## Introduction

Living in the United Arab Emirates, people are used to getting things quickly. People notice that objects that usually take more time to create are made relatively quicker in the UAE. I have a personal connection for architecture & design and would like to become a designer in the future. I noticed that massive and aesthetically pleasing buildings like the Burj Khalifa get built in six years which to me is very fast for a record holding building. The same interest applies to attractive designs like the Burj Al Arab which was built in around 3 years. I also question myself why and how the age of the building affects the years before it collapses due to the structure of the building. The point of these buildings is not only to be used by people but also amaze and interest people and want to go to them. Ideally, buildings should be up for as long as needed by the manufacturer, but unfortunately that is not always the case. I want to find out if a building that is planned to be taller will remain longer/shorter than a building that is planned to be shorter.

## Plan

I am going to collect data on five buildings that have collapsed. I have used buildings that have collapsed to help show the effect of the height on the age. If I had used well known existing buildings it would not properly show how the height affects the age due to the fact that the building would still be standing. will put together this raw data and then process it with a graph and processed table. I will use excel to do this. I will then analyze it, as well as calculate its Correlation Coefficient to see the correlation between age of a building and its height. Building Country Height before collapse (m) Age when collapsed (in years) Year of accident Għajn Ħadid Tower Malta 12 198 1856 Plaka Greece 18 140 2015 Plasco Building Iran 60 55 2017 World Trade Center United States of America 417 28 2001 Highland Towers Singapore 40 16 1993 Rana Plaza Bangladesh 16 7 2013 Ronan Point United Kingdom 69 1 1968This graph shows me that by looking at it there is a weak/no correlation between the two variables. It shows that the height of a building will have very little/no effect on its age and that there could possibly be other factors involved. The points are far apart from each other, especially the one at the far end of the x-axis. The dispersed points show weak/negative correlation.

## Least Squares Regression Test

The least square regression test is a statistical tool used to find the line of best fit. This line of best fit (or trendline) would help show the correlation of the data and how well x-variable affects the y-variable.

The goal is to get a line using the formula for the data set shown in the graph. The y is a y-value, the x is an x-value, the m is the slope or gradient of the line and the b is the y-intercept of the line. To do this test, you need the squares of each variable as well as both the variables multiplied. This gives us the formula .36715. This is the slope of the regression line. What this line can do is help predict the age of a building if one was being built. For example, if I was going to build a high-rise building and I wanted to see how long it would last, I would plug in the height I was planning on making it. Let’s assume I was going to build a 150-meter building. The height would be my x-value 54.4 would be my y-value, or the amount of years my 150-meter building should last. This is only correct if my formula for prediction is correct and if there are no other factors involved. This is called extrapolation. This is when values outside of the given range are predicted.

This trendline is low and not very steep. Its slope is negative. This shows a weak effect of the height on the age. Also, the steepness of the slope shows a negative and almost weak correlation between the two variables and it reflects how dispersed the points are. However, this test is sensitive to anomalies, such as the one in this data set.

## Pearson’s Product Moment Correlation Coefficient (r)

The Pearson’s Product Moment Correlation Coefficient (sometimes just the Correlation Coefficient) measures strength between variables on a scatter graph. The Pearson’s Product Moment Correlation Coefficient is defined as the variable r. This variable is always less than 1 and more than negative 1. In mathematical terms: where r = 0 means that there is no correlation.

The r value can be calculated by excel or a calculator, or through a formula. This can be translated into Which equates to This R-value of -0.29321 shows us the correlation of the height on the age of the buildings. This value is in between -1 and +1 but is closer to 0 than any of these values. The value is also negative, meaning it has a moderately weak/no correlation. This value tells us that the height of buildings has almost no effect on how long these buildings stood for. It is also an indicator on how well this graph can help us predict and extrapolate results for future buildings. It shows that these set of values are not good at predicting and extrapolating results and should not be used for extrapolation on their own.

## Discussion/Validity

The 2 tools used help show how useful this set of data is and how well they correlate. The data given shows two different variables and by graphing them and analyzing them analytically and algebraically it can be shown that the height of a building does cannot tell you how long that building would last for. The least squares regression test is used in proving this and it gives a line of best fit or trendline. This method works by taking squares of the errors and adding them all up to make sure that the errors are as minimal as possible (which is why it is called least squares regression). This test also takes into consideration any and all anomalies, and by looking at the graph it is easily shown that the point for The Empire State Building is an anomaly. This result is nowhere close to any of the other points and changes the way the future data could be extrapolated. The regression line is usually used to extrapolate data. However, regression lines are not always the best tool for predicting. Factors that cannot be predicted by regression lines can happen which will not have the same results. For example, if one of the buildings crashed due to an internal construction accident, and another collapsed due to a gas leak explosion, the regression line would not be able to predict this and it would be unfit to prove any future examples. Because of this, the line of regression is not a useful method of extrapolation in this example. The Pearson’s Product Moment Correlation Coefficient is an indicator of how well these two sets of data affect each other. The Pearson’s Product Moment Correlation Coefficient for this set of data is negative and very close to 0. The negative part shows that the data is weak but the fact that its closer to 0 than to -1 shows that the data has more of no correlation than it has a weak correlation. This again shows that the height of buildings does not impact their age and that these sets of data have no effect on the other. Through both of these tools, it is clear that for a designer, architect and construction planner it would not benefit any of these jobs to use heights of existing buildings to calculate how long their building would stand for and especially not how safe these buildings would be.

## Conclusion

The results show that two sets of data, regardless of how closely related they may be, cannot always correlate with each other. It is important that in real life, we do not only base our projects on math’s to solve the problem 100%, especially not considering human factors. Math’s should be used as a way to prove the solution to a problem or discover and invent new human advancements. Simple graph plotting and extrapolation cannot be used to predict something so big and should especially not be used to try and affect the safety of people. If someone was to use these calculations as an architect, they would be very lazy and it would be especially hazardous. It is important that safety is a consideration for these designers and that these are all buildings that have failed or collapsed. These statistical tools prove that not everything that is linked can be correlated.