performed regression equation models for different series.

Regression analysis is a methodology that helps investigate the relationship that exists between two or more variables. As such the method helps predict the dependent (response) variable based on one or more variables called independent (explanatory) variables. Regression analysis between series ‘Earnings England and Wales’ (independent variable axis X) and prices real estate ‘England and Wales’ (dependent variable axis Y);

Regression analysis between series ‘Earnings London’ (independent variable axis X) and prices real estate ‘London’ (dependent variable axis Y);

From the above results, we can see that the value of R-Squared (R²) for the England and Wales series was 0.9646 while that for the London series was 0.8873. Clearly, the R-Squared (R²) for the England and Wales series is higher than that of the London series. The value of R-Squared say for England and Wales series implies that 96.46% of the variation in the dependent variable (prices real estate ‘England and Wales’) is explained by the ‘Earnings England and Wales’ (independent variable axis X). Also, value of R-Squared say for London series implies that 88.73% of the variation in the dependent variable (prices real estate ‘London’) is explained by the ‘Earnings London’ (independent variable axis X).

Considering the magnitude of the relationships between variables, the p-value of the two cases is likely to be small with the England and Wales series expected to be much smaller than the London series. The smaller the p-value the more significant it is. As we can see for the two cases, we observe the p-value to be way smaller than 1% thus we can conclude that the two model series are statistically significant at 1% level of significance.

Measures of dispersion

For question this question (question 4) we sought to represent linear regression graph between the series ‘Earnings London’ (axis X, independent variable) and prices of real estate ‘London’ (axis Y, dependent variable). The graph has included the regression line and R2, and the equation which represents the regression line.

To calculate the expected price in the average price of property in London considering the linear regression equation for a given earning of £37,209 in London, we have the following.

The actual price in London with an Earning of £37,209 was £460,000. The expected price is different from the actual price observed in London because the calculated price is an estimate which is prone to errors.

This part represents question 5 where we sought to investigate the differences in the graphs. The differences in the dataset if the data has been collected from MSIN0154: Statistics for Business Research 7 MSIN0154 2018/19 samples, and not from whole populations (income, real estate price) will entirely depend on the sampling and sampling techniques used. If a random sampling technique was employed to choose on the sample then there is likelihood that the data collected on income, real estate price will not significantly differ for the sample and the population (Meng, 2013). This based on the fact that well-chosen sample has similar attributes to the population where the sample comes from (Lucas, 2012). However, there is possibility of huge differences if the sample is biased. A biased sample will yield biased results and if the results are biased then automatically the results will be different from the population data. The biased results could be larger or smaller than the population dataset. To solve the problem in the differences in the sample and the population, a random sample should be drawn from the population. Random sampling is also referred to as the probability sampling (Shahrokh Esfahani & Dougherty, 2014). Some of the probability sampling that could be used include; simple random sampling, stratified sampling, systematic sampling among other sampling techniques.

Question 6 seeks to investigate the difference in the graphs. Both the two graphs show the relationship between two variables. Figure 2 shows the relationship between competitiveness and income while figure 9 shows the relationship between institutional strength and income. The two graphs are similar in the sense that both shows a positive linear relationship between the variables being tested. However, the difference arises in the strengths of the relationship between the variables in the two graphs. Figure 2 shows that the relationship between competitiveness and income is very strong relationship (r = 0.9055) while figure 9 shows that the relationship between institutional strength and income is a strong relationship (r = 0.7937). The value of R-Squared (R²) in figure 2 is 0.82 while that in figure 9 is 0.63. This shows that figure 2 has a higher R² and as such a large proportion of variation in the dependent variable is explained in figure 2 than in 9. Actually, figure 2 shows that 82% of the variation in the dependent variable is explained by the independent variable in the model while figure 9 shows that 63% of the variation in the dependent variable is explained by the independent variable in the model. The differences shows that results in figure 2 are best to use in predicting the future behaviour of the series unlike figure 9. This is because more of the variation in the dependent variable is explained by factors inside the model in figure 2 unlike in figure 9 where close 37% of the variation in the dependent variable is explained by factors outside the model.

Percentiles

Figure 11 shows the deviation of the data points from the mean while figure 12 shows the deviation of the data points from the regression line. The consequences of choosing descriptive statistics only is that the researcher can only depict the distribution of data and not make inferences of the data. The limitations of graph in figure 11 in relation to graph in figure 12 is that in figure 11 we cannot make predictions which is possible from figure 12 given regression equation.

Looking at the graph in figure 13, we can identify that there is a negative linear relationship between the variables (competitiveness and inequality). The graph shows some significant variation of the data points from the trend line.  From the graph, I could predict the value of R-Squared (R²) in this regression to be medium. I have reached this conclusion based on the way the data points are spread out from the trend line. Had the data points been closer to the trend line then I would have expected the R² to be high and since the data points are also not that widely spread out from the trend lie then the best expected value of R-Squared (R²) would be medium value.

In relation to the regression line given in figure 1 in chapter 2 (page 24), the situation of Venezuela is much off the regression line as compared to India and Chile. However, Chile is closest to the regression line than all the other two countries (Venezuela and India). The results shows that it is more accurate to predict the data values for Chile as compared to that of India or Venezuela. And at the same time, it is more accurate to predict the data values for India as compared to that of Venezuela. The implications for inferences of future behaviour of both variables in Venezuela, India and Chile, taking account of the regression is that prediction of future values of Chile will be close to the actual data values as compared to that of the two other countries (Venezuela and India).

Question 10 is divided into two parts. The first art seeks to investigate the differences in the data points. From the graph in figure 2 we can observe that the competitiveness gap within regions vary a lot. Some regions have highly skewed information on the competitiveness gap. Some of the regions had negatively skewed data on the competitiveness gap while other had positively skewed data on the competitiveness gap. Among the regions with positive skewness include South Asia, Sub-Saharan Africa. Regions such as East Asia and the Pacific, Eurasia, Middle East and North Africa, Latin America and the Caribbean were found to have negative skewness. However, Europe and North America seems to have a normally distributed data on competitiveness gap.

Lastly, we look at the reasons for coloring. The reasons why the dots in the graph have colours (from blue to pink) is to distinguish the different data points for the different countries. The implications of not using these colours in the graph is that it would be difficult to tell which of the data points represents which country and as such it would not be possible to compare the different countries which is the intention of the graph. Hence the graph may end up losing its purpose.

Conclusion

The aim of this report was to break down the pattern of England real estate series. This report sought to analyze data on the real estate for different states in England. We look at different measures to try and understand the price of the real estate in England. Among the analysis we looked at include the measures of central tendency, measures of dispersion and the percentiles. Results showed that there are significant variations in the real estate prices for the various regions.

References

Benzi, M., & Klymko, C. (2013). A matrix analysis of different centrality measures. SIAM Journal on Matrix Analysis and Applications, 36(5), 686–706.

Brandes, U. (2001). A faster algorithm for betweenness centrality. Journal of Mathematical Sociology, 25(4), 163–177. doi:10.1080/0022250x.2001.9990249

Brandes, U. (n.d.). A faster algorithm for betweenness centrality. Journal of Mathematical Sociology, 25, 163–177. doi:10.1080/0022250x.2001.9990249

Cho, E., Cho, M. J., & Eltinge, J. (2005). The Variance of Sample Variance From a Finite Population. International Journal of Pure and Applied Mathematics, 21(3), 387-394.

Langford, E. (2006). Quartiles in Elementary Statistics. Journal of Statistics Education, 14(3), 21-29.

Lucas, S. R. (2012). Beyond the Existence Proof: Ontological Conditions, Epistemological Implications, and In-Depth Interview Research. Journal of Quality, 3(1), 41-52. doi:10.1007/s11135-012-9775-3

Meng, X. (2013). Scalable Simple Random Sampling and Stratified Sampling. Proceedings of the 30th International Conference on Machine Learning (ICML-13), 531–539.

Shahrokh Esfahani, M., & Dougherty, E. R. (2014). Effect of separate sampling on classification accuracy. Journal of Bioinformatics, 30(2), 242–250. doi:10.1093/bioinformatics/btt662