tasks2020.ipynb

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    "![](GMIT_Logo.jpg)\n",
    "\n",
    "# Higher Diploma in Science in Computing (Data Analytics)\n",
    "#### Programme Module: Fundamentals of Data Analysis (COMP07084) \n",
    "---"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "\n",
    "\n",
    "## Task 1 - counts\n",
    "\n",
    "Write a Python function called counts that takes a list as input and returns a dictionary of unique items in the list as keys and the number of times each item appears as values.  So, the input ['A','A','B','C','A'] should have output {'A': 3,'B': 1,'C': 1}.  \n",
    "\n",
    "Your code should not depend on any module from the standard library or otherwise.   You should research he task first and include a description with references of your algorithm in the notebook."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Addendum: </b> We were also asked to see if we could create a solution that could could use not just strings in the input but also integers or floats. </div> "
   ]
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   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Clarification: </b> You cannot use any part of the standard library that has to be imported. The Python documentation technically includes the built-in, non-language features in the standard library - even though they do not need to be imported: https://docs.python.org/3/library/. You can use any of these built-in features - just not anything you need to import. </div> "
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   "source": [
    "---"
   ]
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   "source": [
    "## 1. Solution\n",
    "\n",
    "In order to solve this task I did some initial research looking for sample code that would provide a solution. After a few hours I had sourced five code samples before deciding on one from geeksforgeeks.org [2]. \n",
    "\n",
    "I modified the input to check how the function would deal with integers and floats as well. Initally the code failed, this I found out was due to a format issue.\n",
    "\n",
    "In Python the `%` operator is used to format a set of variables enclosed in a \"tuple\" (a fixed size list), together with a format string, which contains normal text together with \"argument specifiers\", special symbols like `%s` and `%d`. So in this case I had to change the original code from `%d` to `%s`. [5]"
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    "# Define the function\n",
    "def counts(my_list):\n",
    "\n",
    "    # Create a blank dictionary\n",
    "    freq = {}\n",
    "\n",
    "# Create for loop\n",
    "    for item in my_list:\n",
    "        if (item in freq):\n",
    "            freq[item] += 1\n",
    "        else:\n",
    "            freq[item] = 1\n",
    "\n",
    "# Iterate over key/value pairs in dictionary and print them\n",
    "    for key, value in freq.items():\n",
    "        print(\"% s : % s\" % (key, value))\n",
    "\n",
    "\n",
    "# List of items to count\n",
    "my_list = ['A', 'A', 'B', 'C', 'A', 1, 2, 3, 2, 'python', 4.5, 6.5, 'B']"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "Lets have a look at the output of the function."
   ]
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     "text": [
      "A : 3\n",
      "B : 2\n",
      "C : 1\n",
      "1 : 1\n",
      "2 : 2\n",
      "3 : 1\n",
      "python : 1\n",
      "4.5 : 1\n",
      "6.5 : 1\n"
     ]
    }
   ],
   "source": [
    "counts(my_list)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "---\n",
    "## 2. Explanation\n",
    "\n",
    "#### 2.1 Function\n",
    "I've outlined below how the algorithm works and broken it in to sections for ease of use. First up was to define the function.\n",
    "\n",
    "```python\n",
    " def counts(my_list):\n",
    "```\n",
    "\n",
    "A function in Python is defined using the `def` keyword. A function is a block of code which only runs when it is called. You can pass data, known as parameters, into a function. A function can return data as a result. In this example the function is called `counts`. Information can be passed into functions as arguments. Arguments are specified after the function name, inside the parentheses. You can add as many arguments as you want, just separate them with a comma. In this function we have one argument called `(my_list)`."
   ]
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   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Additional information: A function definition defines a user-defined function object. If you are looking for more detail on functions you can run the  help('def') statement in your own Jupyter notebook. </div>"
   ]
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   "source": [
    "#### 2.2 Dictionary\n",
    "The code also creates a dictionary called `freq`. A dictionary is a collection which is unordered, changeable and indexed. In Python dictionaries are written with curly brackets, and they have keys and values.\n",
    "\n",
    "```python\n",
    "    freq = {}\n",
    "```\n",
    "\n",
    "It is best to think of a dictionary as a set of key: value pairs, with the requirement that the keys are unique (within one dictionary). Placing a comma-separated list of key:value pairs within the braces adds initial key:value pairs to the dictionary; this is also the way dictionaries are written on output.[6]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Additional information: If you are looking for more detail on dictionaries(dicts) you can run the  help('dict') statement in your own Jupyter notebook. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.3 For Loop\n",
    "Next up the code uses a for loop to iterate over each item in the list. At each iteration, check if item is in an initially empty dictionary. If it is, use dictionary `item` += 1 to add 1 to the value to which item maps. Otherwise, use dictionary `item` = 1 to add item to dictionary with the value 1. The `items()` method is used to return the list with all dictionary keys with values. [8]\n",
    "\n",
    "```python\n",
    "for item in my_list:\n",
    "        if (item in freq):\n",
    "            freq[item] += 1\n",
    "        else:\n",
    "            freq[item] = 1\n",
    "```"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Additional information: The \"for\" statement is used to iterate over the elements of a sequence (such as a string, tuple or list) or other iterable object. If you are looking for more detail on for loops you can run the  help('for') statement in your own Jupyter notebook. </div>"
   ]
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   "source": [
    "#### 2.4 Keys and Values\n",
    "The next section captures the items as the keys of the dictionary `freq` and their frequencies as the values.\n",
    "```python\n",
    "    for key, value in freq.items():\n",
    "        print (\"% s : % s\"%(key, value))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.5 List\n",
    "This section of code contains the list of items to count in the function.\n",
    "\n",
    "```python\n",
    "my_list = ['A', 'A', 'B', 'C', 'A', 1, 2, 3, 2, 'python', 4.5, 6.5, 'B']\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Additional information: If you are looking for more detail on lists you can run the  help('list') statement in your own Jupyter notebook. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## 3. References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] GeeksforGeeks. 2020. Python | *Get Unique Values From List Of Dictionary - Geeksforgeeks*. [online] Available at: <https://www.geeksforgeeks.org/python-get-unique-values-from-list-of-dictionary/> [Accessed 7 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[2] GeeksforGeeks. 2020. *Counting The Frequencies In A List Using Dictionary In Python - Geeksforgeeks*. [online] Available at: <https://www.geeksforgeeks.org/counting-the-frequencies-in-a-list-using-dictionary-in-python/> [Accessed 6 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[3] Elance, P., 2019. *Counting The Frequencies In A List Using Dictionary In Python*. [online] Tutorialspoint.com. Available at: <https://www.tutorialspoint.com/counting-the-frequencies-in-a-list-using-dictionary-in-python> [Accessed 6 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[4] Techie Delight. 2020. *Count Occurrences Of An Item In A Python List - Techie Delight*. [online] Available at: <https://www.techiedelight.com/count-occurrences-of-an-item-in-a-python-list/> [Accessed 7 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[5] Learnpython.org. 2020. *String Formatting - Learn Python - Free Interactive Python Tutorial*. [online] Available at: <https://www.learnpython.org/en/String_Formatting> [Accessed 8 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[6] W3schools.com. 2020. *Python Dictionaries*. [online] Available at: <https://www.w3schools.com/python/python_dictionaries.asp> [Accessed 11 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[7] Docs.python.org. 2020. 5. *Data Structures — Python 3.9.0 Documentation*. [online] Available at: <https://docs.python.org/3/tutorial/datastructures.html> [Accessed 11 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[8] Kite.com. 2020. *Code Faster With Line-Of-Code Completions, Cloudless Processing*. [online] Available at: <https://www.kite.com/python/answers/how-to-count-item-frequency-in-python> [Accessed 10 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[9] GeeksforGeeks. 2020. *Python Dictionary | Items() Method - Geeksforgeeks*. [online] Available at: <https://www.geeksforgeeks.org/python-dictionary-items-method/> [Accessed 11 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[10] Edureka. 2020. *What Is The Main Function In Python And How To Use It | Edureka*. [online] Available at: <https://www.edureka.co/blog/python-main-function/> [Accessed 11 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[11] Cite This For Me. 2020. *Save Time And Improve Your Marks With Citethisforme, The No. 1 Citation Tool*. [online] Available at: <https://www.citethisforme.com/> [Accessed 7 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[12] Okada, S., 2020. *7 Essential Tips For Writing With Jupyter Notebook*. [online] Medium. Available at: <https://towardsdatascience.com/7-essential-tips-for-writing-with-jupyter-notebook-60972a1a8901#7aff> [Accessed 11 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[13] Pythontutor.com. 2020. *Python Tutor - Visualize Python, Java, Javascript, C, C++, Ruby Code Execution*. [online] Available at: <http://www.pythontutor.com/visualize.html#mode=display> [Accessed 7 October 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 2 - dicerolls\n",
    "\n",
    "Write a Python function called dicerolls that simulates rolling dice. Your function should take two parameters: the number of dice `k` and the number of times to roll the dice `n`. The function should simulate randomly rolling `k` dice `n` times, keeping track of each total face value. It should then return a dictionary with the number of times each possible total face value occurred. So, calling the function as diceroll `(k=2, n=1000)` should return a dictionary like: `{2:19,3:50,4:82,5:112,6:135,7:174,8:133,9:114,10:75,11:70,12:36}`\n",
    "You can use any module from the Python standard library you wish and you should include a description with references of your algorithm in the notebook.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Solution"
   ]
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    "# Import numpy library\n",
    "import numpy as np\n",
    "\n",
    "# Use numpy random number generator\n",
    "rng = np.random.default_rng(1)\n",
    "\n",
    "# Define the function\n",
    "\n",
    "\n",
    "def dicerolls():\n",
    "\n",
    "    # create a blank dictionary\n",
    "    diceroll = {}\n",
    "\n",
    "# Create for loop\n",
    "    for i in range(1000):\n",
    "        d1 = rng.integers(1, 7)\n",
    "        d2 = rng.integers(1, 7)\n",
    "        diceroll[d1+d2] = diceroll.setdefault(d1+d2, 0)+1\n",
    "\n",
    "# Iterate over key/value pairs in dictionary and print them\n",
    "    for roll, count in diceroll.items():\n",
    "        print(\"% s : % s\" % (roll, count))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets have a look at the output of the function."
   ]
  },
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   "cell_type": "code",
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     "text": [
      "7 : 153\n",
      "11 : 69\n",
      "2 : 29\n",
      "4 : 91\n",
      "9 : 118\n",
      "5 : 112\n",
      "8 : 145\n",
      "10 : 76\n",
      "3 : 50\n",
      "6 : 120\n",
      "12 : 37\n"
     ]
    }
   ],
   "source": [
    "dicerolls()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 2. Explanation\n",
    "\n",
    "#### 2.1 Numpy library and random number generator\n",
    "\n",
    "I've outlined below how the algorithm works and broken it in to sections for ease of use. First up was to import numpy and the random number generator (RNG). This will be used to simulate the dicerolls in the function.\n",
    "\n",
    "```python\n",
    "import numpy as np\n",
    "rng = np.random.default_rng(1)```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Additional information: If you are looking for more detail on random number generation in NumPy you can enter the following statement np.info(rng) statement in your own Jupyter notebook. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2 Function\n",
    "\n",
    "In Task 1 I covered what a function is, so I won't repeat that here. For this task I start by defining the function `dicerolls` unlike in Task 1 there are no arguments.\n",
    "\n",
    "```python\n",
    "def dicerolls():```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.3 For Loop\n",
    "\n",
    "Next up the code uses a for loop to iterate over each item in the list. At each iteration, check if item is in an initially empty dictionary. The `setdefault` method is used for setting defaults while or after filling the dictionary. This will store the results of the simulate dice rolls.\n",
    "\n",
    "```Python\n",
    " for i in range(1000):\n",
    "        d1=rng.integers(1,7)\n",
    "        d2=rng.integers(1,7)\n",
    "        diceroll[d1+d2] = diceroll.setdefault(d1+d2,0)+1\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Additional information: If you are looking for more detail on dictionaries(dicts) and (setdefault) you can run the  help('dict') statement in your own Jupyter notebook. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.4 Keys and Values\n",
    "\n",
    "The next section captures the items as the keys of the dictionary `diceroll` and their frequencies as the values.\n",
    "\n",
    "```Python\n",
    "    for roll, count in diceroll.items():\n",
    "        print(\"% s : % s\" % (roll, count))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] Data Science Unlimited. 2020. *Step By Step: Coding A Dice Roll Simulator In Python | Examples For Beginners*. [online] Available at: <https://datascienceunlimited.tech/step-by-step-coding-a-dice-roll-simulator-in-python/> [Accessed 4 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[2] Medium. 2020. *How To Simulate A Dice Roll And Guess The Result In Python*. [online] Available at: <https://medium.com/an-amygdala/how-to-simulate-a-dice-roll-and-guess-the-result-in-python-9785079af6f3> [Accessed 4 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[3] Codegrepper.com. 2020. *Dice Rolling Simulator Python Code Example*. [online] Available at: <https://www.codegrepper.com/code-examples/python/dice+rolling+simulator+python> [Accessed 5 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[4] Pythonfiddle.com. 2020. *Mike's Dice Stats | Python Fiddle*. [online] Available at: <http://pythonfiddle.com/mikes-dice-stats/> [Accessed 5 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[5] Pieters, M., 2020. *Simulating Rolling 2 Dice In Python*. [online] Stack Overflow. Available at: <https://stackoverflow.com/questions/33069476/simulating-rolling-2-dice-in-python> [Accessed 5 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[6] Lin, S., 2020. *Program That Simulates Rolling A Dice, And Tells You How Many Times You Roll Each Number*. [online] Stack Overflow. Available at: <https://stackoverflow.com/questions/27220489/program-that-simulates-rolling-a-dice-and-tells-you-how-many-times-you-roll-eac> [Accessed 6 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[7] Hplgit.github.io. 2020. *Random Numbers And Simple Games*. [online] Available at: <http://hplgit.github.io/primer.html/doc/pub/random/._random-readable004.html> [Accessed 6 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[8] Darklinkdigital.com. 2020. *Python Dice Functions*. [online] Available at: <http://www.darklinkdigital.com/py-dice-functions.html> [Accessed 6 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[9] Iditect.com. 2020. *Python - Rolled 2 6-Side Die 1000 Times*. [online] Available at: <https://www.iditect.com/how-to/55151873.html> [Accessed 5 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[10] BBC Bitesize. 2020. *Functions In Python - Procedures And Functions - KS3 Computer Science Revision - BBC Bitesize*. [online] Available at: <https://www.bbc.co.uk/bitesize/guides/zqh49j6/revision/6> [Accessed 5 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[11] Stack Overflow. 2020. *Rolling 2 Dice 1000 Times And Counting The Number Of Times The Sum Of The Two Dice Hit*. [online] Available at: <https://stackoverflow.com/questions/60343980/rolling-2-dice-1000-times-and-counting-the-number-of-times-the-sum-of-the-two-di> [Accessed 5 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "---\n",
    "\n",
    "## Task 3 - numpy.random.binomial\n",
    "\n",
    "The `numpy.random.binomial` function can be used to simulate flipping a coin with a 50/50 chance of heads or tails. Interestingly, if a coin is flipped many times then the number of heads is well approximated by a bell-shaped curve. For instance, if we flip a coin 100 times in a row the chance of getting 50 heads is relatively high, the chances of getting 0 or 100 heads is relatively low, and the chances of getting any other number of heads decreases as you move away from 50 in either direction towards 0 or 100.\n",
    "\n",
    "Write some python code that simulates flipping a coin 100 times. Then run this code 1,000 times, keeping track of the number of heads in each of the 1,000 simulations. Select an appropriate plot to depict the resulting list of 1,000 numbers, showing that it roughly follows a bell-shaped curve. You should explain your work in a Markdown cell above the code.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:16.627091Z",
     "start_time": "2020-12-18T09:49:15.471104Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       38, 49, 45, 54, 49, 50, 55, 45, 61, 47, 48, 52, 41, 59, 53, 46, 38,\n",
       "       51, 44, 51, 57, 49, 48, 44, 50, 53, 50, 37, 53, 47, 49, 47, 57, 46,\n",
       "       46, 48, 56, 52, 35, 45, 45, 50, 48, 41, 56, 46, 45, 52, 48, 47, 55,\n",
       "       45, 59, 48, 48, 42, 52, 53, 54, 51, 57, 50, 48, 40, 53, 48, 52, 49,\n",
       "       43, 56, 40, 45, 54, 48, 51, 52, 63, 39, 55, 48, 52, 54, 49, 46, 45,\n",
       "       53, 50, 53, 45, 46, 48, 47, 54, 50, 43, 46, 54, 54, 54, 47, 50, 45,\n",
       "       50, 47, 37, 53, 51, 45, 46, 50, 53, 50, 49, 49, 58, 47, 47, 48, 43,\n",
       "       47, 51, 43, 52, 51, 52, 47, 48, 51, 51, 47, 55, 44, 47],\n",
       "      dtype=int64)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import the required libraries\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Graphics in retina format are more sharp and legible.\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "# Sets the backend of matplotlib to the 'inline' backend.\n",
    "%matplotlib inline\n",
    "\n",
    "# Number of coin toss\n",
    "n = 100\n",
    "\n",
    "# Set the probability\n",
    "p = 0.5\n",
    "\n",
    "# Number of experiments\n",
    "s = 1000\n",
    "\n",
    "# Generate the results\n",
    "x = np.random.default_rng(1).binomial(n, p, s)\n",
    "\n",
    "# View the outcome\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:16.890067Z",
     "start_time": "2020-12-18T09:49:16.627091Z"
    }
   },
   "outputs": [
    {
     "data": {
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EYZ0kSZIkSZIUEoZ1kiRJkiRJUkj8DQwnJLERtTHjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 352,
       "width": 629
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualisation styling code\n",
    "sns.set(rc={'figure.figsize': (10, 5)})\n",
    "sns.set_context('notebook')\n",
    "sns.set_style(\"whitegrid\")\n",
    "\n",
    "# Generate the distplot\n",
    "sns.distplot(x, kde=True, color='steelblue',\n",
    "kde_kws={\"label\": \"KDE\",'color': '#66aa44','linewidth': 3, 'linestyle': '--', 'alpha': 0.8})\n",
    "plt.xlabel(\"Distribution\", labelpad=15)\n",
    "plt.ylabel(\"Density\", labelpad=15)\n",
    "plt.title(\"Binomial Distribution\", fontsize=15, y=1.012);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Explanation\n",
    "\n",
    "A coin toss in mathematical terms can be thought of as a binomial experiment, were we have a coin with the probability of getting a head a success and tails a failure. We assume it's a \"fair coin\" for the task explained below. But what is a \"fair coin\"? In probability theory and statistics, a sequence of independent Bernoulli trials with probability of 1/2 of success on each trial is metaphorically called a \"fair coin\". One for which the probability is not 1/2 is called a biased coin or unfair coin. \n",
    "\n",
    "Wait a minute, above I said a coin toss could be a thought of as a Binomial experiment where as later I mentioned a Bernoulli trial. Are these not different. This needs some explanation. \"*The Bernoulli distribution represents the success or failure of a single Bernoulli trial.  The Binomial Distribution represents the number of successes and failures in __n__ independent Bernoulli trials for some given value of __n__.  For example, if a manufactured item is defective with probability __p__, then the binomial distribution represents the number of successes and failures in a lot of __n__ items.  In particular, sampling from this distribution gives a count of the number of defective items in a sample lot.  Another example is the number of heads obtained in tossing a coin __n__ times*\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1 Import required libraries\n",
    "\n",
    "This section of code covers importing the required libraries needed.\n",
    "\n",
    "```python\n",
    "# Import the required libraries\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Graphics in retina format are more sharp and legible.\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "# Sets the backend of matplotlib to the 'inline' backend.\n",
    "%matplotlib inline```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2 Random binomial\n",
    "\n",
    "In this section code I'm generating results of the binomial. Running the coin toss experiment 1000 times, where in each experiment we toss a fair coin 100 times asking how many heads we see in each of the 100 experiments. I have set the seed for the rng so that the results can be replicated.\n",
    "\n",
    "```python\n",
    "# number of coin toss\n",
    "n = 100\n",
    "\n",
    "# set the probability\n",
    "p = 0.5\n",
    "\n",
    "# number of experiments\n",
    "s = 1000\n",
    "\n",
    "# generate the results\n",
    "x = np.random.default_rng(1).binomial(n, p, s)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Additional information: If you are looking for more detail on random number generation in NumPy you can enter the following statement np.info(rng) statement in your own Jupyter notebook. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.3 View the outcome\n",
    "\n",
    "Now we print the array of results.\n",
    "\n",
    "```python\n",
    "# view the outcome\n",
    "x```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.4 Visualize the results\n",
    "\n",
    "This section applies the visulation style and plots the outcome of the code.\n",
    "\n",
    "```python\n",
    "# Visualisation styling code\n",
    "sns.set(rc={'figure.figsize': (10, 5)})\n",
    "sns.set_context('notebook')\n",
    "sns.set_style(\"whitegrid\")\n",
    "\n",
    "# Generate the distplot\n",
    "sns.distplot(x, kde=True, color='steelblue',\n",
    "kde_kws={\"label\": \"KDE\",'color': '#66aa44','linewidth': 3, 'linestyle': '--', 'alpha': 0.8})\n",
    "plt.xlabel(\"Distribution\", labelpad=15)\n",
    "plt.ylabel(\"Density\", labelpad=15)\n",
    "plt.title(\"Binomial Distribution\", fontsize=15, y=1.012);\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] Python and R Tips. 2018. *Simulating Coin Toss Experiment In Python With Numpy - Python And R Tips*. [online] Available at: <https://cmdlinetips.com/2018/12/simulating-coin-toss-experiment-with-binomial-random-numbers-using-numpy/> [Accessed 17 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[2] Medium. 2019. *How To Code A Fair Coin Flip In Python*. [online] Available at: <https://towardsdatascience.com/how-to-code-a-fair-coin-flip-in-python-d54312f33da9> [Accessed 17 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[3] Umayanga, T., 2020. *What Is Binomial Distribution And How To Plot It Using Python*. [online] Medium. Available at: <https://medium.com/@tharakau/what-is-binomial-distribution-and-how-to-plot-it-using-python-e9d95bd341ee> [Accessed 17 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[4] Unf.edu. 2020. *Empirical Distributions*. [online] Available at: <https://www.unf.edu/~cwinton/html/cop4300/s09/class.notes/DiscreteDist.pdf> [Accessed 2 December 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[5] Mimi Mathematics. 2020. *Fair Coin*. [online] Available at: <https://en.mimi.hu/mathematics/fair_coin.html> [Accessed 2 December 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[6] Python and R Tips. 2020. *Simulating Coin Toss Experiment In Python With Numpy - Python And R Tips*. [online] Available at: <https://cmdlinetips.com/2018/12/simulating-coin-toss-experiment-with-binomial-random-numbers-using-numpy/> [Accessed 20 November 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 4 - Simpon's paradox\n",
    "\n",
    "Simpson’s paradox is a well-known statistical paradox where a trend evident in a number of groups reverses when the groups are combined into one big data set.  Use numpy to create four data sets, each with an __x__ array and  a  corresponding __y__ array,  to  demonstrate  Simpson’s  paradox.   You  might create  your __x__ arrays  using numpy.linspace and  create  the __y__ array  for  each __x__ using notation like __y = a * x + b__ where you choose the __a__ and __b__ for each __x, y__ pair to demonstrate the paradox. You might see the Wikipedia page for Simpson’s paradox for inspiration."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It occurs when the \"*the correlation calculated for a dataset changes direction if the dataset is split into groups*\". In effect a positive correlation when looking at a whole dataset not only disappears but ends up with a negative correlation when the data is split/partitioned. It illustrates \"*the need to be skeptical of conclusions that rely on statistics that depend on how the data is aggregated*\". It is a type of omitted variable bias , the result of which one variable overcomes the explanation of a missing or lurking variable. This leads to a \"*incorrect interpretation of an apparently obvious insight*\". (Abousalh-Neto, N., 2020,(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1 Import required libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:16.905689Z",
     "start_time": "2020-12-18T09:49:16.890067Z"
    }
   },
   "outputs": [],
   "source": [
    "# Import required libraries\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Graphics in retina format are more sharp and legible.\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "# Sets the backend of matplotlib to the 'inline' backend.\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2 Create first dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This section of code creates the first dataset using NumPy linspace for the __x__ values and the linear equation for the __y__ values. I've added some noise to for aesthetics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>NumPy linspace: </b> linspace is an in-built function in Python’s NumPy library. It is used to create an evenly spaced sequence in a specified interval. </div> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Linear equation: </b> A linear equation is any equation that can be written in the form. ax+b=0. where a and b are real numbers and x is a variable. This form is sometimes called the standard form of a linear equation  </div> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:16.927830Z",
     "start_time": "2020-12-18T09:49:16.905689Z"
    }
   },
   "outputs": [],
   "source": [
    "# create first dataset\n",
    "x1 = np.linspace(0, 1, 24)\n",
    "noise = np.random.normal(0, 0.2, x1.shape)\n",
    "a, b = -1, 1\n",
    "y = a*x1+b\n",
    "y1 = y+noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets have a look at the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:16.943447Z",
     "start_time": "2020-12-18T09:49:16.927830Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.04347826, 0.08695652, 0.13043478, 0.17391304,\n",
       "       0.2173913 , 0.26086957, 0.30434783, 0.34782609, 0.39130435,\n",
       "       0.43478261, 0.47826087, 0.52173913, 0.56521739, 0.60869565,\n",
       "       0.65217391, 0.69565217, 0.73913043, 0.7826087 , 0.82608696,\n",
       "       0.86956522, 0.91304348, 0.95652174, 1.        ])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# view x1 array\n",
    "x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:16.959069Z",
     "start_time": "2020-12-18T09:49:16.943447Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.67951846,  0.89271986,  0.98031638,  1.00598405,  0.86163535,\n",
       "        0.6124299 ,  0.51518619,  0.80052795,  0.38660513,  0.65979496,\n",
       "        0.44865481,  0.26476429,  0.70977443,  0.4566235 ,  0.35088484,\n",
       "        0.07668496,  0.69280803,  0.6279839 ,  0.44215756,  0.14625968,\n",
       "        0.27658181,  0.17818195,  0.46759558, -0.0283186 ])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# view y1 array\n",
    "y1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below section of code displays the coefficient of __x1__ and __y1__."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Coefficient: </b> a value, in mathematics, that appears in front of and multiplies another value. For example in 2x + 4y = 7, 2 is the coefficient of x  </div> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>NumPy polyfit: </b> This is a pretty general least squares polynomial fit function which accepts the data set and a polynomial function of any degree (specified by the user), and returns an array of coefficients that minimizes the squared error.  </div> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:16.974699Z",
     "start_time": "2020-12-18T09:49:16.959069Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.6876621 ,  0.86488751])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# coefficient\n",
    "coeffs1 = np.polyfit(x1, y1, 1)\n",
    "coeffs1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-07T14:31:58.403260Z",
     "start_time": "2020-12-07T14:31:58.379847Z"
    }
   },
   "source": [
    "Now lets plot the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:17.306671Z",
     "start_time": "2020-12-18T09:49:16.974699Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 251,
       "width": 374
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x1, y1, '.');\n",
    "plt.plot(x1, coeffs1[0] * x1 + coeffs1[1], '-', label='Best fit')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.3 Create second dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Note: </b> For creating datasets 2, 3 and 4, I excluded the code that viewed the outputted arrays as It was only for illustrative purposes. </div> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:17.328808Z",
     "start_time": "2020-12-18T09:49:17.306671Z"
    }
   },
   "outputs": [],
   "source": [
    "# create second dataset\n",
    "x2 = np.linspace(1, 2, 24)\n",
    "noise = np.random.normal(0, 0.2, x2.shape)\n",
    "a, b = -2, 4\n",
    "y = a*x2+b\n",
    "y2 = y+noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:17.344448Z",
     "start_time": "2020-12-18T09:49:17.328808Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.18794466,  4.27503146])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# coefficient\n",
    "coeffs2 = np.polyfit(x2, y2, 1)\n",
    "coeffs2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:17.676399Z",
     "start_time": "2020-12-18T09:49:17.344448Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 251,
       "width": 374
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x2, y2, '.');\n",
    "plt.plot(x2, coeffs2[0] * x2 + coeffs2[1], '-', label='Best fit')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4 Create third dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:17.692022Z",
     "start_time": "2020-12-18T09:49:17.676399Z"
    }
   },
   "outputs": [],
   "source": [
    "# create third dataset\n",
    "x3 = np.linspace(2, 3, 24)\n",
    "noise = np.random.normal(0, 0.2, x3.shape)\n",
    "a, b = -3, 12\n",
    "y = a*x3+b\n",
    "y3 = y+noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:17.707642Z",
     "start_time": "2020-12-18T09:49:17.692022Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.942202  , 11.81628692])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# coefficient\n",
    "coeffs3 = np.polyfit(x3, y3, 1)\n",
    "coeffs3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:18.030505Z",
     "start_time": "2020-12-18T09:49:17.707642Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 251,
       "width": 374
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x3, y3, '.');\n",
    "plt.plot(x3, coeffs3[0] * x3 + coeffs3[1], '-', label='Best fit')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5 Create fourth dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:18.046129Z",
     "start_time": "2020-12-18T09:49:18.030505Z"
    }
   },
   "outputs": [],
   "source": [
    "# create fourth dataset\n",
    "x4 = np.linspace(3, 4, 24)\n",
    "noise = np.random.normal(0, 0.2, x4.shape)\n",
    "a, b = -4, 20\n",
    "y = a*x4+b\n",
    "y4 = y+noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:18.061749Z",
     "start_time": "2020-12-18T09:49:18.046129Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.8481155 , 19.39807952])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# coefficient\n",
    "coeffs4 = np.polyfit(x4, y4, 1)\n",
    "coeffs4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:18.346862Z",
     "start_time": "2020-12-18T09:49:18.061749Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 252,
       "width": 374
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x4, y4, '.');\n",
    "plt.plot(x4, coeffs4[0] * x4 + coeffs4[1], '-', label='Best fit')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.6 Concatenate the  datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now it's time to join the datasets together and see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:18.362482Z",
     "start_time": "2020-12-18T09:49:18.346862Z"
    }
   },
   "outputs": [],
   "source": [
    "# concatenate the four datsets created earlier\n",
    "x_array = np.concatenate((x1, x2, x3, x4))\n",
    "y_array = np.concatenate((y1, y2, y3, y4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:18.378103Z",
     "start_time": "2020-12-18T09:49:18.362482Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.67301229, -0.36986755])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# coefficient\n",
    "coeffs5 = np.polyfit(x_array, y_array, 1)\n",
    "coeffs5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets plot the combined dataset and see what happens. According to Simpson's Paradox the correlation should change. In the four datasets we created there was a negative correlation between the x and y values by design. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Negative correlation: </b> Negative correlation is a relationship between two variables in which one variable increases as the other decreases, and vice versa. In statistics, a perfect negative correlation is represented by the value -1, a 0 indicates no correlation, and a +1 indicates a perfect positive correlation. A perfect negative correlation means the relationship that exists between two variables is negative 100% of the time. (Investopedia. 2020.,(6))  </div> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.7 Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-18T09:49:18.687388Z",
     "start_time": "2020-12-18T09:49:18.378103Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 251,
       "width": 364
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_array, y_array, '.');\n",
    "plt.plot(x_array, coeffs5[0] * x_array + coeffs5[1], '-', label='Best fit')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-07T16:54:37.326357Z",
     "start_time": "2020-12-07T16:54:37.314835Z"
    }
   },
   "source": [
    "As expected the correlation is now positive. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Positive correlation: </b>  Positive correlation is a relationship between two variables in which both variables move in tandem—that is, in the same direction. A positive correlation exists when one variable decreases as the other variable decreases, or one variable increases while the other increases.\n",
    "\n",
    "In statistics, a perfect positive correlation is represented by the correlation coefficient value +1.0, while 0 indicates no correlation, and -1.0 indicates a perfect inverse (negative) correlation.  (Investopedia. 2020.,(7))  </div> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] Abousalh-Neto, N., 2020. *The Desert And The Dunes: Finding Oases And Avoiding Mirages With SAS Visual Analytics*. [online] Support.sas.com. Available at: <https://support.sas.com/resources/papers/proceedings14/SAS252-2014.pdf> [Accessed 3 December 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[2] Long, R., 2016. *Can You Please Explain Simpson's Paradox With Equations, Instead Of Contingency Tables?*. [online] Cross Validated. Available at: <https://stats.stackexchange.com/questions/221892/can-you-please-explain-simpsons-paradox-with-equations-instead-of-contingency> [Accessed 4 December 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[3] Atri, Y., 2020. *PYTHON: Solving Y=A+B*X Where X Is A Predefined List*. [online] Stack Overflow. Available at: <https://stackoverflow.com/questions/60337609/python-solving-y-abx-where-x-is-a-predefined-list> [Accessed 3 December 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[4] Ebner, J., 2020. *How To Use The Numpy Linspace Function*. [online] Sharp Sight. Available at: <https://www.sharpsightlabs.com/blog/numpy-linspace/> [Accessed 6 December 2018]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[5] utorial.math.lamar.edu. 2020. *Algebra - Linear Equations*. [online] Available at: <https://tutorial.math.lamar.edu/classes/alg/solvelineareqns.aspx> [Accessed 3 December 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[6] Investopedia. 2020. *Negative Correlation Definition*. [online] Available at: <https://www.investopedia.com/terms/n/negative-correlation.asp> [Accessed 7 December 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[7] Investopedia. 2020. *Understanding Positive Correlation*. [online] Available at: <https://www.investopedia.com/terms/p/positive-correlation.asp> [Accessed 7 December 2020]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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