Historical Temperatures Trends

In this project we will look at historical temperature records for several cities and use statistical methods to determine whether the data shows any significant patterns or trends in temperature over time.

The SPSS data file for the project, TempRecs.sav is posted on Piazza along with Excel version. The file contains the Annual Average Temperature records for two cities: New York, USA and Sydney, Australia. For each year, the annual average temperature value is calculated by averaging high temperature readings from every day of the year, observed in a specific location, Central Park for New York and Observatory Hill for Sydney.

In the project data file, three variables are recorded for each data point: the year ("year"), the Annual Average Temperature for Sydney ("Sydtemp"). The data are sorted by year in ascending order. For your convenience, Sydney temperatures have been converted to Fahrenheit.

Original data sources:

http://www.erh.noaa.gov/okx/climate/records/monthannualtemp.html (for NYC)

http://www.bom.gov.au/jsp/ncc/cdio/weatherData/av?p_nccObsCode=36&p_display_type=dataFile&_startYear=&p_c=&p_stn_num=066062 (for Sydney)

Exercise 1

a) Use SPSS to produce a scatterplot of the temperatures for New York City using the "year" as

x-axis.

b) Provide a paragraph describing whether you see any trends or patterns in the data from your

graph.

c) Produce a similar plot for Sydney.

d) In a paragraph, describe what you see for that city.

e) Describe any similarities and/or differences you observe between Sydney and New York City.

Extra Credit:

Online, find the temperature records for the city of your choice, the records have to go back at least 120 years. In one sentence, explain why you chose this specific city. Repeat Exercise 1 for your city.

Exercise 2

a) Use SPSS to find summary measurements for the annual average temperatures in New York

City over the entire recorded period (1869-2013): min, max, mean, median, mode, and

standard deviation.

Identify the hottest year and the coldest year.

b) Use SPSS to make a boxplot of the data set.

c) Repeat this exercise for the historical temperature values in Sydney.

d) a paragraph describing how the two cities differ in temperature. Hint: Base your answer

on any notable differences you observe in the two Box Plots.

Extra Credit: Repeat Exercise 2 for the city of your choice.

Exercise 3

a) Use SPSS to obtain the frequency distribution histogram of the annual average temperatures in

New York City. Describe the "shape" of the distribution.

b) Repeat the process for Sydney, using the same class limits you had for New York City.

c) In a paragraph, describe any similarities and differences you observe between the shapes of

the two distributions and interpret the meaning of these differences.

Extra Credit: Repeat Exercise 3 for the city of your choice.

Exercise 4A

Limit your attention to the most "recent" temperature data, (which we define as years 1990-2103), for New York City. Answer the following questions:

a) For how many years during the recent period, did the annual temperature rise above the

historical mean calculated for the entire period? Does this represent a reasonable, relatively

large or relatively small percentage of the recent years?

b) Of the 25 warmest years in recorded history, what percentage occurs during the recent period?

Do you think the recent period has more or less than its fair share of warmest years?

(Hint: It may help to re-sort the data according to the temperature).

c) Is the mean temperature for the recent period higher or lower than that of the entire period?

Calculate the z-score for the recent mean based on the mean and standard deviation for the

entire period. What does the value of the z-score tell you about the difference between the two

means?

d) Draw a Box plot for the recent years and place it next to the Box Plot obtained from the data

corresponding to the years prior to 1990. Are there any noteworthy differences between the

two?

e) Write a paragraph to summarize your findings: are New York city temperatures notably

different in recent times from what they were in the earlier part of the observation period. In

what way?

Exercise 4B

Repeat the process for Sydney

Extra Credit: Repeat Exercise 4 for the city of your choice.

Exercise 5A

a) Use a statistical package to find the value of the linear correlation coefficient between "year"

and "NYCtemp".

b) Is the correlation significant? Explain the reason for your answer.

c) If the correlation is significant, what does it imply about the trend in temperatures?

d) Find the equation for the least square regression (LSR) line.

e) Interpret the meaning of the slope of the LSR line.

f) Based on the equation of the LSR line, what is the best "predicted" value for the NYC Annual

Average Temperature for 2013? How accurate is the prediction?

g) Can we use this LSR line equation to predict the Annual average Temperature for the future?

Explain.

h) Write a paragraph to summarize your findings: Is there statistically significant evidence of any

pattern or trend in temperature over the observation period in NYC?

Exercise 5B: Repeat the process for Sydney.

Extra Credit: Repeat Exercise 5 for the city of your choice.

Exercise 6

Does your analysis of the historical temperature data for several cities, provide evidence for

the existence of the temperature increasing trend around the world? Why or why not?

Include a graph or char to support your claim.

Based on your analyses, can you conclude whether the Global Warming is occurring? Why or why not?

NEW YORK CITY TEMPERATURES

Year temp Year temp Year temp Year temp

1869 51.4 1914 51.1 1959 54.6 2004 74.1

1870 53.6 1915 52.2 1960 53.1 2005 74.1

1871 51.1 1916 51.1 961 53.9 2006 73.6

1872 51 1917 49.7 1962 52.4 2007 72.9

1873 51 1918 52.1 1963 52.5 2008 71.8

1874 51.3 1919 52.8 1964 53.5 2009 73.2

1875 49.4 1920 51.7 1965 53.1 2010 72.7

1876 51.9 1921 54.4 1966 53.9 2011 72.7

1877 52.8 1922 52.8 1967 51.9 2012 72.9

1878 53.6 1923 52 1968 53 2013 74.4

1879 52.3 1924 51.1 1969 53.7

1880 53.2 1925 52.7 1970 53.2

1881 52.4 1926 50.2 1971 54.1

1882 52 1927 52.6 1972 53

1883 50.5 1928 52.7 1973 55.3

1884 52.4 1929 53.2 1974 54.2

1885 51.1 1930 53.7 1975 54.4

1886 51 1931 55.1 1976 52.8

1887 50.9 1932 54.3 1977 53.4

1888 49.3 1933 53.5 1978 52

1889 52.7 1934 52 1979 54.1

1890 52.7 1935 52.3 1980 53.6

1891 53.8 1936 52.6 1981 53.9

1892 51.9 1937 53.5 1982 53.5

1893 50.4 1938 54 1983 54.7

1894 52.8 1939 53.5 1984 54.1

1895 51.3 1940 50.7 1985 54.2

1896 51.7 1941 53.6 1986 54.2

1897 51.6 1942 52.8 1987 54.3

1898 53 1943 52.6 1988 54

1899 52 1944 53.4 1989 53.2

1900 52.4 1945 53 1990 56.4

1901 50.6 1946 54.2 1991 56.4

1902 51.2 1947 52.8 1992 53.1

1903 51.2 1948 53 1993 54.7

1904 48.7 1949 55.9 1994 54.4

1905 51.2 1950 52.6 1995 54.4

1906 52.7 1951 54 1996 53.7

1907 50.4 1952 54.8 1997 54.3

1908 52.5 1953 56 1998 57.1

1909 51.4 1954 53.9 1999 56.5

1910 51 1955 53.9 2000 53.8

1911 52.2 1956 52.7 2001 56.2

1912 51.7 1957 54.7 2002 56.4

1913 53.9 1958 51.8 2003 53.4

SIDNEY TEMPERATURES

Year temp Year temp Year temp Year temp

1859 70.5 1905 69.6 1951 71.2 1997 72.3

1860 68.8 1906 70.7 1952 70.7 1998 72.9

1861 69.6 1907 70.5 1953 71.1 1999 71.8

1862 70.5 1908 70.3 1954 71.1 2000 72.9

1863 69.8 1909 70 1955 71.2 2001 73.6

1864 69.1 1910 70.5 1956 70.9 2002 73.6

1865 71.1 1911 70.3 1957 71.8 2003 72.9

1866 70.3 1912 70.5 1958 72 2004 74.1

1867 71.2 1913 70.9 1959 71.2 2005 74.1

1868 70.5 1914 71.6 1960 70.9 2006 73.6

1869 70 1915 71.4 1961 71.2 2007 72.9

1870 69.3 1916 70 1962 71.4 2008 71.8

1871 69.4 1917 69.8 1963 71.1 2009 73.2

1872 69.3 1918 71.2 1964 72.1 2010 72.7

1873 69.6 1919 72.7 1965 71.8 2011 72.7

1874 70 1920 71.1 1966 70.9 2012 72.9

1875 70.5 1921 72 1967 71.1 2013 74.7

1876 70.3 1922 72.5 1968 72.7

1877 70.5 1923 72.3 1969 71.8

1878 70.5 1924 71.2 1970 71.6

1879 68.2 1925 70.5 1971 71.4

1880 69.4 1926 72.5 1972 71.4

1881 68.9 1927 70.2 1973 72.9

1882 70.2 1928 72.3 1974 71.1

1883 69.3 1929 70.5 1975 72.5

1884 70.2 1930 70.5 1976 71.8

1885 70.9 1931 70.9 1977 72.9

1886 70.3 1932 70.7 1978 71.2

1887 68.5 1933 69.6 1979 72.3

1888 69.8 1934 70.3 1980 73.4

1889 69.4 1935 71.1 1981 71.8

1890 69.1 1936 71.1 1982 72

1891 69.3 1937 70.9 1983 72

1892 68.7 1938 71.8 1984 71.6

1893 68.9 1939 71.4 1985 72.6

1894 69.6 1940 72 1986 72

1895 69.8 1941 70.9 1987 72

1896 69.6 1942 71.1 1988 73.2

1897 70.7 1943 69.1 1989 71.8

1898 70.3 1944 70.9 1990 72.1

1899 69.8 1945 70.5 1991 73

1900 69.6 1946 71.2 1992 70.7

1901 69.8 1947 70.9 1993 72.1

1902 69.8 1948 70.3 1994 72.7

1903 69.3 1949 70.3 1995 71.2

1904 69.6 1950 70.5 1996 71.8