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Old January 19th, 2010, 10:50 PM   #1
wjfox
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Skyscraper heights, 1900 - 2100 AD

This is something I created today for my website. It took hours to draw. It shows the tallest completed buildings each year, from 1900 until the present day... plus some additional planned towers for 2011-2016.

Those marked in red are the ones which set a new record (e.g. Empire State Building, Sears, Petronas, Burj Dubai).

Anyway, I'm trying to extrapolate a trend from this data, to calculate the most likely heights for 2017-2100. It's proving very difficult though. Does anybody know how I can do this? Is there some statistical method I could use to make it as accurate as possible? Should I include the record breakers in red, or do they bias the results by "inflating" the average height? Any help would be greatly appreciated...



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Old January 20th, 2010, 04:37 AM   #2
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If you could get me the raw data (Each year with the corresponding height) I could probably use statistical software that I have come up with a prediction for the heights of the next few years. Of course, that just takes raw data given, determines a trend and produces predictions. It doesn't take into consideration any other factors (like the current economic climate) so it would probably not be very valid.
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Old January 20th, 2010, 10:34 AM   #3
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This is fantastic. It's really interesting to note the overall decline in building heights between the 1930'3 and the 1970's.
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Old January 20th, 2010, 01:44 PM   #4
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Quote:
Originally Posted by 540_804 View Post
If you could get me the raw data (Each year with the corresponding height) I could probably use statistical software that I have come up with a prediction for the heights of the next few years. Of course, that just takes raw data given, determines a trend and produces predictions. It doesn't take into consideration any other factors (like the current economic climate) so it would probably not be very valid.

Thanks! I would greatly appreciate that. I will even credit you on my site, if you want.

Which software will you use?

Anyway, here's the raw data:


Year ... Height

1901 ... 167m
1902 ... 105m
1903 ... 96m
1904 ... 73m
1905 ... 111m
1906 ... 104m
1907 ... 104m

1908 ... 187m
1909 ... 213m

1910 ... 117m
1911 ... 129m
1912 ... 164m

1913 ... 241m
1914 ... 177m
1915 ... 164m
1916 ... 129m
1917 ... 132m
1918 ... 66m
1919 ... 161m
1920 ... 88m
1921 ... 127m
1922 ... 117m
1923 ... 131m
1924 ... 159m
1925 ... 141m
1926 ... 165m
1927 ... 145m
1928 ... 188m
1929 ... 198m

1930 ... 319m
1931 ... 381m

1932 ... 259m
1933 ... 259m
1934 ... 163m
1935 ... 156m
1936 ... 180m
1937 ... 163m
1938 ... 143m
1939 ... 111m
1940 ... 108m
1941 ... 61m
1942 ... 80m
1943 ... 131m
1944 ... 45m
1945 ... 122m
1946 ... 91m
1947 ... 149m
1948 ... 110m
1949 ... 135m
1950 ... 156m
1951 ... 159m
1952 ... 154m
1953 ... 182m
1954 ... 138m
1955 ... 183m
1956 ... 174m
1957 ... 147m
1958 ... 179m
1959 ... 168m
1960 ... 215m
1961 ... 248m
1962 ... 188m
1963 ... 246m
1964 ... 228m
1965 ... 198m
1966 ... 192m
1967 ... 223m
1968 ... 215m
1969 ... 344m
1970 ... 256m
1971 ... 229m

1972 ... 417m
1973 ... 346m
1974 ... 442m
1975 ... 296m
1976 ... 262m
1977 ... 279m
1978 ... 240m
1979 ... 225m
1980 ... 230m
1981 ... 234m
1982 ... 305m
1983 ... 302m
1984 ... 233m
1985 ... 284m
1986 ... 280m
1987 ... 269m
1988 ... 275m
1989 ... 310m
1990 ... 305m
1991 ... 271m
1992 ... 309m
1993 ... 296m
1994 ... 238m
1995 ... 280m
1996 ... 325m
1997 ... 348m

1998 ... 452m
1999 ... 283m
2000 ... 311m
2001 ... 310m
2002 ... 302m
2003 ... 407m

2004 ... 509m
2005 ... 323m
2006 ... 300m
2007 ... 319m
2008 ... 489m
2009 ... 357m

2010 ... 828m
2011 ... 595m
2012 ... 412m
2013 ... 541m
2014 ... 642m
2015 ... 640m

2016 ... 1001m
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Old January 20th, 2010, 08:09 PM   #5
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Hey, thanks for the data.

The software I'm using is called Minitab. There is a free trial on their website if you are interested.

Anyway, I came up with 2 possible equations that you can use to 'predict' the heights of future scrapers for each year. They go from least complex, to most complex (and thus, least 'accurate' to most 'accurate').

1. Height (in meters) = - 6015 + 3.20(Year).


Just insert the year into the parenthesis and it should give you a prediction of the height of the tallest built in that year.

For instance, for 2017, "Height" = -6015 + 3.2(2017).
That means, the tallest in 2017 is predicted to be 439.4m. The 95% prediction interval is 220.83m to 640.34m, which roughly means that, if the equation is valid, then we can predict with 95% certainty that the tallest built in 2017 will be between 221 and 640m tall.

Of course, as I said, this formula was the most basic and probably least valid of the two that I came up with.

2. Height= 197504 - 204.7 (year) + 0.05307 (year)**2, where "**2" means, 'squared'

So for 2017, the prediction would be 528.19m
2018=537.63m
2019=547.17m
2020=556.83m

Its probably the better predictor equation than the other, but its not even close to being a perfect model.

The reason it seems so far off is that the model predicts height solely on the basis of the year in which is was built. It doesn't take into account anything like future economic developments, advancements in technology, etc. Additionally, this formula takes into account all of the data you have given me. It creates a model out of the increase in heights over the entire span of 1910-2016. The heights of the towers increased at a faster rate between 2010-2016 than they did as an historical average

Also, according to the software, if the equation is valid, only ~60% of the change in height of skyscrapers can be attributed to the year. The other 40% is either just random variation or, most likely, other factors.

But, something else to consider. If you look at the graph, you notice that the exponential increase in the height of buildings that occurred between 2006 and 2015 coincided with the global real estate boom. That being said, the idea that the tallest towers of 2018-2020 are shorter than in the previous years is not completely far-fetched.

Summary: Basically, the bottom line is that the data leaves out too many factors to come up with any type of valid conclusions. There is just too much uncertainty. But I tried. lol.

BTW, you don't have to credit me. I would hate to get credit for something only to find out my statistical analysis was a bit off. LOL
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Old January 23rd, 2010, 06:55 AM   #6
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I took the liberty of creating a lengthy list of all the tallest buildings constructed each year from 1900 to 2010.

1900-North American Building, Philadelphia
1901-Philadelphia City Hall*
1902-Land Title and Trust Building Annex, Philadelphia
1903-Hanover National Bank Building, New York/Club Quarters Downtown Hotel, New York
1904-St. Regis Hotel, New York
1905-One Times Square, New York
1906-Minneapolis City Hall
1907-United States Express Company Building, New York City
1908-Singer Building, New York*/Bell Telephone Annex Building, Philadelphia
1909-Metropolitan Life Insurance Company Tower, New York*
1910-Liberty Tower, New York
1911-Whitehall Building Annex, New York
1912-Bankers Trust Company Building, New York
1913-Woolworth Building, New York*
1914-Municipal Building, New York
1915-Equitable Building, New York
1916-Adams Express Building, New York
1917-Bush Tower, New York
1918-19th East 40th Street, New York
1919-Travelers Tower, Hartford
1920-Garment Center South Building, New York
1921-Crown Bank Building, New York
1922-Wrigley Building, New York
1923-Magnolia Building, Dallas
1924-Chicago Temple Building
1925-Chicago Tribune Tower
1926-Ritz Tower, New York
1927-Sherry Netherland Hotel, New York
1928-Penobscot Building, Detroit
1929-Chanin Building, New York
1930-Chrysler Building, New York*
1931-Empire State Building, New York*
1932-70 Pine Street, New York
1933-RCA Building, New York
1934-Field Building, Chicago
1935-International Building, New York
1936-Thurgood Marshall United States Courhouse, New York
1937-Cathedral of Learning, Pittsburgh
1938-Hampshire House Hotel, New York
1939-Hotel Vancouver
1940-Terrazza Martini Tower, Genoa
1941-The Capitol, Jersey City
1942-Prudential Building, Newark
1943-Mercantile National Bank Building, New York
1944-Bureau of Citizenship and Immigration Building, San Francisco
1945-The Tower at the Central Station of Rio de Janeiro
1946-Torre Contigo, Mexico City
1947-John Hancock Tower, Boston
1948-Edificio CBI Espalnada, Sao Paulo
1949-100 Park Avenue, New York
1950-1407 Broadway, New York
1951-US Steel and Mellon Building, Pittsburgh
1952-The Building on Kotelnicheskaya Enbankment, Moscow
1953-Moscow State University
1954-Republic Center Tower I, Dallas
1955-One Prudential Plaza, Chicago
1956-Latin American Tower, Mexico City
1957-Torre de Madrid
1958-1271 Avenue of the Americas, New York
1959-Southland Center, Dallas
1960-270 Park Avenue, New York
1961-One Chase manhattan Plaza, New York
1962-Place Ville-marie, Montreal
1963-Pan Am Building, New York
1964-Prudential Tower, Boston
1965-Richard J. Daley Center, Chicago
1966-Home Insurance Plaza, New York
1967-TD Tower, Toronto
1968-General Motors Building, New York
1969-John Hancock Center, Chicago
1970-United States Steel Tower, Pittsburgh
1971-One Shell Plaza, Houston
1972-One World Trade Center, New York*/Transamerica Pyramid, San Francisco
1973-Two Torld Trade Center, New York/Standard Oil Building, Chicago
1974-233 South Wacker Drive, Chicago*
1975-First Canadian Place, Toronto
1976-Water Tower Place, Chicago
1977-Citigroup Center, New York
1978-Sunshine 60, Chicago
1979-Parque Central East Tower, Caracas
1980-Enterprise Plaza, Houston
1981-Three First National Plaza, Chicago
1982-JPMorgan Chase Tower, Houston
1983-Williams Tower, Houston
1984-Wachovia Financial Center, Miami
1985-Columbia Center, Seattle
1986-Overseas Union Bank Center, Singapore
1987-One Liberty Place, Philadelphia
1988-Scotia Plaza, Toronto
1989-Library Tower, Houston
1990-Bank of China Tower, Hong Kong
1991-Key Tower, Cleveland
1992-Central Plaza, Hong Kong
1993-Landmark Tower, Yokohama
1994-Empire Tower, Kuala Lumpur
1995-United Overseas Bank Plaza, Singapore
1996-Shun Hing Square, Shenzhen
1997-CITIC Plaza, Guangzhou
1998-Petronas Towers, Kuala Lumpur*
1999-Cheung Kong Centre, Hong Kong
2000-Emirates Office Tower, Dubai
2001-Menara Telekom, Kuala Lumpur
2002-Kingdom Centre, Riyadh
2003-Two International Finance Centre, Hong Kong
2004-Taipei 101*
2005-Q1 Tower, Gold Coast
2006-Aspire Tower, Doha
2007-Nina Tower, Hong Kong
2008-Shanghai World Fnancial Center
2009-Trump International Hotel & Tower Chicago
2010-Burj Khalifa, Dubai*
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Old February 1st, 2010, 12:40 PM   #7
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Quote:
Originally Posted by 540_804 View Post

2. Height= 197504 - 204.7 (year) + 0.05307 (year)**2, where "**2" means, 'squared'

Thanks for this. However, I need to know the exact arrangement/grouping of calculations, since there are various different ways of inputting the numbers (if you see what I mean). Could you possibly repost this in a simpler way, e.g. one line for each calculation/grouping... or even better, just describe each step in sentence form. Thanks.
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Old February 2nd, 2010, 09:42 PM   #8
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Quote:
Originally Posted by wjfox View Post
Thanks for this. However, I need to know the exact arrangement/grouping of calculations, since there are various different ways of inputting the numbers (if you see what I mean). Could you possibly repost this in a simpler way, e.g. one line for each calculation/grouping... or even better, just describe each step in sentence form. Thanks.
I'm not 100% sure what you are asking but:

197504
minus
the product of 204.7 and the year (204.7 x year)
plus the product of 0.5307 and the squared year (0.05307 x Year^2)

The number you get should be the predicted height in meters
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Old February 3rd, 2010, 01:33 AM   #9
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What about my list? It took me over an hour to make that list of the tallest skyscrapers' names to complement the raw data on wjfox's post.
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Old February 3rd, 2010, 12:15 PM   #10
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Quote:
Originally Posted by 540_804 View Post
I'm not 100% sure what you are asking but:

197504
minus
the product of 204.7 and the year (204.7 x year)
plus the product of 0.5307 and the squared year (0.05307 x Year^2)

The number you get should be the predicted height in meters
Thanks, that's exactly what I meant.

I'll have the new graph ready this evening or tomorrow.

Btw, is it possible you could do a trend/calculation that excludes the values from 2006 onwards? This might improve the accuracy. As you said earlier -

something else to consider. If you look at the graph, you notice that the exponential increase in the height of buildings that occurred between 2006 and 2015 coincided with the global real estate boom. That being said, the idea that the tallest towers of 2018-2020 are shorter than in the previous years is not completely far-fetched.
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Old February 3rd, 2010, 12:20 PM   #11
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Quote:
Originally Posted by Jim856796 View Post
What about my list? It took me over an hour to make that list of the tallest skyscrapers' names to complement the raw data on wjfox's post.
Well, that's great but... I don't see how it's relevant here. We are discussing a mathematical graph/trend.
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Old February 4th, 2010, 02:16 PM   #12
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Did I forgert to put in the heights of the buildings? You put in the heights of the buildings, I hasd identified all of the buildings with those heights using skyscraperpage.com.
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Old February 5th, 2010, 01:28 AM   #13
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found this on Ctbuh, thought it was interesting.
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Old February 11th, 2010, 10:47 PM   #14
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Quote:
Originally Posted by 540_804 View Post

2. Height= 197504 - 204.7 (year) + 0.05307 (year)**2, where "**2" means, 'squared'

Okay, here it is. Like I said though, it would be better if we excluded the data for 2006-2016. Also, I think it would make sense to exclude everything before 1940. If you look at 1900-1939, there isn't really a trend there. However, there is a much clearer trend between 1940-2005... The future projection might be more accurate if we focussed on just this range. Could you possibly resupply a formula/calculation based on what I've just described? I'd really appreciate it.



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Old February 11th, 2010, 11:08 PM   #15
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The graph looks pretty nice.

When I get the chance I'll try to come up with an equation using 2006-2016 and 1940-2005.
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Old February 11th, 2010, 11:19 PM   #16
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On second thoughts, could you do 1940-2009?

It might make sense to include a couple of the towers in the property boom. China for example is in the process of becoming industrialised, has a massive population, and is likely to see many additional towers on the scale of SWFC (2008).

However, I think Burj Dubai and the 1km tower in Kuwait (and some of the other towers currently U/C in Dubai) are so ridiculous that they're going to really skew the data.

In other words, please use only the following data -



1940 ... 108m
1941 ... 61m
1942 ... 80m
1943 ... 131m
1944 ... 45m
1945 ... 122m
1946 ... 91m
1947 ... 149m
1948 ... 110m
1949 ... 135m
1950 ... 156m
1951 ... 159m
1952 ... 154m
1953 ... 182m
1954 ... 138m
1955 ... 183m
1956 ... 174m
1957 ... 147m
1958 ... 179m
1959 ... 168m
1960 ... 215m
1961 ... 248m
1962 ... 188m
1963 ... 246m
1964 ... 228m
1965 ... 198m
1966 ... 192m
1967 ... 223m
1968 ... 215m
1969 ... 344m
1970 ... 256m
1971 ... 229m

1972 ... 417m
1973 ... 346m
1974 ... 442m
1975 ... 296m
1976 ... 262m
1977 ... 279m
1978 ... 240m
1979 ... 225m
1980 ... 230m
1981 ... 234m
1982 ... 305m
1983 ... 302m
1984 ... 233m
1985 ... 284m
1986 ... 280m
1987 ... 269m
1988 ... 275m
1989 ... 310m
1990 ... 305m
1991 ... 271m
1992 ... 309m
1993 ... 296m
1994 ... 238m
1995 ... 280m
1996 ... 325m
1997 ... 348m

1998 ... 452m
1999 ... 283m
2000 ... 311m
2001 ... 310m
2002 ... 302m
2003 ... 407m

2004 ... 509m
2005 ... 323m
2006 ... 300m
2007 ... 319m
2008 ... 489m
2009 ... 357m



Thanks again!
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Old May 10th, 2010, 11:34 PM   #17
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Bump. Is there anyone who can help me with this?

I'd really appreciate it.
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Old May 11th, 2010, 02:28 AM   #18
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With out meaning to piss on anyones parade but given the inputs you'll be just as accurate getting a ruler and drawing a straight line at an angle which best fits what ever answer you want to get....

I realise I'm being negative, but thats all I can be for this scenario!
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Old May 11th, 2010, 04:38 AM   #19
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Awesome thread, though one thing. Q1's (2005's tallest building, iirc) spire height is 323m (I believe you've included spire height for Burj Khalifa and Taipei 101?).
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Old May 14th, 2010, 11:24 PM   #20
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Well, I was really hoping somebody could help...

*looks at 540_804*

... so that I could produce a more accurate trend line.

As explained in post #16, I'd like to run the data again, using just the 1940-2009 range. If anyone knows Mini Tab, or has any other statistical software and could help, I'd be *really* grateful.


Quote:
Originally Posted by Dimethyltryptamine View Post
Awesome thread, though one thing. Q1's (2005's tallest building, iirc) spire height is 323m (I believe you've included spire height for Burj Khalifa and Taipei 101?).
Thanks. I'll edit the data list.
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