featureEngineering5.ipynb

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    "###  What is the difference between Ordinal Encoding and Label Encoding? Provide an example of when you might choose one over the other.\n",
    "\n",
    "Ordinal Encoding and Label Encoding are both techniques used in data preprocessing to convert categorical data into numerical format, but they are used in slightly different scenarios and have different characteristics:\n",
    "\n",
    "1. **Label Encoding**:\n",
    "   - Label Encoding assigns a unique integer (label) to each category in a categorical feature.\n",
    "   - It does not consider any inherent order or ranking among the categories; it simply maps each category to a numerical value.\n",
    "   - Label Encoding is commonly used for nominal data, where there is no meaningful order or ranking among the categories.\n",
    "   - It can be problematic when the model misinterprets the encoded values as having some sort of ordinal relationship, which can lead to incorrect model predictions.\n",
    "\n",
    "   Example:\n",
    "   Suppose you have a \"Color\" feature with categories: \"Red,\" \"Green,\" and \"Blue.\" Label Encoding would map them to integers like 0, 1, and 2, respectively.\n",
    "\n",
    "   Red   -> 0\n",
    "   Green -> 1\n",
    "   Blue  -> 2\n",
    "\n",
    "2. **Ordinal Encoding**:\n",
    "   - Ordinal Encoding is used when there is a clear and meaningful order or ranking among the categories within a feature.\n",
    "   - It assigns integer values to categories based on their order or importance.\n",
    "   - Ordinal Encoding is typically used for ordinal data, where the categories have a natural order (e.g., low, medium, high) or for features where you want to explicitly convey some form of ranking.\n",
    "   - It preserves the ordinal relationship between categories.\n",
    "\n",
    "   Example:\n",
    "   Suppose you have an \"Education Level\" feature with categories: \"High School,\" \"Bachelor's,\" \"Master's,\" and \"Ph.D.\" Ordinal Encoding might map them as follows:\n",
    "\n",
    "   High School -> 1\n",
    "   Bachelor's  -> 2\n",
    "   Master's    -> 3\n",
    "   Ph.D.       -> 4\n",
    "   \n",
    "**When to Choose One Over the Other**:\n",
    "\n",
    "1. **Label Encoding**:\n",
    "   - Use Label Encoding when dealing with nominal data, where there is no inherent order or ranking among categories.\n",
    "   - Label Encoding is often used for features like \"Gender\" (e.g., \"Male\" and \"Female\") or \"Country\" (e.g., \"USA,\" \"Canada,\" \"India\").\n",
    "\n",
    "2. **Ordinal Encoding**:\n",
    "   - Choose Ordinal Encoding when dealing with ordinal data, where categories have a clear and meaningful order.\n",
    "   - It's suitable for features like \"Education Level,\" \"Income Range\" (e.g., \"Low,\" \"Medium,\" \"High\"), or \"Job Seniority\" (e.g., \"Junior,\" \"Intermediate,\" \"Senior\")."
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    "###  Explain how Target Guided Ordinal Encoding works and provide an example of when you might use it in a machine learning project.\n",
    "\n",
    "Target Guided Ordinal Encoding is a data preprocessing technique used for encoding categorical features when there is an ordinal relationship between the categories, and you want to leverage the information from the target variable to assign ordinal values to these categories. This technique aims to improve the predictive power of the model by encoding categories in a way that reflects their relationship with the target variable.\n",
    "\n",
    "Here's how Target Guided Ordinal Encoding works:\n",
    "\n",
    "1. **Calculate the Mean (or any appropriate aggregation) of the Target Variable for Each Category**: For each category in the categorical feature, calculate a statistical measure of the target variable. The measure could be the mean, median, sum, or any other relevant aggregation depending on the problem and the nature of the target variable. This step involves grouping the data by the categorical feature and computing the aggregation for each group.\n",
    "\n",
    "2. **Order the Categories Based on the Aggregated Values**: After calculating the aggregated values for each category, order the categories based on these values. You can either sort them in ascending or descending order, depending on whether higher values of the aggregated measure imply a better or worse outcome for the target variable.\n",
    "\n",
    "3. **Assign Ordinal Labels**: Assign ordinal labels (integer values) to the ordered categories. The categories with higher aggregated values (better outcomes for the target variable) receive higher labels, and vice versa.\n",
    "\n",
    "4. **Replace the Categorical Values**: Replace the original categorical values in the feature with the assigned ordinal labels.\n",
    "\n",
    "Here's an example of when we might use Target Guided Ordinal Encoding in a machine learning project:\n",
    "\n",
    "**Example**: Predicting Customer Churn\n",
    "\n",
    "Suppose we're working on a customer churn prediction project for a telecom company. One of the features in your dataset is \"Contract Length,\" which represents the duration of a customer's contract and can take values like \"Month-to-Month,\" \"One Year,\" and \"Two Years.\" We suspect that there is an ordinal relationship between contract length and churn rate, with longer contract lengths being associated with lower churn rates.\n",
    "\n",
    "To apply Target Guided Ordinal Encoding in this scenario:\n",
    "\n",
    "1. Calculate the churn rate (target variable) for each category of \"Contract Length.\"\n",
    "2. Order the categories based on churn rate (e.g., from lowest to highest churn rate).\n",
    "3. Assign ordinal labels to the categories accordingly (e.g., \"Month-to-Month\" -> 1, \"One Year\" -> 2, \"Two Years\" -> 3).\n",
    "4. Replace the original \"Contract Length\" values with the assigned ordinal labels."
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vHkCbrB6YlYuy5aUonOsCfjOAtsMNaOx0PgiPmXzW3Zc/kwt0/ATfrBuHwHdW\nAVbfdzdK5stniw2g8ZEd2M/omoiIJhBr8IiIaGJkrsAX/yIP5zvOIvXGIiwpmIOLccX4/H1/iuRf\n9+DEwHtI+vgSLPnTAqSdDb+mxXXTvfjyujy4BqL9rLtEpBeXYOUn/wfu/WQhstSz3UZPtuL7rwV7\nNiMREdH4Yw0eERFNiJIHHsft7ufxxA9cqN6yDnkJYub5HuzfVYdGNZCDa/V6bClNgbvjBWyua9dn\nOqGedZf+uyF0tvZg+AM1P2wzkJyehqQZYnJmIlI/6kLcTOMh2Gaj6D34GHY0qLdEREQThAEeERFN\ngAIR1C2D+4dPY3ffSmz6RjFSMYLju7+BXa3qK0Lq2k3YVDw7vABPDjbz8D3IS1TvrwR3D+ofqUOz\nektERDRR+JgEIiKaAMPo/I8mNHeJydJ0XCNnnenCQVNwJy1M06O0C8Nvaf86UVK5DAs+PIrR96/c\na+SdDgZ3REQ0KbAGj4iIJtSSv3oca/PiMdxWh6//sEfNlW5F7beWaQ9XPvL009hzWs0mIiKigFiD\nR0REEygbOalyBMpRDPeZgzth2ccxT3Z3Gz6JNgZ3REREjjDAIyKiiePKR3qy+Hd0ACcO67N08Vh+\nfRpkfDfY+Sq6xb+Fa2pQVT5b+5SIiIjsMcAjIqKJY/S/Oz+E49oMQzFy0mV4N4Tu5iHt/ZJCEdyd\nPqd9SkRERPYY4BER0YQpzEjRaumG+9oxqM/SzU1Gkvzg4jn0no7Hws+VIutMOw526B8TERGRPQZ4\nREQ0YdJnyf53lzDYael/d7oJx94dBRIysfzhL2NdxknU7zzgGwSGJR6p12Ug1aXeRkFWYQGy1DQR\nEdFkwVE0iYhowrhSMpA+8xy63x1Rc8xkUJaORIyg/50huNXciJTX4Jt3ZeBs89N4+sVIm3nq25OV\nU4CFBTcgb+4wGtfvwH71KRER0WTAGjwiIpow7qG+AMGddAmD7/Sge6zBnXTiTXR2tODgy2Ppw5eO\nm8qXYeE1blwY8wYRERGND9bgERERhamw+nFU5rMGj4iIJh/W4BERUQyLx8LydaiuXoHCWWoWERFR\nDGOAR0REMavwvi9i+bU9GPxIMSpFkGeMsSL7/uXkZjt7zU9UvyIiIpr8GOAREVFsci1DyZwe7PnR\nOSQlxmF01O3py5eU9XEsys939srN8ASGREREkx374BERUWxypSA98QL6r12DJ6pzcfbgY9jRoD4b\nI/bBIyKiyYo1eEREFJvcQ+gfuoTC4mwkvn8Sx6MU3BEREU1mrMEjIqIYVoyab6xEet9L2LwvHlVl\nI9j1o1ZkrV2PmsJk9Z3gLg+1oG7bAfSq9xJr8IiIaLJigEdERLGrqApbKjPRu/tJHLquFhXnn8WO\nhkvqw8gxwCMiosmKAR4REcWuuSuwYcNiXO4aRlJSD3ZbauLCtbz2ayhLB+Jmxukz3h/FKEZw7Pmn\nsbtdn0VERDSRGOAREVFsm5WGnORR9L8z5BlFk4iIKFZxkBUiIopt5wfQzeCOiIimCQZ4RERERERE\nMYIBHhERERERUYxggEdERERERBQjGOARERERERHFCAZ4REREREREMYIBHhERERERUYxggEdERERE\nRBQjGOARERERERHFCAZ4REREREREMYIBHhERERERUYxggEdERERERBQjGOARERERERHFCAZ4RERE\nREREMYIBHhERERERUYxggEdERERERBQjGOARERERERHFCAZ4REREREREMYIBHhERERERUYxggEdE\nRERERBQjGOARERERERHFCAZ4REREREREMYIBHhERERERUYxggEdERERERBQjGOARERERERHFCAZ4\nREREREREMYIBHhERERERUYxggEdERERERBQjGOARERERERHFCAZ4REREREREMYIBHhERERERUYxg\ngEdERERERBQjGOARERERERHFCAZ4REREREREMYIBHhERERERUYxggEdERERERBQjGOARERERERHF\nCAZ4REREREREMeLq67Kvf0JNx5wt25/CXXdej5k/PYq31TyPoips+Zt1uGvhTDT85wk106uw+nFs\n/OyduGX+WbzS9itUbHwKX/jUzcg4exhtA+pLREREREREk0hM1+D1XpT/T0ZqkfbWR2FBJlxyIj0b\nFdocX+mz4sX/L6G3vV2fQURERERENMnFdIDX1ntJ/D8eWQUF+gyPAhRmyQBOSsOCVWrSYwUWpIt/\nLp5EW6s+h4iIiIiIaLKL7QCv/STc4l9Xlgjo9FlKGpISAHf/gPZ58hxLALgqGzK+c/e2o02fQ0RE\nRERENOl9qHzZmt+r6Ri0Ahu2l4pgbQCN63dgv5qLVbV4Zmka+g+/gAtF65CHLuzevMsTzMn+d5X5\n8eLzh7Ftrz5P9sErS7+Ezt1PYrBMTuvzJfP3fKj1eOm/rzPVCprX1ThHn4Zle/V1qzfSRd/tJSIi\nIiIikmJ8FM0DONEv//VthlmRI4OuAZzY247B82IyIROFnn56RvNN+bk+xyseeZWWYEtIX/oUNlia\necqgzDe4k/Tfb6m2NhkFkouM4M5MBqj+60NCLiq3P45qY5vlgDHie8+Y5xERERER0bQT849J2N+t\nD3mZnrNC+1cGcKmzxD/9PVoNmf55PJLmyc+EogJkJYh/1ef+ZC3cw3hovf5q1AJI8/KFVbVaUObu\neMHzPfP3XfmlfgO7uBL0Wjz9e3rtXcVGWfvouz791YR+GSyWmdZJRERERETTXswHeNjbI4IhYVaK\n3g9PBXDu8+pZB+pzT4A2L1EbXdPzuUX/Yd8mlvsbu7R+fJ7lC3oNoQzk1uEZrWbN+9Jr4/wHdpHB\noG8zTzXQi6r1812ODPwEYwTQ1l3YrAV+vttGRERERETTS+wHeBjABfm4BNUMU388gvnxB+pzFSzp\nwVmgxyNcwoVTatLQOoRhNalTNYRhGj5jWV9RCpLVJBERERERkRPTIMBr93lcgvZ8O5/HHxify+fl\nRePxCPoIndpAKD7NKn1ftoOymBk1iTbNPL0v08AxREREREQ07U2DAM/0uIRZpXoAd37IZwRK/XMR\nAJZl67Vmls/DowZ28Rm4xaTI+siGAFTTUf9HPOgKxXKIiIiIiIjMpkWA52lGmZ6m9V3r7z4g33mp\nz13ic1lr5vd5mIyBW/IqraNarsCGynWo3O4/6qY/I1DMReWWKt8gb1UtKsVyntle6zdYCxERERER\nTV/TI8DzPC5Bsnv8QajPw7R3hxpd0zpAij44iv+AKvb2b5WjZQraYxFMy9EevyBH11RNNPmYBCIi\nIiIiEqZJgGfUqgkXR/SgySLU5+Hav/VhPHTYOhKn/siDzXV2A7jYOYBt672PYvDQ+vdxxEwiIiIi\nIvL1ofJla36vpomIiIiIiGgKmzY1eERERERERLGOAR4REREREVGMYIBHREREREQUIxjgERERERER\nxQgGeERERERERDGCAR4REREREVGMYIBHREREREQUIxjgERERERERxQgGeERERERERDGCAR4RERER\nEVGMYIBHREREREQUIxjgERERERERxQgGeERERERERDGCAR4REREREVGMYIBHREREREQUIxjgERER\nERERxQgGeERERERERDGCAR4REREREVGMYIBHREREREQUIxjgERERERERxQgGeERERERERDGCAR4R\nEREREVGMYIBHREREREQUIxjgERERERERxQgGeERERERERDGCAR4REREREVGMYIBHREREREQUIxjg\nERERERERxQgGeERERERERDGCAR4REREREVGMYIBHREREREQUIxjgERERERERxQgGeERERERERDGC\nAR4REREREVGMYIBHREREREQUIxjgERERERERxQgGeERERERERDGCAR4REREREVGMYIBHREREREQU\nIxjgERERERERxQgGeERERERERDGCAd4U5cpZiQ3feARVRWpGDCq87xFs+dIyZKn3REREREQU3IfK\nl635vZomxCP1pttQcfMNyEpJhGsGMHp5FBeGenDk4D4c6hwRkVURqjcVY/DJHdivfnXFZa7Ahr8u\nBpqfxba9fWqmRWYxKm68FmIX/LhPvY6DR4fEVDwWli/DgiR9vtcoBn9xAM0n1VuHskpWoDA1Tr0z\nu4T+lgYcOa3eKnlLVyLvGvXG8P4Aml9uxaD2JgMVG+/HzWjBzq0H0KvNIyIiIiKiQBjgKa6cW1G5\n7jbkzREBivscejvfwNGjfTgrgqB5hbegbGEKftPegO6MFShJH0Lj+okK8HJR+VgVFo004Im/fxVu\nNddPeTW2lGeKAC8OcTPVPOl9EWwdfQ7b6nvEm2ys3VSFJXNNQdnoKEZ/N4xf/Mt27OlS8xyZjfIH\nanB7lguYIdZp1A1ryxvCkX/YgXqfAM9/3aPvj8LdfQBP1LWoOYLrVtR+dRmu6XwBT3y/Xc0kIiIi\nIiI7DPAE18J7UPsXRUiNG8Vw+wH84w9aMKI+88gsRc3nVyAnUb4ZmLAAL2vtJtQWA0f+/mnscVTD\nlouqx6uwcJaYdPeg/pE6NOsfKBlY+2gNliQMoPnFXahv89vz8C2txjdXZYvQEhhp34UnfhAoUtS3\nLe+DLvzsR8/jUPclNd+Xsc9tdU9jd4eaSUREREREfq6+Lvv6J9T0FLMCG7bfhzV3luMO8brB9XO0\nvKU+CsfcFfjiA8WQFUnuzv+Dp79/FBfVRz7e60PryHzcsmgOZojwr/enR/G2+uiKcZXiM+sWIWng\ndXz3pz0YVbODO4vT1y5CSUYCMCMJrt+/iqOy8k4TjyXVX8Ad1/Riz9e/i0Pv/lbNH6OTCVhw6wIk\nizSdGT8D7x4+hjPqIy+57s/jttm9ePHpXWgaCrw3599JQO7SPCy49gM0v94bfL+LqrDlb9bhrtL5\nOPNKOyytQsOk8pjNsgqrH8fGz94Zeb6bTqJ6TCaDwPli7MZz2ZOEkR9CXLeNc+yOSZUWwY+PZ5vv\nvB4zg/yNmJz7RkREsWKKDrJSgOotpUhX76T0pY+jOuwBR+JRvq4Y6bKqabQPzT9sDdzkUWp9Hkf6\n1fQEcN1RgBzXKHp/2RB8Oy0GX+6CvtlxmHf9Mri06XjkrL4fq687h0Pf24Uj4SwwpCYc61W1cbMy\nsCRfnzTLWiXWnTuCRifrdjegs38UcZkFWD5XzSOiqal1Fzbv7tKuYelLa1Ghz/W1qhaV+fHAxS7s\n3rwLbWr2ZNdW9yR2d8hrXxrKNq7QZ/pZgTK5b7IlyBTaNyIimjqmaICXhqQENekRj6R5atKpuctQ\nmKn3ARvtfRMHQwY5l3DoHTk4yUQQwWhOmtjQAZw4rGY55X4FnSf1eq+4zHwtSJIB1v3FwGv/vBMH\nwxxMxYnm4/0qCE1EVlGuNmVw3VSFqk/E4Rf/+iz2O1x3c69M9xRkLZEFoyBk4XH9w3iIBafJg8eE\nrGSeODwgJkQgtKUKhfpcZQU2LBXXOnG97dw79fJMW90+dMpmIOml2LBKn2dWsVG/Odl/eAIH6iIi\nopg2RQO8AVzwa0d5CRdOqUmHUks/jlQ1ffb0G2oqOHffuQC1Z4nIW3oPajZtwpa/exyPbqpBdUWB\nmGuWi5Kl+cjJzfa+im9FWZ7+aepNy1BerM9fsmwlVi81B0bFyJIbe34Ix/UZYbiEg2+cVNudgkXr\nalBVmogTP3YeYIWtuRW96hglLij2FOBcN92LL69Lw6n6ndhz3L7PnR135xCGxb+pWSIqJaKpb+8O\nNMqmBQm5WF1doM8TjADI3bEPda36vKmlHXV7VQ1lkSV4XVWLMi26a8K2vfosIiKiaJvCg6zIvhDe\nZpr9hx8O+w9m+Ze+huVaDd4ldP7oSdQd1eeHbVYxqmpXYKFrCEd++grafnUJro8VYfnyAlxzsR31\nW19QzRCXofbvSjHPPMrk+6PobXoMO14GFn72EVQVqpDwg1GM9jbhyzsa9PcF9+KJz+XD1X0AX/5O\nkz4vLKbBVrT9/abYX+cBViTyPvcIqgvk/lxC94tPYucpccxCPd4hoFtR+61lyHJ3YNdXngsS5Kp8\nYW3aJfv9VOaq5qk6d8cL2FxnPzKn7COjNRGzMPKZ8bl83zjH97sBl2uzDY7zrePfyubL65BnruH2\nSQvjvBF5YLfI89YCtCiAPiNrT0QB9KGtB3znmfit29g++bvGFM+26t8LcExCbqsuorT22+YA+xvR\nMTHvzxDKTNehgOuRQqwrcJ57AReK9HSyblvFxqdEwGBdp5GulvlO00TQl6veSDbHxbzuwTLf74dO\nQ4MlP86zyX8h+G2r3SBYAfKnxmbfNNb0Mh/vQL8xMY6nN48a+zpxg3QREdH0MEVr8KQD2CabfamX\ns8KEL1ec3jxT84H6N2y5qKxdiYXJIzjyzzuw53AHurt6cFwUyp7e2YoLyQVYu+Ee9bDuBuz428fw\n5a0t6jlv53DkH/TgTjr+w29gT6cIuka6sGez+J4R3EnzZ2u1gZffj3SUyy689s45NQ3MmDG+wZ3U\n2dqnRiONR3rBPaj+fCmSuvZhZ9jBnXQO7vfFP65ET62rY7KgZilYS678dXjGr3lYeNKXPuVXKJfL\n3WKqkZBkYc9uG+TvnwnYV0fn+LeyELvdEjBJCSKPbjf6qIrzRmsaF4+sAt9tlCpkM2BZ2G7UC9fa\nui3BnSTXbd1HzazFfkGMPVnYDbSt9v2ynKa1LPD7b3M88ip9t3ksx0Sjbas5uJP81yONbV3tIgiT\nxwxInmNe7gos0FZuaZ5eVIAsma79b3iCN6dpoh8Xa8Ak+OQhM30Z1u/L/bJrnujPmx/lcvRtFAGQ\no+BOBrI22yqbfdpuq5Be6n8c5L5ZrgO2+d72eAdmNNV05d+tbYu3ZrKJwR0REY2rKRzgTQ6pa1ag\nMFlMnH7Lv7njyZfRKYdHE4WyiuWmgunp19GtdeWbjQXl2dosXQrSr4nH4LED/gOPXK3/M3wmwmfB\nZZbi9gWz1RtRuF9sDLYyjjreQO95fdKVU4QFF5qwS5Q47Zu4hjKAC/KHIigPd7v1oEWvVTBuCMiX\nHAzBLbYv3aYgKAdLeGh9kz44jbxbH+RGgnm5+gALYn+zCrwFRhF4rZaBiaw9UN/z+X764sADBBm/\nFXy3X22b57eisLtKFVwt69GawckC9CpViN3bo/3WZxs1KmAwAgNj3ab9115agVz8fpY1YBAS4vVa\nEvXdQDdevP2QTMtd/4LedwnJSA2QHiHTWgTzeoFf1giZlq0G9XDll+rB41iOiVmgtFGFeo3DdQXN\nc3bHbFW2J9hIzzEFifMStXzQ3+2tgZVpImuSrOuXecOTJoJ+XCxpp73kdok8VGYXjPp+X89vlm0K\nxmiqqTjtm1ZYfbd2g8C6X0Z+D9gn23wcVL5AQiYKrcdLsD3nHDMCc1MQLI5rfYBWA0RERNEyrQO8\n/vN6AVGOLjnDWpMQUDxS56eoICMeN2WlaFPu4T6bwOUSLms1g3HIyrtNm6MbwsH2Pm24/+TriqG6\n4AG5tyIvuQ/HX47yQC6uIlR/fgVS+17CIctgK+OrC8f6VRq7e3DwOwfQq7+LwJBegxcx/z6askC9\neesu7LdpouaULFyag5i2ujf0QmBCoqfwXViQqecXWXuw/Smfl14jZV+bJhm/lQVN32BJr/noP7xP\nbyZm1NrIwMBS+7F/qwqcPIXYA2iUgUVCLspMtSyF1Yv1oMsIDAINjqKCDcxKsQSIgs367ezfqhea\nffepHW3a6Kv2hXMnae2pgbQ2PRT7Ut8xIOaLQrpIg7EcEy+bURBFsKIHnt7fR2ddB3BC7qwpECmc\nk6ylt3Ys07O9QZqWBgM4odLKuMGh1Vhb1q8Hw2lYoOUDb42gVpvm811Vc2Vaj6H/sG9a729UQZNd\n/gjAey12Tg+IH/Zroru/2662U7HmT5Ev9JGRvXnOOF7W/Kadc0ZA6JRP8Cry5RQcNIaIiKaeaR3g\ntfUNqWeqxSE5VQ/UQrsNlRvWoVyb/jhStT5tgXkKLsm+hR33wTfRKwOWWdkoK9Hn5X0iG66edtvR\nPF1XmZqThsOVjdUP3o2s4Vexq67FZ7CVvFKn+xypFOSk6nfCR4d60BhWySh69m9VtQ+mQquz5mOh\n+deo+g8AlD5LT4NI6L8NMICQKDxu2yuCIlm4VrU27l7xXvvQzD9wamvX84G3lqUAhVlyXd7AwJfe\nHM6nsG/n/FD4BVjZhFYdF2sTTLPQaV2gzsdhDNoE7W11O0QgoqfXWI6Jx8URPcC0MNLWqOGMyroE\nPXAxgkF1vER679fWZwnS+ntULZiRJg4UpUA2RgiPTd5s1QdEckwcf/NxD/johGCKZPNklT9tmhR7\n2ORPa3BpnHO97TY1bSL/GINHOeUJeC+e1M9VIiKicTa9m2g2iD/WKuhIzv6Es75dshA0ck7VRF3G\naIi+ezOMFH7fjQtqUmc8Ky4e6QvlyJDFKMudgf7jLdqnVu4Pgj7eO4AMVDxYhSVoQd3fN+jb3NyE\nbtVsMjlvmbf2cFzkewqXg732++VcClwz1WTYzP019WZWWt8nWRh00tdqTIwCthxYwdgG/5f9YC9h\nFM7DZRRUjRoZVQNo7R+k9UXSCs42/eXGRO/rFbJAHha7x6fYGcsxCVcU12U005SBozpeWm2rCqi0\nGivVbNNTC2ukiay5slmv8dJqqoybBDZNOb2vaA8OIvKBdvz1Zp567afdoxPsmG46OOr3SUREND1M\n8z54Lag/OqDX4qXcgOU2D+S2ks13MNCjRnHswKlhPfCy7Y8kpCTpd6bdv+5Dtzbl1dzUow1C4sou\nwPKl+Uh/vweNzfpnfn6n/2Pb7MhWPJZU34uypB7U+zSN7MLBDtUE1FR7OC6WZmOeVvF4DoNy8Jgx\nEQVVWYIbHVU1kJHyBnt6/yf7Z1VFj1F7ZtSwWIiCeuCCrH/Nm49Vtd5tPzWi1xr59auTjNo5c22L\n0T9I3y69WZql1sJTs2LtkxVuXyQrWTBXtYCWfml6AT9SqhljgD58hdW1ql/cWI6JialpqJmnid95\nmb5RWpdG7Z8MyrVgzKht1efLY18hm2165kv+TTt9mNcfsG+mrlB8N7q8+cBo5imbXWpNGhN8H51g\np2KjuulgDV5VP8hI6TV6AZrNijTQmkITERFNYtM8wAMG9+7Da/0ySEvEwnVVWBLkNrB8QPfKnGEc\n2eetjTr0Wpc+UmRyGvxjpVLMmyP/PYfOJpsarI4WnJC33uMyUPbnmbjQ0YBO/RN/757T1jNjpu+T\n9ezJ4G4D1mYMYM9Tu/wGbBls7lGjeIpCjJPBVlxFqHrsa/jmtzah6iZvU6pQcjKSocV3F4fQ2aXN\nGoPZeg3eheGw+/HJEQT9R3w0gh4HAhTknfI0h/QbWVAOjLIOldsDjEgpBP6tXvMh52u/NWrk5Eh/\nllpJb0HY0kRMFejTc6r0tLB8rvXxEqx9rIy+epEz1Sr59NdbgbIgTTSdMJox5lVaRlHUBs5I05rp\nynQcyzHxsqlpMgXFRrAc0boC5Dl9/8R6Za2Xpxmmmi/7VMp1m+ZLAdNE5qFKff36dhnBoP+oktp+\nie8+E2CE00gYg6TIIN/c101vUi0uO+aBavyYakZ9+kGKNC0aW42wp4lt/jr/c441hURENAVcfV32\n9U+o6WnqPbz9yz585I8WIePaFOT/6fX4yEgvevsvqv55usTCe/Dgmj/ChcPP44e/fE/NFQbehjv9\nRuSnfwzzMn+DX/ziFH6rfZCIkr/6FEo+drUoIP8rvttk+o3HOQylLEJJRgKuuuoM/uv5n6Pz/6mP\nrH51DRaWZyNZbO9/NXXCvxuIKBDmzkfWDaW4595PozTLBXdvG5re+RXOX/TZE6SnfwTzcnNxrQiY\nrpo1C7MGfwX3R124fHZEbbvF8nvw2es/KrbRhdTUmfgvEdQG7oYSj9TrMjE35QbcftsiJH9YzDrf\ni+Zf/xZJV7st2xKG3CW4/aaPYUZ/G/a8EewxCwtQfGcmki6fxfFX2nFaFEy/sDARM8T23HFnuel1\nA66V2yaCjP3/S3xP/7FFAvJL5fcSkaV+d8v8s3il7VeYW1iGRSlxGDn5c7S8pb6u+RgKb5O/GUHv\nT4/ibTlroB3n59+sfT8py2YbRAH3b78d4NmGAX8r9lF+7vntr9B2YT5uWTQHM5IyTd8rR5b2xUvo\n/PE/4GWfyo0TeF8uO/tj2nb0tzyDetO+nL7qD7XlJfust1zbFs2H52BR6XyckemcVoDb5LpH+tDw\nnyf0zz0sx0Ssd85CsV3XiN+bluvZJ0Hu6w0uPW3DSuu3jmKmXHZSHK5dZFq23DbxsWx++PX//aux\nHRNjf+SkTAPPb8UrS78B4+74Cbb+m1iPFNa6Auc5zVtzcINat/vd10PPlwKlifF9I02Et/9zpr4c\n2/2SNblP43mVh3L/VC5zFGeOH0abT76yHm8bIuB+8M/E+SyD/C0/tnznBFrOyrz8McxddD1mGsfW\nh9je62Sazvakk/5SaSrIc96TdkHyp1/+CnXOScH2zcpYt99vZDPl+7BGLNvI60RERNEw7WvwNO4e\n1G/7OnYdkjVbaSj5zHps+dYj2LShFhvEa9NXv4bNazIwtH8bdhy0BheXcOT727Dz5S78JmslnvjW\n1/DNv5O1XY9gdZYbnS/vCvrct8GXO9ArYp7Rkx04GLS00IF+Wds3KwUL9Rk+Ft4ntvWBalStKkbO\nHL0A7spdhpr/Ifv3eenfW4k8T0XgbBR+rho1D9SiZk2AQVda30S3EdElJAetvUleU4NNtXJ5K5Bj\nNGVKKRLvq1H712tst90JV54cAGIUp955Q81xaO+OwE3/RMHab4RIH+2o2xvmqHkBaCP+2YzApw3D\nHmLUSce/1Ua9NB41YCL3c71lVEnFqK0QpVr/wVXk8vzWa+4rFTk5iqZ5aHyNtp1jbf6pL9u/mZ6+\n3ea+bmM5JhqtaaB1e/3XIzlfV6g8ZzRDtQ4CYgw4Yz84iNM0kcuXTZj9jo22r/Z5KGyrjOdSivUH\nGlVSG/VUb9paFqDWUKapXz7UttPmHAiTdrys6WV7vImIiCafD5UvW/N7NU2aeKQuXIybFszGjJkz\nEPf+ZQyfbsWRlgH10O7gEudnI/UPxMRvhtD9rpNf6L9JGulBvxr8JJDUNeuxqSQZ3Xsfw87DauaV\n5FqJTY8m41DQoGh8lH/pa1iePoBDX9lpO8ooERERERGxBs/GJQweb8L++pdQ/6OfYI/495DD4E4a\nebcH3V3i5TC4k+RvQgV3kl7bF4esP7kCDym3U5qOpDMnr3hwB9cy5KXHwR3gERJERERERKRjgDeV\nuBtw6Ng5xGUWoCJTzbtiMrB2cRoG/3usjzsIX1ZFAbLizuHYwSu/biIiIiKiqYQB3hTT+cMGHB+Z\njRs/eesVrMWLx8K192DR5Tewv2Fsfa/C5roVFYtnY7jleew5qeYREREREZEtBnhTTjt2fa8Jg+m3\noWZVhpo33pJwDXpw8Lsvhf2IgrGRD2q/DfMGm7B7T7CRM4mIiIiISOJjEqai906g/f8mYvGflyP3\nvSa0WwfHi7qL6O3owrtXuPKu8L4HcfuM1/Hdbf9+hQNLIiIiIqKpiaNoEhERERERxQg20SQiIiIi\nIooRDPCIiIiIiIhiBAM8IiIiIiKiGMEAj4iIiIiIKEYwwCMiIiIiIooRDPCIiIiIiIhiBAM8IiIi\nIiKiGMEAj4iIiIiIKEYwwCMiIiIiIooRDPCIiIiIiIhiBAM8IiIiIiKiGMEAj4iIiIiIKEYwwCMi\nIiIiIooRDPCIiIiIiIhixIfKl635vZqeYlZgw/ZSpKt3/Ycfxra96s0VV4DqLeuQl3AJnbufRF2r\nmh0RY1kDaFy/A/vVXE1RFbZU5sLV34SHth5QM6cjdewvdmH35l1oU3OnisLqx1GZH69Nh59vx7jv\nq2rxzNI0uDtewOa6djVzEjPy/BiOtZHeE3uNICIiIroypmgNngyCvMGdlL70cVQXqTdEk5Q5uCMi\nIiIiirYpGuClISlBTXrEI2memrzi2lG3+WE8tH6stXcU2wpQmCWDO1nTK/MLa5RCat2FzSKdHpqC\nNbVEREREE2GKBngDuHBRTXpcwoVTatKxDJR8phobNlRjbWk2XNq8eKTetALVtbVifg2qK4qQqn9A\nFCXDGOSNACIiIiIaB9O4D148llRvwHLXmzj2wZ+gJCcOvQ0/weDCu7FoRj+OHRuA+9pc3LwwBXi3\nCdu2HcCg+qWdio1PoSzd2gfPdxs1wfrPqf5RVp7+UuY+eI0p+rT6DgL1UTJ+o95KodPK3M9rCGU+\n+2DtGxhmn0HzvO5sn/31208133/fgm1fkH6QTtLCvH2mNA6eZkYaqLeSZZsDNc0MulxrfjDvr1+a\nhNoGm881luNmkwfHll+CHA9H6zIv29gXp/lTfU+bNrFbljatBDtHiYiIiCa5KTyK5gFsk0231Ct4\nAdTG3GVYmnsOR+peQn3/sJgRh6xl9yCr90V8/et12LP/APZ/vwknLopP5mfjJv1XzslAwa5wmV6K\nZ7bXokK9jYhchiVQQUIuKrdUoVC9lWRQ4fc9IX3pU3hm4wr1Lgi5TL99SBMF6jFuvyT3wVK4d+Wv\nw5YtNttss28a2+2LR17lU9hSXaDe68JOi1mL/YJBW9pxtgmctG2LvF+otr2W9LHfX0kGKYG2wfmx\nsl2nINPImp62wjge8oZIoHU5ypuS7frCyJ/jeY4SERERTZBp+5gE15JMXNP/Fg66gSUpydq80Xdb\n8IM9HRCzFBdmxKnJMBUWZGrBgayVMoJQ7XV4AOgXH6zSvuZr7w7xnRfQqTU/lTUR+m9sRzuUtQzG\nMnd36duckIlCI6AQhdfVssbI/D312t1xSRRiFzsLPmRth+e3Tdqmy0L0ArvtD5dp27RtElwJspbL\nu++2+2bms33iJdNXcOXf7d2/SNJCbIdWi6e+Z38DoQDVq1QQaFl2o5ZQIrhZpQembXVPivn+x9Z2\nucb2CrJGy7tcI/19VWzUgxTf7xrrSkaqtm+qn6hKH2++VLVdxjoDpecs/2DMlpPjsaoWZVpU5e2L\nqL2MYy0CrA1O81fQ/KnfBDLylid9VO1dROcoERER0SQ3bQM89LyJn/28RUxkIydVFqZH0fsLSzPM\n3DQkzxT/XhzBkD4nbMNnLMGZDOK2ikJ1uDWOZrJQa25C1roLR1RAYQw0YxRe9dqIp3xeelPBeGQV\nhKqVEYGITzPAA2hUheXkOQ5qdIKx7ENb3T4VkMhCv6nJoNi3em2ddoPoWLdPEOmrF+i9+xdRWljT\n2E5RAbJkrZnNd/dvVQFWoMA0CHPg4RsAioDFCIJM9m/VAxPf77ajrTdQutkINJjJ3h49aJqV4l+D\n6sfZ8ajI0YPF/sOWpptyG1RAmJ7jpBYvOvlzXM5RIiIiogkybQM89/FXcei4KAy68pEuK/BGB3Di\nsP6ZIeemTGgfne7BEX2WY0bAojU5U8GEo2ZuTpwf8i1EC/3n9YKtIX2WXgM0JiKwtdYYtZ2RzVmj\nwGYfdGEMQGKzfVJb+0ktCDJqnSJKi4DbZzIvUQ/EekUwpc8xCTPAMtG39xJ6221qblvb0asFwgHI\nfm0+wWskZH89I9/aNQkNwNHxKEDqLDlXnG92AVQ4AeUY8+e4nqNEREREE2T61uAZStNxjfxXFOiP\nazMM2ViSNVv8O4pTJ5r0WWExHp0gX3ptjuxjphUk7fqTRZW3EO1p6mjzmhIPuh6z6ZAWsg+eClJs\n+rU5pfXB05ZjNxhLLJrIc5SIiIhofEz7AG9JVgpkN7vhvnbf5pn5xVggq+/cJ9HWIP6deyuqHlyJ\nhdqH4TIVJGUTtIRcrB7XmgKj9ihAX7mignEovBp9vUxUDde4SUi0rV3yNHE8L5v7jWNanBrRa6ay\n7JbhfeZduI/v0GtjAzShNZqFesjaNlXLZukHaPQ9c2RVrarxs/SLC9Dvz5bD4zF4Xs4NcDxWZevL\ncFKDGlVX+hwlIiIiGh/TPMDz9r8b7uvRZyk5hWlIFP+6+zrQLP5NLSlA3oxL6NY+DU2rDbEZDdDo\nfxSaTcAUBqNZnGx+5jtghRwYZB0qt0erOZpRYI9HXplpf+UIhWOoTXImDWXWmhZToGI0cRy3tDCa\nS8rRHC3HumKjqgW7eBJtTpucKp4mjfnrLNu7Ahv8RvZUD/336we4AmVBmmhaB00pnKMPNGTtF1dY\nvdh5E02Hx2N/t+pnt9Qyyqgpz/R3h+j/GAFrv7yxn6NEREREk88Ufg5eFLhEgfkbpUgf7cPBv9mJ\nQ2q2VPbg10RBL04beW9b4zLU/m0RRl78BnYFKKz7PAcPoqAadIh92VzQNJCIhb4s9UaSNTOy8C4L\nwHK5xnsTWViVBWnzc8SMebZsluGlng0mgwbroBmyj5cohHueWWeaF5B5XQH3QdZEyaDIP238901t\nn/apPZ/tExynRZA0tmV8X731ZX0GXOB9tAq6vZLp2PjlFxuetPPbXqd5VrDLD5rwj0fQbfZJe7u8\nONb8KdJ/9wiWBN1f4xh59818bhERERFNVtO7Bi8/RRtEBYMntVo6s8YjXRj5AEj94/V4YlMxcPi5\ngMGdH2NEQjUioA9ZKA1RuN+/NYxmcUFoQ/PbjLooC6qOghen5KiD1n2VhXSbdUeVlpbWtNKbGFr7\n1I1bWmjH2ngkgYnc//WWUSLDoG2vNU1t91fmF+OxDCba+m3ykWdUUgu5H37po6el46aeYRwPbeRP\nv/ND/25U86Yk8qdf+ozxHCUiIiKarKZ3DR4SkZ47G6N9fRi0i0RmpSEn1QX3YA/6tWaIROQvSI0a\nEREREV1R07wP3gj6uwIEd9L5AXR3MbgjIiIiIqKpgY9JICIiIiIiihEM8IiIiIiIiGLENO+DR0RE\nREREFDtYg0dERERERBQjGOARERERERHFCAZ4REREREREMYIBHhERERERUYxggEdERERERBQjGOAR\nERERERHFCAZ4REREREREMYIBHhERERERUYxggEdERERERBQjGOARERERERHFCAZ4REREREREMYIB\nHhERERERUYxggEdERERERBQjPlS+bM3v1fT05spH+fJsJKm3Ps52of5wlzaZVbIChalx2rTZhRMN\nOHT8kno3VcVjYfkyLLBNhHPorG9Cp3qnS8GSuz6B9JnqrcGUXkREREREdOUwwDPk3oNNf1mAa8Rk\n3ExTADc6ipGuA3iirkV7W/7A41ieG69Naz4YxejlUfQeehI7D6l5U1Y+1j68Bjd+VOz/jDjEGfW7\n74t9dPfgpSd3oVnN0t2Kmi23ISfBm16j71/C4NHnsK2+R80hIiIiIqIrhQGen3gs/9KjKM+UQcsQ\nmp/ejvrT+ie6eJQ9+CgqskbQ+dOfYPehHrjVJ7Ekde0mbCqeLaZE8Nrwdew4GKB20rUMtV+9Famn\nW1D//ZfQdl7NJyIiIiKiK+7q67Kvf0JNTzErsGH7fVhzZznuEK8bXD9Hy1vqozEZRffV2bjl+mTM\nQAI+4upF07Fz6jMga1UNPrPoIv7j29vx/C/PiW9PIUVV2PI363DXwplo+M8Taqa9i8Mfw+KSNLhw\nFT4S93s0v95js68ZqPjSJ3HDxWZ895l/Q+cUaqFasfEpfOFT0cw3JjbpPJb1hftb/fs3I+PsYbQN\nqJnjQp2DpfNx5pV2+NwHcWRsvy+sfhwbP3vn+BzD8WDki4jTqwDVW/4nKiuux8yfHsXbam40GGkZ\n3WupDSMNQqzHsz0Rp9V4CJ5fvWkY/PhMzn2bLAKn8bhesz3Gek0jIpocpuggK7KgU4p09U5KX/o4\nqovUm7FqbkXvRX0y+bpi5OmTSCypQtUnXDj242ex/6SaGatON6FzSJ+MS89GmUuf9orHkup7UZbU\ng/rvHECvmktEU4sMOCrzTc3Ox1PrLmze3aW1ekhfWosKfa6vVbX69lzswu7Nu9CmZk92bXVPYneH\nvMuVhrKNK/SZflagTEvrATROoX0jIqKpZYoGeGlISlCTHvFImqcmx6wdzSdG9MlZIrgpAVw3VeGh\n1Wk4Vf+P2H10qg+m4sSQSAMjwktDTplvATBr1f1YnTGE/d/bhSNTsI3q/q0P46H1D2PbXjVjnI1l\nfVd6W2mcyOBGHMeHJlXBvgCFWfLcvoTO3Vcon8l0OCyrlkUgtKUKhfpcZQU2LE0T/4rt2Tv1AqC2\nun3olDcH00uxYZU+z6xio35jsv/wDuzXZ5FDvA4SETk3RQO8AVxQNWxel3DhlJqMgs6GNzGoTcUj\nq6QGNZ/KxoWm51A3LYI73eDLXejXpuKQlX8bjEq8rFW1qPkE8Nr36tAY6zWZRNPCMAZb1eSVsHcH\nGuXFJSEXq6sL9HmCEQC5O/ah7kpuT9S0o26vqqEssgSv4rpZpkV3TQxSiIhoXE3hQVZkW3lvM83+\nw9G+s2cebGUUg03P4un6Pv2jqJFNTdchz1wbadMsSfY9KEuXd9ifxGCZnFYfCIH226/ZlShUPNSY\ngi2VuXDJ6a0H1AfB+A84c3B+Fb68Lg2nXtg25mBX3y/1RjOAxvW+d7aN/ZD72TjH2Cff7/ktx0HT\nLvNyjfSzX5fO3fECNte1q3deTtPZd31G3tWPqV9BVhQEn5G1GOr3dtuq8z0H9FoYI4+Yli37PQU4\n7gGXbfxGvZX800Ct30lTOmOfDNpvhlBm+/tQ54V1vxXLcpzkLz/mtDKOo/oo6O+t+ycEPF7m7Qy2\nPvP3bJYv+R4Tm3SxOeYGv7yr+Gy3o3wQ4Brld1ytjO1VeXWeb753wtExdprGZmHlV39G2nrTythX\nB3nQw5xf1LrFXJ/0tzk+/vlOcHAczdcC6/Uv2DFxfv21Oa9Nyw2VH32vVZa8E+IaqnGUVuY03wUY\n22S7/8b+BNgGIqIJNIUfdH4A22RzJ/Xy+4M2Zpdw8L8H1MAiIsC5Kto1d/IPieWPnZSQi8rtdn1T\n4pFXaS3MyH4sT/k1BZJ/cP3+UKaX4hnLH7fQLqGxy0iDFOSU3xOlmkz5h9F/X7QmW9vt+1ImF9n9\n8ZdpaLMcLQ0j75Mp09S6Llf+Omwx1TRIkaezyLtaE7V4ZBX4LlOqyJEFS1FoaAxSyJWFFVXg87LP\nI2GThSObfZBp8EzAvkWByYKZX3CiHSPr9kvhnhd2ws9ffmyPo/y9/flmF3zJfOQ4vezWJ/fZrwlj\nALb5QZDLdZxuvrTjFigfBNiurFXh5D/veSDzrZ6GIgByFNxFcIwdpnF4+dWe0VTTlX+3ti3emskm\nh8GdWSZW26w70PHxy3fBzmeb42h3/bPPR2Fcf7X8aXNeR5w/w7uGOk4rC2+T22z/bSwqQJbcn/43\nGNwR0aQzhQO8cebKx9ob02Rop0nNX+YZbCWkWWnImZ+o3tjz9sXwBqkPrX9B/2OCZKTaFVC0u5Xe\n72tNnIT0HN8/5vofXN/vPqQGNgiXu7EHp9TwmamFRUjq2oede4PVZCYiPTdN/D+wwuq7tT/08g6y\nZ/s8+2Pfl9KVoN+51b+r3wHX09Cyn9qrCf2y0FgWfjBiMB8XfeAEsQ1ZBd7C0FjTeW+P1vzVZ5ma\nFVigZYxghQZRuF2lCivyzrKxbvEy8kTkRKHNKGibluvZr1kptgX7gETBbrUqLPrmdXmM/Dk7L/Sb\nO8Zx8XxX1RpEkr9sWdLWWJ/P4CCh8oEowNr1xbJlXp/x+4RMiNNOa9LoTQfvsTFqYAoLMrX8YN3n\nh2QhWO63zTbIQUHslqndLAt13EQh3ty0UhcvzlNTOoSo5dIYTTUVp33TIj7GwdJYCjO/BtYuzl9v\n8KrlkYtdqLfUfDoirn0uWaOktkU75sZ2WvKofGn5NH2xJ8DSgx3r/ujfc58XX7X5W2N//ong2RQM\nOb/+hrpepWGJyEt6flTpbNrfgDdvnV5Dw0grf+1o65XnfRoWWM4h/ZwT+x/sRhwR0QRhgGcrAxUP\nfho3Xm5BfbvvYCuhZaOythY1NesQ7Ov2HcaNPyb2BZT+w77NQPY3+he6vX/MLU1GPAMbhMndgF69\nMyJwphW7xEK1dQaQU1mDDQ/cj3uD7Lz+h9xbODXs79a3L3mO/x1ZWZDzTSv1R1wVoJ7Zbn6pu912\nd10dsK6rre4NVagVwas2JxrpfACNsnAhCsplpoJDYfViPcDpDlZ7p+4cy0KQpbZj/1ajMBYpo2bc\nUtBubddHljWlgRPmwMP3+In12ATDkZwXVpHkLz82aSuXaxRIjcKek3zgcwMmEOv6xO+PaOsKIyAV\nhs9YAggZGG4Vx9InPUNzctz8C9Y26eBA/3l5bMMT0TF2kMbh5tegfIJXEQhEPGiMCL4twbKxnXoN\nmO/1T699s9Zs+fdRl2m4eesu7LccL/99F8HqZhV4ea6pYVx/PTVdIsDyu16J5Yr59ZZs64yza2j4\naeXLuP779qlUo6FePIm2MPM7EdGVwADPTyJK/upe3Ox6Uxv+v9k82EpBqTYVXD+OdXTh+KEGNKs5\nIckmND5/cOzYDCLTOoRhNakrQOos+e8ATtgV6NQdz/CUYt4cfWq4TxTy9cmA+o+9hc72V3DQ6c6L\nP5pbjD+4Ns3cDH4F16IUJKvJaPNbl0hP30F9opPObe0ntQKjNwAwRjQMsFzDvES9ENorAh99jokR\nDEWH1vxQOz42zascSJ8l9+cSetttSnBG0BiIo/MiBIf5y8/5IdvCuG8A4TAfOKn1tFlfOIGP0ZRM\na3Km9tfapDgcjo6bX7AfwUBX4hibj23ARycE4/QYO0jjMeVXG56bcGMJBC6O+F1P9O10RguiLIFY\nsFpl/+ufdAAntI1QtejhXH+N69V5uxtfInAWQV+bSNtIOLmGhpNW9tS+m2t6V2Vred/+GkxENPEY\n4PmQz3arxep5A6jf+oI+/P/pBhw/qXriZd2A5dqtwGAu4Xj9Lux6JdSALHr/hZCFkomWm4bkmXLi\nEgY7e7RZwbiPv4S6HzSFCAT1/jPavtv0i3DEKDR0WJqk+bycDmYwQYwCo+VOd2T9dKLIFFj59a8Z\nd9E4L6KQv6YcWcti5Hu9FlfrYyXTwGk/vivOaA6sN/PTm8Cm2Tw6wc50PMYG740Fn2bUlpe3dtOo\nlZcvvSbOcyMggj61mjCuv4VzxutWnBDyGhpuWtnTb+x4a/r0mvsBHAnxOyKiicIAz0R7tlvuCBp9\nnu12CQff0O8SIi4DC+9K0ebayizG6uoqrC3NDlHgkIUT1YzF0i/A6OcTmXYMnpf/+vcX0Ki7juFI\n/eNM/U7t6BB6g96BzkDJmipUf6YYOSFKWxUbVW2QqZ+F9gqnCWnA/he6QvGHfvxEK52Nfjr6cvSm\nRAFqD8xOjWj50X7fjTvYNmxqkvzubsvaEBVY2ffDCY9eQxKgCZTRdMsjOudFVPJXgFo3o0mmXsvh\nMB8EqA0cP6ZgT+6zbX+54BwdN5uaJee8x9po1ulpAutge6NyjG2El18nilFLHyDfie0MHCB7gz29\n/5l/H1H7JsxGk0z1OI0wrr9GLZtrlt0NGxHkRxpkakJdQ8eSViZ7m/SbJtr+Gn38eib3DUQimtYY\n4Cnas91KgNe+vQP7rc92a+5Avwr4Ag62Mlf8obo3Hxc6R7Fg9b2oDNhpW1IParf2CRF/OLR2/WNg\nNCFLX2ozilkENSIL09RwKYMngzQ5TUHFhk9j0YUujOasRFVlsMKZ6Y6qT78SUeArCmf7jGYzNiMN\nymZflbL2IrLRA52IWjqrglJ6jtgHGZg5acrlaSIn9t1SOPIUfM2Mprx+fVUe96+hM92Z9+mHs6o0\noiaansJd/jpLQVKcL341L5GdF74F0ijlL5u09aaXt/mXk3wQtD9lRPwHYdJGCbQpKBsBabicHLex\nNE8zBkmRgbw5n+nNCeV69dEn7UXrGuIvvPw6cTxNE5dam1uKNFi1DpXbvU10ZTNr/+a6gW8E+e+7\nNxj3BjVhXH89tWylfnlUG6hFzrcuI5y+viGuoeGkVWAqUJTNNKv1GzfRP6+JiKJnCj8Hb6zikXpd\nOhJTM7Ck+BYUzhd/GIZaseu5Bhx/Vw2sopHfy0bJ6k+jJF2OqXkJ3Qefw89OXsZIXx8G5V8OIe9z\n61H27k7sjPtLfHN5Io7909PY3aV/Zkf+0Q3V/E3WoMjCj/5d2YzJOoCBKHTIDu2yQGwq6IRctk1n\nd19yJMwUuFwFWC0i1VSx2+6uBux6tQ/uQfHHVKu1MMm/F5vKTmLHd+JQ/a1lSDpWh6//MHBzTlkY\nDdWnSgYYstmM8V0jLXyp/VfvfNmll5fdcgOvSxZwZOAkm/l4m32Gk87B9sOcHsE+9/lMBhBBC5y+\n+x9qW73LDpamBiMd7POflXn/bJl+H855oTUl9Qmm9e3qD7U+wchffkKmq/8xCrrNPueaTXoZ67M5\nJ+2Ou9+65O/8ntdn5ZtvfdnnbSnocbO95gQ/5zyMfQ6UbzzHIPB2h8xTgucYh5nG4eTXkALuq/c8\ns+Ynr+DnV9DtNPbV7xyxMC07dJpaj0ewa4UlL3iOqR3zco38qL3ROPlbYN72UJ/7CXWOGsz7YJdu\nAY4TEdFEmL41eBX3Y1NtNWrWLtODOymlCFVVK5Cjv9Np37tXBXdSPHKWi989UIPazxWrecCpV17A\nc68Ay69PQ9zwSRwJEtxJcrRA7whrivxDE/Zw3P7ksv2atMllOxwFruSBDdjwgNjHz+nBneTKXSb2\nuRob7rNpTtP/CnbvbhI7/3HMizuH3qPB++rJplh+2yf/OIbdDFBvbuSXjtqyHBQ0x2is6Www7jDL\ngk7QwVXM5CiNfnlFFqps0kOwy2+yIOTf9FGmqX8elN+NtPmbNuKh9bfaMfJfT1jnhWWIfUNU8pft\ncZQFUf/Co9xm/7TRj4U1oBgro4bLh5YXAhwfbb8DBXfBacfNJi9reSHSgqwMOLRCskifQKNKiv2p\n146ffKadfS189K4h/sLJrxMp6PEx8p32eI0ATZxlHrc5jrbXBe0ctOajMK6/Wh61OTZ+y21H3d7w\nrp9SqGuoo7QKxTPqqgg6ObgKEU1y07gGbxy4VmDDN0rhatmOr+8ZUjOni3hUbHwcZTNb8fTXf6JG\nHiWaYoLU9hBFl15bldQaqAbvygpWQ0ZS4NpuIqLJhn3woij1rlykYwidTUMoXHMvll+nPpgO5i5D\nXjow2NWEwaKVqLorQ31ARER+tEFbIni0BE0Mox8yB1choimAAV4U3ZSVIi7+XTh4vhRLMi6j9x31\nwXSwJBOpGEDnyxdQVpSJy72hHhNBRDRNqZri4QgeDE9XlqzZ9D625RI6G1mzT0STHwO8KOofHsHo\nzDRUfakI7tf2oVPNnxZOncPIqAvzPleDm37bgvoONZ+IiHypfpNsCjm1GI/0ICKa7NgHL6r0kTnj\nhm1GmpwGXCkZSJ95Dt0+o5ASEREREdGVwgCPiIiIiIgoRrCJJhERERERUYxggEdERERERBQjGOAR\nERERERHFCAZ4REREREREMYIBHhERERERUYxggEdERERERBQjGOARERERERHFCAZ4REREREREMYIP\nOg9kVhpyUl3qjT33YA/6z6s3McCVkoH02TPUOzuXMdLXh0G3ektERERERJMKA7xAVtXimaVp6o29\n/sMPY9te9SYGFFY/jsr8ePXOziV07n4Sda3qLRERERERTSoM8IiIiIiIiGIE++ARERERERHFCNbg\nGVz5KF+ejST11sfZLtQf7tIms0pWoDA1Tps2u3CiAYeOX1LvpgCH++sxtwjLi9Ng7ZU43PkSGjvV\nGyIiIiIimlAM8Ay592DTXxbgGjEZN9MUwI2OYqTrAJ6oa9Helj/wOJbnmvqpfTCK0cuj6D30JHYe\nUvOmggKxv2vE/opdNe/v6PujcHd799ejvBpb7siGy/iq3G/3EI78cAfqLbEgERERERFNDAZ4fuKx\n/EuPojxTRjJDaH56O+pP65/o4lH24KOoyBpB509/gt2HejC1B5VMwdpH12PJHDE52odDX9mJgwF2\nyLW8Bk8sS8Fg8z48+2I7RtR8otAKUL1lHfISAHfHC9hc167mU2RWYMP2UqSLqVgb7ImIiIjG5urr\nsq9/Qk1PMbKAcx/W3FmOO8TrBtfP0fKW+mhMRtF9dTZuuT4ZM5CAj7h60XTsnPoMyFpVg88suoj/\n+PZ2PP/Lc+Lbk5McEXPjZ+90kC4XcWbujSiZ7wKuSsBVv2vB0W6bvcpcgS+uux4Xm76HbfVd+K2a\nPbmpPFI6H2deaYc5TneePhQNhdVfwG3pcQzuouYEWn56FhmlN+C6Bddj5k+P4m31SdTIkYS/8Ent\n+nrL/LN4pe1X6gNdxcan8IVPieuvzfnl5b1OT6ZzLfj5791mu/32mpz7NjnIGzr/E5UVNnmzqApb\n/mYd7gqab8aO13gims6m6CAr8o+HfvfakL70cVQXqTdj1dyK3ov6ZPJ1xcjTJ5FYUoWqT7hw7MfP\nYv9JNTMGDDa9hUFtKg7zcm/x62cHVxGqP1+KpK592Lm3T80kckgU6FbLx29c7EI9g7soakdd64D4\nNw1lG1fos6LFwWNi9m99GI39YiIhF6urC/SZPrzX6alVy3gA29Y3Qe6aK//ugH9XCqsXa/smb1qw\nBpWIiCaTKRrgpSEpQU16xCNpnpocs3Y0n1ANEGdlo6xE/KG/qQoPrU7Dqfp/xO6jU2gwFSdOv47u\nIX0yLl3sr0+El4GKB+/GvMED2FXXOsWbo9JEqCjL1W4a9LfuQps+i6JlbxM65c2o9MXRu8ElVOTo\nwZ0MzB5a/3DAWtf9W1/Q1u/KX4cNq9RMpbD6bq1JLvqbpmAAJIK8wzJ4jkfeqioU6jO9eNMicuI6\nsFnkqYc283pARDRepmiAN4ALqobN6xIunFKTUdDZ8Kaq1YpHVkkNaj6VjQtNz6Eu1oI7zRAOdsrC\njBCXgbw7jEFkRHC34X7cjBbs+k4TetVcIudWYIFW1T6AE6zlGAftaOuV1yRxnSqwq0UbCyfX1HbU\n7e3SbvykL61FhT7TGwCJ49649YA+b6rZu8NTQ1nmE7wWoHqVvGlxCZ17GaQQEdHkM4UHWZH9H7zN\nNKPfBMg82MooBpuexdP1Y2me6B1kwuNiF3Zb7mLKfi1l6aLgsPtJDJbJafWBYL+P/suV32uc8zgq\nRQHLcbq4lqH2q7ciSxtbpgVPP9WArOoNWJsxgD1P7cKRSKvubJp6+W2T7JNRKQpM/U14qDFFnxaz\nfb7ntxw9jepa1VsL2f9C7r+VsUzjc3NaGQL2EwtzGzTmfevO9vm9Zz3Gd9R8u3yhs8lDcrl2Begx\npLvGdht8zzlNoPUbjO2IaDu9++u37ZKx/T7b6iSN1H5ovxtCmdonn+PuJP0Uv7xmTk+7/XaYj/zz\ncID8ZpsOAYTaL5vPpVB9Jz3bqu3vgDoGDs4Pg/UcEPzXaX/cdCKQXL8D+9U7r7FeH408712+sa+h\n0sTM/nrju836tV+9kQIcT7/v+e17sHQKckxsjkHA9AmWh0PmIfP27QJ88o71GmEcP9/tdpJW5jTf\nttc4jgH239hm220gIpp6pvCDzmU/Cb35kHwF/yMdiUs4+N8DahAVEfVcNZaaO/nHxVLolBJyUbnd\ndNfbIx55ldY/4vIO+VOWZlD2y5Xf0wsQYXD/B7r71eAqKdkoX3s/VueOoPF7kQd38g+s3R96uX1b\n7PrszFrsV8CQ5B9z/+XoaWS7nDDYpZVsbmZd7pi3Ib3U7/faeraINLLus8wXWyzNwmThyy4PyeVa\n8lDY6S6XEWobtPWbC4qKzfrNCucka/+6z6saYpPQ22mqHcrx72NWWJCpbbOn6WcYaaTLxGqbfQon\n/WS+8DvX7NJTcZqPbJcbKL+1DmFY/puQ6H98TOzXre/XM2Psw9dWt081FZVprR8Dd8c+Z8GdLFzb\npJc8P2y3S7tuWo9bmghkrMc4GtdHo6mm6uco8phRM3nEYXBnllxkBHdmcjv9r/f6fpr7lstgx+Z7\n2r5b/zYItulkn4e0PG9zDOzyxpivhRbevJPtf44WFSBLHr/+N1RecppWVt4mt3Y13XqTZBH8NTK4\nI6LYMIVH0RxnrnysXV2MjAQ9Bv5IUhLePXwMZ7R34anYeB8WJel3Q5/8h5+j4afypY+Ad+2HZ8B9\n9jDaVPk390/LkaU9fVzeaXwMf/cv+vdnLtTnJ82YiYb/PKF911iudvfyy8/gB9pyf44z82/GohT9\ngXUjJ52OIDaK/tkfxy3ZHxVRfwLmzge6XvgOnv/vCMcJFQWhB//sY5hh2bYG1/W4IysRMy6f8+wH\n0gpw26I5mPHhOMyQd1Af/yftu9p2i8LfFxYmand///ap3foy1EumyYLsZNsRBE+3HRbfmYkb7sxE\nkmkbjLSYW1jmSSPzcTHSbkbCDO8IbxFug8bYNzlt2jfPesQ+63fgv4Edcpln5+MWLS0+ghmefCEK\ndv/fUsz9sOl7xkv7/h9injHaXyTpLqdN22a3DYUr7kah2F6/NJDLFQvoTRH7b5PPim67U8u3Q527\nffOh0+0U675OnifXzLCkcQHuWl2Aay93Yf//kscpjDTCAhTLfCHzm2n9YaefyhfWc9WTfvI7I31+\n3w+dj1bgzz8lts+cL7SXvGbk4IPzI3i/7YRp9MEE5NtcS3yE2takTH20wb1HPduTleT9buCRJA2/\nQtsF036L9Nuz9d8djJAoCuxfuMF/X43tuvqSaaRFddzkpM/xUec5xPExjZgYtevjW7/Vr9XXZOIO\ntX/9h7+BH4T6nYlxvZHnu/d6o+dnfTstx8WzX9m47hp1zS+6E6tvFOu35k3te2KrTs4R+yLzWqB0\nEi8jH6fkIMPIK0aeN18D1EtLq+x073dD5CNXisjD/7BDHEfj75v3uHrzkNq+y2dxXDu2Yv518pjM\n9jl+kn7dGUXn/jpt/Y7TSjDS3HOM35qj5ZNk87Vdo863/hb83YvqXCUimuKmcA3eeJIDi3waN15u\nQX2772ArkZCjzfnXMnr7ztgNDtN/2LcZyf5GvSYDs1JUrYq3b1OjpWlKW92Tet+RMLkPnlT9DoHh\nljH2NwzUkX5vjzY6nXc/TGRhxNI8xhjsQbubv/0pn5d+FzcNC6x3rsMgC9vm49JW94a+fabakKhs\ng2XfPHettYKSqXmVSLf6Dku+MO5iqzv1Ptug7rq7sgr09IxGuotlHNG+7J83h89Yai327sBDW8X2\nh1uD7ng7vSNFLjHXDqwq1WuJesV5JN+Hk0Ye/udOOOnnHYjE0uRLLkOrLfAVdj66OKKv00OkxeYn\nsa3ugO+2OeBkW+1qScNi1CSGxWiJYW5iKLS26yMZ29ZKWo/bATRq5wyQPMfII9G8PnprkjUiEIq0\nxYj1euPdTr0GzDdfqNo3a83W+SHL8ZdpuEMs11r7ZJO/xfm6W11fjJosoyZcr3313Qa9ttH7XT0f\nyWuWfz6q7xgQ85vQH7AWLTDjupsugk3vOboCZXL9F0+iTdXehZ1WPlQ+SfDtU2mMhtrfzdo7Iood\nDPD8JKLkr+7Fza43Uf+dA2g2D7ZSUKpNjcmqWs8fpcDNhGwGN7AWnopSoDV+6+/xLRgp+7v9C5gh\nLU1DqjZxDr3/Fc3HIehNi3z+ENvxK7gUIHWWmhwnfgGLKBT5DuATpW3w2zfDMAbNBSU78xL9mk45\nE2m6i2x13je4NwJSrcmWyr+RNMeyF2I7VXBlDtCMgmZvuzp+kaSRXwBlFWy7jHwRYPCYUyOWEWfD\nyUeqOZnW7MxYf+BmsKGF2NZgwb9jMq1MaSS23f7RCcFpzf+0/bVpamuwOW5tZyyhZbSvjyKA0W96\njC0Q8LveGNvphBZEifPSHIhZm3KbBcjfbe0ntbzpmqUH/emzAv0dsjLykf01q61uhwj62lUwFq4D\nOCE3NiEThUaAuCpby0/emzhhpFUAxr57b2aIa0qW3H8OAkVEsYUBno94LKmuxep5A6jf+oLe9+x0\nA46fVD3xsm7A8ohK2nq/Ae0Psk0fmMkiJyNZ9jYUBYMhdHZps8ZE69cRqrAWlHochqxh0u7y278i\nvZvuzMRvg9GPTTbtslu39jLdqR97utuRtUfG+rxD44cqZBqBordmxcv5dloLf+pOvqdfTvhpFMz4\npF+Y+UjWjBrzjT5g2jbZ9LUylu3kZsE4MT8S4SHPM+T8H51gy3TTy79/WYxTNyZkzZ45H/i+vLWb\nsvbRmK/VxHluAkT6HFhv8N/os07flz44it3jiaJHD7qttYWmvo5hppUto2bYqOlTNf/ujqbgvyMi\nmmIY4JlkrbIbWOQSDr6h3/WTjxBYeFeKNtc5051trfDj/WOkN5WJkFGjF6BJitEky7kUFGbM1qZG\nz5x0VBAOShTa9BpK2ZzH/AdYL/w5Y3NX10z8cY68xsGpid8G/7vOZmL95u2KSrqHYgr2VE1ToNoa\no2bFqC3wCHM79SbKqvCn7uyba1LCSqNgHG9XOwbPy38DNM/1q1EcQz7yBHt6YO3zOALJqNkIWCMZ\nYltVegauZQ7BSDNPU98D2Lbb5tEJdoqqsEXd9PINzvV9jVjUr4/jxKZ22qxQ5ItAvMGezJvx/s/r\nCzDojtEkUx/4yOgqECBv+ORLlYdFbku1ycOF1bVjexajeqajnhbGTRxTDewY0srL2+Rb7q+eFqaW\nAEREMYIBnpIlCik1JcBr396B/SfVTENzB/pVwJeavwx5+qRDpjv3Pv3LVP+CiBl/bNNQZqlBkTUQ\n4d8Jz/c0IRvsbdEnxsBbo+LbV8Po7+CUcVc3r9J6h3oFNlSu0+5eh6wlCDG6YChR2Yax8Nx1LvUb\n0U7WnFTK/igqD0Qr3a20Wi2bEQ1DFpSN5n+WgnbY26nSQBbuqtWdfZ8mVWGkUTDhbJfRzC99qSVf\nmIIWM+f5SNb429TIiAKs3s/Ql6fAbjRls+FkWyNreii2Vfu9CIjNz4QzmhPK65NNvvEw1cr41IKr\nPpaRi/b1cbwYgX+u/8i5MnAW+cLTPFceK7umukaA7sd/3803MIygxnNzZKn1OibOtVV6vjSaYwfM\nw2LbVuenaX3jfJdhHwzaU8GmvAlS7X8TJ6y0CkZdk9JzxDJk80xPHz8iotgxhZ+DN1bxSL0uHYmp\nGVhSfAsK54sL/VArdj3XgOPvqoFVNPJ72ShZ/WmUpMsGjJfQffA5/OzkZYz09WFQBX7ByH4loQoU\n8u61LODo35W1B5ZO7Fqhr9Tz7CC9IKXmadP2jOUGNCsNOakuuP54Je4tTkGc3L+Xxf6968Zg1wDM\nKREWWRgJMFS8h7EvxndlDadlkBUpWPrJgmHgZ1HJ2lPfZnbG92UhTxZ0/NPH+I1ssuRt7hPxNgTc\nN/v1SLbbFjQ9TcuIUrr7bMOpUMv03wczI+2c74/ik9cFUYgzmjjbprnTNLI9l5QwtyvkuW1JWyf5\nKNQyfffdyEd21wxfQZdru53OlxnoOmN8HvgcCX0N8x67IMdN5Q3f9UTh+mgSaF896Rrg+iUFvt5I\nwbbTOAb+1zIr77JD77f1eBjbZyuCPCz5fc+znCDH0bztoT7345tfg6W5edvs0s3+OBERTR3Ttwav\n4n5sqq1GzdplenAnpRShqmoFcvR3Ou1796rgTopHznLxuwdqUPu5YjUvODmKpt+obfKP3ZibzcnR\n0/ybMsk/Ts6afxajZlOt2JdqVGnBnST27y65f7W4P+St0CDk6HyqmZaX/AMcftNUbRRSv1EJ9WXZ\nFxoNltHvxiDybYgSmZ52zda0fGQKrqKY7h7auu32X5CFsCDBnWSMAOszQl4k22nUBorv2TapcppG\nwYS5XTJf+M2X6/Nbhs5JPtK+E6CJojy3ffKbUdNl6o8YSLB1BwpMApMBhzewCVQY3r9Vv8bJ/nj2\ng/LIa5j/dVDup21+C8tYr49XitxOm78R2rllBCxGs2i7vxn6MfQ7Btrvrd/3zWsGrbmnTZ7VjoMl\nbzi9FhrHPjxGzasIFm1rpJ2kVWieUamtLQGIiGLENK7BI6IrxbibHrgmZ4qSfZTkyIHqrYdR2yiD\nvbCDJ6cC1wLTlaXl71lvjOOxDkewGjLS2Nb4EhHFDvbBI6JxZzxmIXBNztQjm3k9I/vOWfuYyWae\nqinp+D1bSxbi9SZ7/YcZ3E0sEeRnxatBS2jyK0B1kd5vlIOrEFGsYg0eEVFEgvUHEsa19o4mB1WL\nen4yHWvW4NmznK88P4kohrEGj4goIgH6Awl2fZcoFqm+cTzWU4sMfnnMiCiGsQaPiIiIiIgoRrAG\nj4iIiIiIKEYwwCMiIiIiIooRDPCIiIiIiIhiBAM8IiIiIiKiGMEAj4iIiIiIKEYwwCMiIiIiIooR\nDPCIiIiIiIhiBAM8IiIiIiKiGMEAj4iIiIiIKEYwwCMiIiIiIooRDPCIiIiIiIhiBAM8IiIiIiKi\nGMEAj4iIiIiIKEYwwCMiIiIiIooRDPCIiIiIiIhiBAM8IiIiIiKiGMEAj4iIiIiIKEYwwCMiIiIi\nIooRDPCIiIiIiIhiBAM8IiIiIiKiGMEAj4iIiIiIKEYwwCMiIiIiIooRDPCIiIiIiIhiAvD/A1Af\nwiHHot67AAAAAElFTkSuQmCC\n"
    }
   },
   "cell_type": "markdown",
   "id": "70a621e2-7e0a-4a28-b2a7-e8262e7e0c0c",
   "metadata": {},
   "source": [
    "###  Define covariance and explain why it is important in statistical analysis. How is covariance calculated?\n",
    "\n",
    "**Covariance** is a statistical measure that describes the degree to which two random variables change together. In other words, it quantifies the relationship between two variables and indicates whether they tend to increase or decrease at the same time.\n",
    "\n",
    "Covariance is important in statistical analysis for several reasons:\n",
    "\n",
    "1. **Measuring Relationship**: Covariance provides a quantitative measure of the direction of the linear relationship between two variables. If the covariance is positive, it suggests that when one variable increases, the other tends to increase as well. If it's negative, it indicates that as one variable increases, the other tends to decrease.\n",
    "\n",
    "2. **Assessing Dependence**: It helps determine the dependence or independence of two variables. A positive covariance suggests a positive dependence, while a negative covariance suggests a negative dependence. A covariance close to zero indicates little to no linear relationship.\n",
    "\n",
    "3. **Understanding Variability**: Covariance is a key component in the calculation of the correlation coefficient. The correlation coefficient (Pearson's correlation) is a standardized version of covariance and is used to measure the strength and direction of the linear relationship between two variables while accounting for the scale of the variables.\n",
    "\n",
    "4. **Portfolio Theory**: In finance, covariance plays a crucial role in portfolio theory. It is used to assess the risk and diversification benefits of combining different assets in an investment portfolio. Low or negative covariances between asset returns can lead to reduced portfolio risk.\n",
    "\n",
    "5. **Multivariate Analysis**: In multivariate analysis, covariance matrices are used to study the relationships and interactions between multiple variables simultaneously. This is essential in fields like economics, psychology, and social sciences.\n",
    "\n",
    "Covariance between two variables X and Y is calculated using the following formula:\n",
    "\n",
    "![Formulae.png](attachment:a06fe5b1-0f65-4e0b-b4c4-c9bf85cc05fb.png)\n",
    "\n",
    "In practice, software tools like Python's NumPy and libraries for data analysis provide functions to calculate covariance. It's important to note that the magnitude of covariance is not standardized, making it somewhat challenging to compare covariances across different datasets. This is why the correlation coefficient is often used, as it provides a standardized measure of the linear relationship between variables, ranging from -1 (perfect negative correlation) to 1 (perfect positive correlation)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91f9d306-1811-4216-88a0-03a794d1421d",
   "metadata": {},
   "source": [
    "### For a dataset with the following categorical variables: Color (red, green, blue), Size (small, medium, large), and Material (wood, metal, plastic), perform label encoding using Python's scikit-learn library.  Show your code and explain the output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "02c7ac58-9020-4d6c-9187-4e207f39817b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Color  Size  Material\n",
      "0      2     2         2\n",
      "1      1     1         0\n",
      "2      0     0         1\n",
      "3      2     1         1\n",
      "4      0     2         0\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import LabelEncoder\n",
    "import pandas as pd\n",
    "\n",
    "data = {\n",
    "    'Color': ['red', 'green', 'blue', 'red', 'blue'],\n",
    "    'Size': ['small', 'medium', 'large', 'medium', 'small'],\n",
    "    'Material': ['wood', 'metal', 'plastic', 'plastic', 'metal']\n",
    "}\n",
    "\n",
    "df = pd.DataFrame(data)\n",
    "\n",
    "label_encoders = {}\n",
    "for column in df.columns:\n",
    "    label_encoders[column] = LabelEncoder()\n",
    "    df[column] = label_encoders[column].fit_transform(df[column])\n",
    "\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dacfc461-bf72-48fe-9ab4-2dbf846c4b3b",
   "metadata": {},
   "source": [
    "In the encoded DataFrame:\n",
    "\n",
    "'Color' column: 'red' is encoded as 2, 'green' as 1, and 'blue' as 0.\n",
    "\n",
    "'Size' column: 'small' is encoded as 2, 'medium' as 1, and 'large' as 0.\n",
    "\n",
    "'Material' column: 'wood' is encoded as 2, 'metal' as 0, and 'plastic' as 1.\n",
    "\n",
    "Now, the categorical variables have been replaced with numerical values, making them suitable for use in machine learning models that require numerical inputs. However, remember that label encoding may inadvertently introduce ordinal relationships between categories, which may not be appropriate for all datasets. If there is no inherent order in your categorical data, you should consider one-hot encoding instead to avoid potential model misinterpretations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95a12eb6-620c-4504-b608-3a1a3bec05f3",
   "metadata": {},
   "source": [
    "### Calculate the covariance matrix for the following variables in a dataset: Age, Income, and Education level. Interpret the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "43cb0364-4f7c-48d9-befc-4c38033e9f5d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                     Age       Income  EducationLevel\n",
      "Age                 62.5     112500.0            22.5\n",
      "Income          112500.0  255000000.0         37500.0\n",
      "EducationLevel      22.5      37500.0            10.0\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "data = {\n",
    "    'Age': [25, 30, 35, 40, 45],\n",
    "    'Income': [50000, 60000, 75000, 90000, 80000],\n",
    "    'EducationLevel': [12, 16, 14, 18, 20]\n",
    "}\n",
    "\n",
    "df = pd.DataFrame(data)\n",
    "\n",
    "cov_matrix = df.cov()\n",
    "\n",
    "print(cov_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34bda338-b188-4747-8b10-b1f6b52f9bcb",
   "metadata": {},
   "source": [
    "Interpretation:\n",
    "\n",
    "The covariance matrix provides information about how these variables vary together within the dataset. Positive covariances indicate that the variables tend to increase together, while negative covariances suggest they tend to move in opposite directions. However, the magnitude of covariances is not standardized, so it can be challenging to compare the strength of relationships. To assess the strength and direction of linear relationships, you may also want to calculate and interpret correlation coefficients."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e1ce5cf-475a-4dfd-a6b9-0bea132470b9",
   "metadata": {},
   "source": [
    "### You are working on a machine learning project with a dataset containing several categorical variables, including \"Gender\" (Male/Female), \"Education Level\" (High School/Bachelor's/Master's/PhD), and \"Employment Status\" (Unemployed/Part-Time/Full-Time). Which encoding method would you use for each variable, and why?\n",
    "\n",
    "The choice of encoding method for categorical variables in a machine learning project depends on the nature of the variables and their relationship with the target variable. Here's a recommendation for encoding each of the categorical variables in our dataset:\n",
    "\n",
    "1. **Gender (Binary)**:\n",
    "   - Encoding Method: Label Encoding or One-Hot Encoding\n",
    "   - Explanation:\n",
    "     - **Label Encoding**: If there are only two categories (Male and Female), you can use label encoding, where you assign 0 and 1 to represent the categories. This is simple and sufficient for binary variables.\n",
    "     - **One-Hot Encoding**: If you expect that gender might not necessarily have an ordinal relationship (i.e., one is not inherently \"higher\" than the other), then one-hot encoding is a safe choice. It creates two binary columns (e.g., \"IsMale\" and \"IsFemale\") where each category gets its own column with binary values (0 or 1). This avoids introducing any ordinal assumptions.\n",
    "\n",
    "2. **Education Level (Ordinal)**:\n",
    "   - Encoding Method: Ordinal Encoding\n",
    "   - Explanation:\n",
    "     - Education level typically has an inherent order (e.g., High School < Bachelor's < Master's < PhD), so you should use ordinal encoding to capture this order. Assigning ordinal labels (e.g., 1, 2, 3, 4) to the categories preserves the ordinal relationship. Other encoding methods like label or one-hot encoding might not correctly represent this ordinal information.\n",
    "\n",
    "3. **Employment Status (Nominal)**:\n",
    "   - Encoding Method: One-Hot Encoding\n",
    "   - Explanation:\n",
    "     - Employment status likely doesn't have a clear ordinal relationship, as being unemployed is not inherently \"higher\" or \"lower\" than being part-time or full-time employed. Therefore, it's best to use one-hot encoding for nominal variables like this. Each category gets its own binary column, allowing the model to treat them as unrelated categories without assuming any ordinal relationship."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fa32820-ff7a-4a00-9858-423e676b3e22",
   "metadata": {},
   "source": [
    "### You are analyzing a dataset with two continuous variables, \"Temperature\" and \"Humidity\", and two categorical variables, \"Weather Condition\" (Sunny/Cloudy/Rainy) and \"Wind Direction\" (North/South/ East/West). Calculate the covariance between each pair of variables and interpret the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ddc450d7-bb1b-4fb8-aca7-98efde4559cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance between Temperature and Humidity: 13.040000000000001\n",
      "Covariance between Temperature and Weather Condition: 2.0\n",
      "Covariance between Temperature and Wind Direction: -0.7200000000000001\n",
      "Covariance between Humidity and Wind Direction: -2.32\n",
      "Covariance between Humidity and Weather condition: 4.6000000000000005\n",
      "Covariance between Weather Condition and Wind Direction: -0.2\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "temperature = [20, 22, 25, 18, 23]   # let\n",
    "humidity = [50, 55, 60, 45, 58]\n",
    "\n",
    "weather_condition = [\"Sunny\", \"Cloudy\", \"Rainy\", \"Sunny\", \"Rainy\"]\n",
    "weather_mapping = {\"Sunny\": 1, \"Cloudy\": 2, \"Rainy\": 3}\n",
    "weather_numerical = [weather_mapping[condition] for condition in weather_condition]\n",
    "\n",
    "wind_direction = [\"North\", \"South\", \"East\", \"West\", \"North\"]\n",
    "wind_mapping = {\"North\": 1, \"South\": 2, \"East\": 3, \"West\": 4}\n",
    "wind_numerical = [wind_mapping[direction] for direction in wind_direction]\n",
    "\n",
    "cov_temp_humidity = np.cov(temperature, humidity, bias=True)[0, 1]\n",
    "\n",
    "cov_temp_weather = np.cov(temperature, weather_numerical, bias=True)[0, 1]\n",
    "\n",
    "cov_temp_wind = np.cov(temperature, wind_numerical, bias=True)[0, 1]\n",
    "\n",
    "cov_humidity_wind = np.cov(humidity, wind_numerical, bias=True)[0, 1]\n",
    "\n",
    "cov_humidity_weather = np.cov(humidity, weather_numerical, bias=True)[0, 1]\n",
    "\n",
    "cov_weather_wind = np.cov(weather_numerical, wind_numerical, bias=True)[0, 1]\n",
    "\n",
    "print(\"Covariance between Temperature and Humidity:\", cov_temp_humidity)\n",
    "print(\"Covariance between Temperature and Weather Condition:\", cov_temp_weather)\n",
    "print(\"Covariance between Temperature and Wind Direction:\", cov_temp_wind)\n",
    "print(\"Covariance between Humidity and Wind Direction:\", cov_humidity_wind)\n",
    "print(\"Covariance between Humidity and Weather condition:\", cov_humidity_weather)\n",
    "print(\"Covariance between Weather Condition and Wind Direction:\", cov_weather_wind)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ae8a88e-752f-48c2-a9a2-f9d9734c6d8a",
   "metadata": {},
   "source": [
    "Based on the calculated covariances, let's interpret the results:\n",
    "\n",
    "1. Covariance between Temperature and Humidity: 13.04\n",
    "   - Interpretation: The positive covariance value of 13.04 suggests a positive relationship between Temperature and Humidity. In other words, when Temperature tends to increase, Humidity also tends to increase, and vice versa. This indicates that there is a tendency for both variables to change together in the same direction.\n",
    "\n",
    "2. Covariance between Temperature and Weather Condition: 2.0\n",
    "   - Interpretation: The covariance of 2.0 suggests a weak positive relationship between Temperature and Weather Condition (numerical). However, interpreting this result directly is challenging because Weather Condition is a categorical variable, and the numerical representation doesn't necessarily capture the full complexity of the relationship. A positive covariance suggests that certain weather conditions may be associated with slightly higher temperatures on average.\n",
    "\n",
    "3. Covariance between Temperature and Wind Direction: -0.72\n",
    "   - Interpretation: The negative covariance value of -0.72 suggests a weak negative relationship between Temperature and Wind Direction (numerical). This indicates that there may be a slight tendency for Temperature to decrease when Wind Direction changes, although the relationship is not very strong.\n",
    "\n",
    "4. Covariance between Humidity and Wind Direction: -2.32\n",
    "   - Interpretation: The negative covariance value of -2.32 suggests a negative relationship between Humidity and Wind Direction (numerical). When Wind Direction tends to change, Humidity tends to decrease on average, and vice versa. However, the relationship is not very strong.\n",
    "\n",
    "5. Covariance between Humidity and Weather Condition: 4.60\n",
    "   - Interpretation: The positive covariance value of 4.60 suggests a positive relationship between Humidity and Weather Condition (numerical). This indicates that certain weather conditions may be associated with higher humidity levels on average.\n",
    "\n",
    "6. Covariance between Weather Condition and Wind Direction: -0.2\n",
    "   - Interpretation: The covariance value of -0.2 suggests a weak negative relationship between Weather Condition (numerical) and Wind Direction (numerical). This indicates that specific numerical representations of weather conditions and wind directions may have a slight tendency to change in opposite directions, although the relationship is not very strong."
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "fce7b76d-3e2c-472e-bfbf-1eedad2e929a",
   "metadata": {},
   "outputs": [],
   "source": []
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