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   "source": [
    "# 2.19 Statistics for Geoscientists class test - 14:00-17:00 29th May 2015"
   ]
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    "# Test instructions\n",
    "\n",
    "* This test contains **5** questions each of which should be answered.\n",
    "* Write your program in a Python cell just under each question.\n",
    "* You should write an explanation of your solution as comments in your code.\n",
    "* In each case your solution program must fulfil all of the instructions - please check the instructions carefully and double check that your program fulfils all of the given instructions.\n",
    "* Save your work regularly.\n",
    "* At the end of the test you should email your IPython notebook document (i.e. this document) to [Gerard J. Gorman](http://www.imperial.ac.uk/people/g.gorman) at g.gorman@imperial.ac.uk"
   ]
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   "source": [
    "# Question preamble\n",
    "\n",
    "You hypothesise that there may be a link between temperature and the level of green house gasses in the atmosphere. As part of your investigation to establish if there is a correlation you analyise ice core data taken from [Vostok Station](http://en.wikipedia.org/wiki/Vostok_Station) in Antarctica. The data file that you will be using, [VostokStation.csv](https://raw.githubusercontent.com/ggorman/Introduction-to-stats-for-geoscientists/gh-pages/data/VostokStation.csv), constains reconstructed temperature, CO2 gas concentration and CH4 gas concentrations stretching back 160,000 years."
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   "source": [
    "## Question 1\n",
    "\n",
    "* Read in the data from the file [VostokStation.csv](https://raw.githubusercontent.com/ggorman/Introduction-to-stats-for-geoscientists/gh-pages/data/VostokStation.csv) into NumPy arrays called *year*, *temperature*, *co2* and *ch4*.\n",
    "* Print out the *mean*, *minimum* and *maximum* temperature, CO2 concentration and CH4 contentration from this data."
   ]
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    "#Question 2\n",
    "\n",
    "* Plot line graphs of temperature, CO2 concentration and CH4 concentration against year.\n",
    "* Remember to label all your axes."
   ]
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   "source": [
    "#Question 3\n",
    "\n",
    "* Create scatter plots for both: temperature vs CO2 concentration; and temperature vs CH4 concentration.\n",
    "* Using linear regression, fit a straight line to each set of data and plot this line on the same graph.\n",
    "* What does the p-value from linear regression tell you?\n",
    "\n",
    "**Remember** to label the x-axis and y-axis. "
   ]
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   "source": [
    "#Question 4\n",
    "\n",
    "* Plot a histogram of the difference between CO2 concentration values and the line fit in the scatter plot above.\n",
    "* Use *scipy.stats.normaltest* to determine if this data is normally distributed.\n",
    "\n",
    "**HINT:** Take, for example, CO2 vs temperature. When you use linear regression to fit a straight line $y = mx+c$, where $m$ is the slope and $c$ is the $intercept$. The variation in C02 around the straight line model is therefore:\n",
    "\n",
    "    co2_variation = co2 - (m*temperature+c)\n",
    "    \n",
    "where *co2_variation*, *co2* and *temperature* are all NumPy arrays."
   ]
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   "source": [
    "#Question 5\n",
    "\n",
    "Using the approperiate correlation test in each case, determine if there is a correlation between: temperature and CO2 concentration; temperature and CH4 concentration. Explain both your choice of correlation statistic and your conclusion.\n",
    "\n",
    "**Hint.** Use the *scipy.stats.normaltest* to check if the samples are normally distributed."
   ]
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