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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="pandoc" />
<meta name="author" content="Stefano Biffani" />
<title>Practical Machine Learning Project</title>
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xaXpygKB5dWVlFrb5mQOydwB7i0J6ubFjh7npdh1XXdKUdEAmoj3W5Db4m4QE1LVCapO1XgH2D%2FkB08JF83SNM9ZhZf5I9%2B7Rz8J%2FI3IIfrMb5LHcjByu%2BUvGUKxQ%2FkcaLYdZ40f8JWOkw%2BA4iEBtlYSmddP1HFw%2FdKtShd1YQrncW61ZeqsIAcmYleEIEKAhx1ry8ND6aFh%2F8V9VHtiPdBPGObFcRVTzQgcz40RO7WEpW0ba3k2z3i6zBvlL9xO4ka%2F1EVnLTSa%2Buo%2BmkNzrwWDyPcz4lWOAxAp2%2BTrKORXoPGvm6d5aKpzt50u4573rAOfhP1CUXfpbjl36l4XWpysmXBCr6PbGqqsTnSRvReJFj4Xl9rvYfHFko%2FqPrb9YYEpV1CsKxTiSrXhisap%2F%2BC%2B6uu%2F8CZVz1iWlY7fGdnKxd2eM7WS2lcof2ANfjrBHRsoomvoE%2BuiF%2FpXpsCFnJYVZIVk7UsM85PYeLXYofPYf9H42YsMdtUq%2FMTd79Ho4bf2S7Gq9PVRxDC6lKG1VpVBV9cvFXGr6oVycSFZ%2FauXWquCnKooTpFvcfy0YiWVX%2BI%2FD8UOPXvp%2BE5%2Bom3JHt0IXP6MxS5U%2FAqovYd3l62%2BltAxkkq6q7T7LR3xT%2Bcz8gICtekEZU28Hq3d9JkEXhcfclufMmmZusgqh%2B5ww%2B7k3Vwcd9XbHh1JbiELt3Fu67QYbvmRs%2FCg5by%2Fr3TnRlZXhu7ijl5o6qlZ%2BrQrpkGp3PTVTZFKpwyqWabnH%2Fce5T6T%2Ba%2BNhiV5b7vOiQWG1XNvGNzngqewJWX%2BO7%2BPupIVbDas6n8HPju1ZMXmrvkcJ%2FhQ1Ya89RaqlV9P%2Bu0DacBdfrcx5rlPXMqW5%2B%2FVv8cfLHuP4t%2F6ZgDdhPFR8DGRmRoMk6R6Yc9MgU65TdN%2BKH32y1gyJruJn9x3%2BQ4%2B1zUvkZZYoyqq52HfJR1T3OUca8Ss9VrVhgoR1nngEaUXl%2BEwnEj%2B5Lg7fIsNx%2FsEWwXdT%2BI%2FD8UOO75zqXdKad2WS2XFS9L3XHH%2FH3m9r4nePnO%2F7Ys%2Fk6qErLYy0lJ6agZeeN%2FwwccYGT1QoEPwJqvCIveWiGhaw0jqw4olppFhqa8b%2FC%2BdTSMfJ8SlX%2Fp%2B918A8%2Bor5fxP%2FNTuvM3TtoeHe%2FThlVC9NKslFVNwNc6blq86mEHcyuYlSiOqOvmLPKAkLhPzbxCP6j62%2B9f0qwwjHOiiWI80kKVVktH0mD79lpNHuEPZ9yx6Q3iKpAKUiIS%2BdKK4ZmEpg0z1gZ%2FjhD12TDPydq2A6DMfTF%2FCCSlRZO0fLXPJsLM9o5%2FJ%2BS1UU8jHffrIaAVo2H93qXRX3g%2FV5fZeaqtAxwpeeqH3Trtr4z%2Boo5qyzjqus%2FuvixZ5JszVn3T9bAuDz2jM54qngC1XyGupJhFtiO%2BapVZZeFqvBG9bLT64cJ8zEW2juBk3sMRUbTMA9ggQX%2FxuNExVKRpvwrklXWFA5ZaUTl2d%2FRNOseP4pZYB18QoGHvnMyyNx5aXCbSf9x47s%2BV9Vv%2FQ2nBFacueFU%2BfxH298aemcj%2BAollosRz0QwI9ygM56qmBNbdKZpA5nYorobKAtV1yzEXc4xMjWQ2Xzu%2BE7FzK0BZnfYN3ezIOaa7cYL%2BL91Kw6%2BwooX2cJdqES1Yl3fwkumIJzZeGJX6gvVmzcdfOOV0JL6h1jjlZuVAa78e1Xd1scYiWP5mRhHlc9%2F9PFYhwhrwqz%2BfBOLKP8AaClJVcxhKRb%2FbHAgM5D5bBD67tR1UFX8XUSS8JcpqS8QN340V4kWuHQHNRnlvBhKfbH7Vr8H6fkKWPUwq6eGeuYgy1ZNqcPGOz6%2BR9SZ1V7of6CvfPi4Z0Y6zuSjamFa6bv2XhUpNzRDI2ruGXdyLNC1U%2FVs9fxHH4912DsxkOnMds9tPgd%2FPNEpvw99qvKrPL3r8FZaC3Vl26BE558ratV5h5brrxqrSjZWe2oL%2FbGSS62BPrSGWgP31eFR1ZYP7%2F23Jv5tWjqelgG%2BMe9VoU1C5X6i5fIfCh7GYRjtwIM65C%2FhnJc6S%2F9XnldPHdKgJoWtn6q6WQa0qq4yZuwG%2BY%2FxN2PGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYseVnpcgqGjNm7EYTNd1MEGK0kaUITo7BMiNUZj1D6RBgIRmWfxAO%2FFpHr1Vl6qOHh2WCxTJWwxWpzzycMW1rU6TJ5QMexTRpz5cqLpp7Tvw4WJlhBGp%2BBo7p79qA4m5Bmngs%2F5fXJWZFOsN86VmYRFb3agsKnuuswqLabGc2wig6q2t%2BjKX3TfZN4tc1P6Y0CV1XT7c%2Buvjor4tXpcgXo5daH5QVaUf8fJhRy0f8ShZltOdLW1lj1bW5cG1qRVxmL77HjjgmvE9R%2FzPNIBmL4pz2%2FS4zGXS56nQyJ70tVuA43%2FnhhXCDWLVTsHLHWSNKIav78VHwuOp%2FIIMipCx1YtdARq2zGvoUS986vnXcXu35aXmpqlsfXTwuQ3eviwCdg68rVx9cjSm%2F72K8qp0Ka69yLaEXBOWD7i5NogZ0pBfagNRNqJFxxsqEFfWPwLL%2B09uwHqe3jaYjJJ1eWCSe0SKcjaeJvbvxVmCVVIo0mRsZbeHSfvd3JVC1cDG3mnyFKyZVeNRZBYmKOKvFKsJysjg6o%2BzmrAAX9OBrN1HQg9KAVKq66wPik8r6uPCT1iQBH4jbAtCO9c7Gmb8KgVM%2BfqdTH%2Fyu9bWEasxz4a06Nd5xLnewJl9aLgT0WD2Vqon8Ot6IYncG62CUwRrSIF%2FgCGtkgnsnosow2zrYZMcO3HPU%2FiPwqxhxq40cvmkhMjI00%2FaV%2FG5xiVySOYQtkapLVRdU5HNTVb3sG3VWD28VlUA7vFWus3rbPl76oT28l06y2%2FaVj6ru%2BnC8vD4Cb%2FWFUMG%2FT4XH2hcKkKBASfsT6vpA4Buj1ydHk5BqNakbb68qVa4%2BFe7kXqsqkWWbd4sS5D7Nq8qnh9fhq6ASUbCGlDUMzYSvyueGPCTnI541tkrS2bvxqGrS9jZl7inw218N%2Fe75%2B2RdsdMygrCWQjrAh6pe8igqsjo4SsrB0VkV1VPprIau8tLvS92Xk%2BgMXVU0X8ZyaqQIe9z14TWS14fjYceRL%2B1585dWnQL%2FP5PsR790%2F%2BRHvwQRrA%2FU9YliQHhQVZ%2FkNwJPM6d8qumNqgkP%2F0mw8lE1zh7dUfyzR3fECSoZKDuzd6IZZrcwKtdQ8FVVjzwQWaTGlIj%2F8bZ2hrK8%2FmKhznTC9jV7MiHrLH2pir3s0qaWj5Q6KQe3zmoyT2uZzqoVE5InEAzWijBJLnFcKMQlb2pRH8sWpuLEltWH42E86rbr1I2LlGV43EFndIv7J6NbZDvXuNsHHvmrqvpgcshjZLvsG56mlmoIoIpQuUZV3SSUF1VlSr1JNtlU%2FLPJJlp9qqruehS%2F3vUolXr3DHZmdah6zyC%2Fm3sGfdu%2F353R5d2ebHiTzlX1GloX7%2Bisiscu11nlsp9izM7nFX8lu4aOEJeoD253wLdAkNfHqb%2B4Uzne1nzFunMl2j7LFl%2F1byOn%2FJ452FykRVV%2B%2FwUv3dqB93QSKHKdW71RtRSqWnUDmQP7T287sJ%2FL6B3bIU1yVbtd284wVNPqYwVwRMWR1T8ALqz12mMbzupQde2xzeesGEaAsoCZ%2B7I7D5y8HqqKTF%2B5qaqrs4r5U97TYn24Ui%2BMSl%2FL5w4rGd%2FUaKUyJBf1YbWjaZALrVXVx6m%2FuFM5Pr%2BN0IR9NxOqNnLKB6m1enX53u354H7lm700rf1vxKgKMUqcrYAU0Qq1jF6xzJjjwH6jGB6jaR4AQ964gTXA%2FzUUPFDv2r6dcu8vxEe%2BHv9Z62vgq7WUlzWibUsKgIsTMuWnqp7OqjUswt%2FeP%2FExJx8CD9Nqw5NRlPrAcBdU67668PbGCiq8837RST9I1ded8qspOrT6urVcqfn5%2B%2Bj4So%2BqOjPn0bQXVUcVbylY8MQuzMOLvLHqKgJ%2Faotc974YP33f44mOxUd%2BQXtZI8ZXERIvM6rq6ay2vyHKvOOP%2BD3f70P2ZwTFdQkq1P71dV%2F18N6uK6tRZeuDNcJ3rzr4ys9V6Ybqy0upij9VnFeLGzFqXMfGUzUvHTyrAXo3UF7W8PeqPBMsU6QUvxVqiFVVOPzcEKrq6Kx2LIoyh1%2FG74dfFt%2F7adrru4qu7qseXp%2BqpdYHE1IDGTUeXnak9k5sPkfXuV36Z4X%2B9Xf2vHMO%2BW4LelR1Tz2KPy8Pk9Pb%2FXrGsmM%2B2v4Gzp8YYrYjN9a7Y2eS5mu%2F%2Ft6bVJ1VlwJqkPepKi1UPRVd3fro43V1fa%2BjPt2o2k7QrQ3Z%2BA4dnVsNXeKUBzolL1%2BbDK7rU%2Fd6XTZELtRtroeDrMTsRDdVxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjBeb6o%2By0Pt5KEzRo61BQha4rq6dBmzsnnUdfrlhLodptTKuFmDVJLn0sd0ZGdafebSRTli2lRY0tO8OVCkMzSS0VYAfPQuvfUp3VeDG%2BiNKTVLFK3ZU7aM6KnDijC0TqWfiqSo2CGxdvO7TnwP7e2RBZwpo1jB9Nss3n5Eu3rMmwTX%2BdtTuaqr4lULqUjgBkOUvuaJT4gG7ntEQYW3qvxWdWaOgsrn8SpSdDAxm6CnAhXk3WKLNXSzKqWKU%2BVVGCxCXi9rBegxCbcDgJy73WXiOQzpbYhBUUKy5Al9TxZ%2BpD6nolyZQaBC1QcgsKloK4S79Y%2F4gKvIWCpm7TwRa3Pr271z2L1ZTe0ajwxWVTFnZSl9cVo5JMl3qq8r3WNSU5VVFTIKKhAlyMV5HVq9nKS9X2J9xomXApF8O0Ckq3lHKYaKHfDZ7unU0wykYMos4oZh1fpFI18QcvyS8vpwJH7%2BQrGPOqi%2FX%2Bo7EOtngJHDEi6L%2F%2Bs6hlU%2FD6CzWFkAqt1jpU9fZmf77wPSuKNxTJURXJp6cCXIyXk7WyVEWioaCnc%2FzgvKzvcsbf3lmuczj6G5UcJoZr7ez5%2B7b%2FraojcFPVijWdBE3gs1SqYquqRNyKW05noTVR0lxzxxrtADVQQkBb8QA4yaiRVjGqFKqipK%2BsJvamNFdzeR5bmse%2BCp930lWAvfEyslaWqrbu7DcFwcI3lIBq78TU0NTQ3olkXn5ZZrftQ6mrX4LAaDthLszH6iaGTa4KaZ0gHqcWFMJVlqq6Gha6AapXcHpzA2A%2B9y%2FWIqTUJ0%2FySZ324drbsueLHBt5BYmKm4AEFqw6G89CemT1w%2FuTtfJUjRf0n3HCo%2B%2BdPdC5iq1iBzqFgrAi%2FL26%2BW2rL74B0S0vUNwd91fBRFHzx7TNkOL%2FNcnu%2Fh83n6q6Ghb6qhf6AW3lAmD0F0j9pR0lQZ3a81a10iHJSLzUm9e%2FpRIXtfdACCJRo7YAeuPFHN6LfOvfklTWB7%2F%2BLe%2BzKk9V%2FV66%2B9KmNvy6qa37EiHI7otDd4QCa9F8aKImBUhkNY5MRVngeRKRjifZxqM3n6olvSrTPEMnQK1sAIyEG5liIXcATLtXVxooBCX40ttDEN%2FmjzQUr4MXg4Hm%2B6O5M1y7%2BhSTD4SzpPvQeOGt9Pq3vM8qjaq9s6e3UUa80qgahTzx6W2nt4UfjhK6g9DfgxxnP9%2BJzB7D%2B6ikuB8SXrEPKUSKfYZ731WOqtaYHXyNUQitm8%2FVPUMnQK18AIwZdXcATLvXglGwRa89kT%2F%2BeCvWeKUNIr7b%2Fpdn%2Fd3kUxHVC%2B9P1NKoauvk14gNLtTBZnFqW%2F3om1ngo8BHzaT9Q8Ps4eeEk20%2BB3vo%2FD0prRSwxlqvJdmdv6dQCbuMB%2FoqR9Xm3F3rB8CVyAAvlwC4OANMFwHUzQB3gbokPzh%2F%2FPFNuSlcxK%2BrEeSjELUYLyOqN1WHZmQ3Jza0EBtcEGgx7wp2AkmSGGaURUlymJjHPZB%2FvTH4d%2FbcXPJXS9YenlZaBcRIEBNL%2FJxn%2FlqJg82hnSQGbaTkeLeLydIgJQWcyw1%2F3Rlgan3UVHVUHIGB9lFKWq%2FoKkg%2BKlHdeGtMRlS%2FEMAf7955hpNV1RTFfwKhLYYpkcO0DmK%2BrmlBqNnzfHFgwb9GrQUbJ8GfH9QrCZjh5zReUbZ5C7R4i85IKZIe7iPEdF6tlT9AXV4ZYEHVUupTiqpxGahqZ55COsVyPGjMhsoZUhVuEYUC1cp61BaU31DOpsspEafyWxUrlW4L6tJN2VgB%2Fkghh6a0uX8w5o3nSQ%2F3gYmUcgacyw2v73NLz6HVpxRV41Iy8MtUCVj9ZwDGtNqzRf0TY8aMGTNmzJgxY8aMGTNmzJgxY8aMGTNmzJgxY8aMGTNmzJgxY8ZujsFqucCyqMe0eRbGjEmI2nhR%2FHG6FDdmTYPuyzRFFsxGn7Euw%2FqXMzQ8LucGaZThkjub4WXQkmmasrIxYyU5%2Bbrm7ksJ6coR7obNoDIUgX%2FNSo1DlOxuxtV32QT8D%2FgMRcKk%2BWOQRvmKgrSGoRNgjuA1djarJcu%2FXfgzuKpUq%2Fx57MRgjX6dmqhhorKyW1sW20ofqz5LDw%2F327dsPDLvLTS%2FWYrnS%2BJoZ1GwrvZM08R4nFand95Qtux%2B0ckDH00N9c6mvpCPkbgwbCAzmsaF1mHFiklUiBnIgGh3SqwTbbyorOjBqK2ZFHhJTaTVuaW4fJ2rVTd4y4ZTvbN%2BMp0C35UdP4prB1cxaw%2Bl%2FL0TQzNd2eM7Wa2VblPeAZe60pFBF%2B0fZbpYyll6%2BDgsJ4J4iTwNEms3SxV4kZ2D3sJd1vkks6V4viSOdhYF67RnmFQjd%2FuTO2%2FwH8n98sJACwjIeqFfVtDa923hbnyiHUjWte%2FLaB3l2FpnLV5UQW6rry2HDCmD4JavQB40nVsq1Dl4S%2BPFxovn1sGysmoFPsUaISwHAaxWdMs6Zfmw1A%2BXwnESbjglb2gUssrpU4QoMuhcUYfLXulhaWfp4fEa7bhGl7gzgLN2s1RVRBlWuGySUcjqhaesV6Vj3e0ZJZJV4OWqZY5xqTSf0p3Cui%2FtvlW%2BEA2lJIZf5p9RFSHC5LQ%2BvLX4EcnVdNd86SDXLMibAkc8FnTfQ%2FelwVvUeFRYbWZ87AO3PKnET9qhr01U2QJ8KHc6zNzjX1jaFQik0%2F5qN3ewtLN08bzlEyC7CkFY382mqnDZJIkaXnhaq1Kx7vakkdXB62qseJTuFObWYPAzFD0R4l6xD%2FEcf2xssSvLl2W7H1HiG9k4HGc4VguHkSv%2BOU3L7wHrL6OqwAeejwCWb%2BgxNHNunWIUmwyhHut0WNncjRfbc4r9yfzXdkXAbCtAXIySZbgcLOUst2PRruI8pyiGwmn1SFZZqnKXpVHDC08VN6Nh3e1JqZE%2BUSVk1SNqVdWGs3w7DEiv2FtiyMLB7rnOrMcjysrG4aEZHKvzAixX6XM3TlQZMQR%2B3dTpbRAmx7uyeycgXK2W45%2B%2BtwuSYu1CS0oSvm845SW3IQ%2BYhYAklapRl5uoz2o6qYcvplJYKSRTeaoW3rN%2FDOSNp%2BsQUrCFRFVnX0T7g%2Bi7psZKz1zR%2FeoStapq306uqNaWU1U7frc%2FtvdPibxomHNz%2FRdk4fXGo32TDjbOKFQNPBbN1V%2BeNMnv3BJiNfj11BbWIKNeTguq9vhOjCU4UWVqRrw3dG%2FnpO5NedvTqepgKWedW6eHL6bS0MzH99x8qrrvwT8G8sbTqUrB5uV13Eenuv3jTO%2FlnZWOF94vfz2jQ1TcoGhkymlmSLrU%2BGPHnoH55tniRzT2jCy87vjz4fWOsmCSRNWew3sneP2jykdfcC81%2BOKJQG0gK9ckalbUSKi8ijPVYQ8ihZAqxakcLOUsoftIv0rSta8PyLiFVF5ReaqibyZJw4kXnkpVGlZ3Vx%2Bn%2FcNM52VNuPh%2BA4%2Fx1zN0oqK9kxCPHLK7QanjNvTO2sFyzN13yaTKNpyNstW%2F7b8g0PKdXDBIwEwlTKoaWDXqkmOoocbnk0CgSEjDgwRai7p8Tlbcyys3V02rwx57%2FK2mqB4XY2ln6eKF4Cq8zuqkyLhVmqrcN2nDiReeGqvQsXqKiPpk9SAqzAw%2FFa9ndOTHWPWR7Tju9cydT6mwWM0I7rA67%2FRdMvzJjV3ZcF6wuCsr8sc%2BwfgTuEGU6NtW2ptF7Xvi5uELkwK0REIuyCaoHi%2FF0s7Sw%2BM1Np%2BDqUHjcnhZI9yVFvd54Sn0o2NLURR0yKrzsqbgfq0AzvC2%2F63q9YzHxSEg7Jk7tkN9HsqD7p0YyHRme%2BY2n4MkTqf8HFZzagv%2BuQF3dXCYWil6xYH9fPotlHcP7Gcrbh7eTVZqxi8fZCtVj72wlLMEyn7Nr8Tb6sUdsmmNl%2FM6X2l4mqMLd7XqaHGfg3I%2Bqemngy3NeKvrvKwput%2Fdt9p50MZSBD0hIOyW08gdBsOsOgX4DopKL2zMFMpJa4fUDsNWQLlu5d0VNxfvNDc14%2Bc4q1r12AtL0UrmKP6cVXiaevGNMXedKV7qoFyf1KOeBvZ6yKrzsqaoY4IGqKkyZszYjeh2qiuHNmbMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmLEym65O7%2FcNb59Dlp1cnvWvuA8FoEYxnda02A2oVVr3SlbMmlyuNM3p9MYZTaf3%2B4YXZ3EZMXp7JrOdWZ36VAp%2FoyzwEUhYfkStC3XBXMGdZ%2FT3fXj%2BPr0rWbHAAuhkTt7Mrobvb5ETbA24WrRYK0al01sani9qw%2F8rU34yL2pW7vK5OPNKG7tyXq3b7%2Bges9SJXQMZSn1Kxe%2BdoOkq2488o%2B0yGtSwJqNK3aPrpWoUBU%2B19k1A4tGvBCMw4BPgpU%2FfW4n6U4nK97ewh4ZY00JeBg11evllhR6QXKfXwbudXYXvnf1kE67f%2FGQTLrClly%2BEoNR4WEUKomYndtHrT7tftKaTHYtIiiR76CUQO5VrGOd0jzfegd9tvIPFkXzy%2BgidZHthoQbeirVeo9QfhcebFqLajkWnhjUcyoum0UJyXVe3%2Bqw9qF%2B5mtHDU0G8E7uGZij4MAggIB6F2W8eVdc1xxdxfwssH%2BsfX1zXbP8CdXqdy6p1eh28%2B5Dju7K49g7Xb%2BKaPRxZaeX3zn58D6eICg8SMCusPVaM1fK19pTyhQCoSpfYqguz3S%2ByBpvejQ%2B91HpN1tBc9xh6QxTlTMP%2FscNbVfUROhd8awUqXjgitpBcV9maXA0uqO9YVGpYgTULzlNrvUYZi3VcHZQx54MgrZ6XcSeO9m2%2FEsSjL%2FEHUb%2BdlFXYlaMqq0HJvUROWteuP1%2BoGlsUI4wNy400%2Fjq9Dl4canzCFRY1nUwQykf5rYEMEnx8AKmtwsO4wkJXezZbdVFGqb%2B4A7UuMYq0JHFGyA7tObTHAodJSGcpXPeY1Q7N4J41sOofPkPDfyPHw3X2WAHcWqHpJBGfIyo8yAYZHgPfkKtzUsl2uTFUagQ%2BSri6bRgRPiqnq%2BPGI4miKK7pCsnpW0amaMRz16n1NfUc1SpqUcq8liaahugm1%2F0mUOqI47vniptMrtNbGt5RlOGqMSr81BCrhyCvmjukGp%2B0FY9YfdNJlc6wwFsFUYQ%2F3nEQqFG9Wg1I6B7z%2B%2BT33ZmV1Qfx1p5WtopFc0KSBLxD1Fo5vulKVEu2ywurogaX23R1gZ2KGXChq8u3uuoLL6lP7%2ByxHbQsLmuhEFVkiXODT0hNZx0RND0tKe8r2L%2Fo%2FZNoMsF%2FuU6vg3f3L3J8V9ZRbj23DkdJVfkBO5OYJ6oSjweEaiys1Bl28O5m8cez%2Fs8G7Zlwv2WPrKj6JBP14LrHVgxHVBxZ8XNCWh%2FET4cxcOdqOgT8mJuocvyxHY4ibqlUVVNDZ5ycGnILx3Zlp4akQezbmLEYmcKYRugSQyvVliOLW0qWuPJUZf0ndjkt1DMHCUTubajTu9R1%2FXV6Hbz7kOMTtpg%2Fzt0wu5UglG%2FL%2F%2FcJotLq4w5o1XgR8Kt1iVn10AwmkxC37qcdi7tflDU01z1mtdDAMDeH%2F2vXnFXVB%2FAwh7ddEEQ61PjmguSHHM9qsWR30C8XHiue2lCooUdVVvPkU47nPPmUXDKoHXWmu2F0tGMa1V4IelncUrLEhW1D1CvU0je0Arz%2BvCOL4wYsfPqBOr3FaRaZTq%2BDd%2Fe6KnwUXnPg3G3lfJRYPu6WktCqj1793TGBXJcYI4HB0825lAkmmKSPJad7LDLAuFWIqj6ID92OLghjMAGPNYF62COqCm%2FrZ4X2TuCj108rqalRyuyTrRCS7yCCrhCVA6IG8xHFLM7My5fFLSVLXPm00u5bU19g%2FXmKqyub%2BmL3rblfOYrrNJ3e0vAio1Wp8iuH586OYXCSfbJJrbjo6B5b800sQqqPLt5OdBHxnODHd6oFSJcE2wRqlOa8rIUH%2FKxFiQy675z6EoWeTNLNEt%2BADDBEWCipa4%2Fatae2uJQLhU5vF1Wn93uGF2dxdXoKUuged2vVp1J4JxDWdRpa4Fua8x7Z3jMnn6V63Xl5srjXkyWuPFWFjmhOW7mm6K71dHq%2Ff3gx4yBjl2P9q%2FVdRgvdr9VCqCJdAWFbSha3mKz6RNW9W2PGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzVgaDZXN7TCsYM1ZICw1dWVC6QQmPPvtzn72m%2F6DGlfrg%2FDNqWUZc2dpzuOL3PW0xqhwm1PqMVtkZlcJBHsm8P2tcK13GNnkOD%2B%2FvvpO%2BHbsxisPqZ3TdT0lXFzf2Ye9sfDEIq%2BytySDoqfXOxj4kXWUMnTfI2tidv1evSQi8FGU%2F3qbRAUwjleD%2FPh18x%2F%2B98wrtj9KtsQi0Dl3a0gpwsU01Ta0CVY1kSfqyoDYx7f3UoPtlHse8f1m9R%2FDw%2Fu67aO1PoG6H1DPn1a1SOl4QFddrXydZdXVxI%2Bzh53D1IwoQ4kq%2Fh5%2BLqB0y1nilmfHrbD7X%2F09qqq4F2cz1D9hjWZ2y6aaDrJ0hldqhK%2FBzWi%2F87eze1wtEkX3P4TKeoAZBHINZDW2ZlK4AiHASrmMPI8Y8J3i7z1NLeJafYOWmKldbLGV8kY824rdC%2F0gp47aka2qVyNlwmbtEvlUoMnF6eIeoOenV0skqdHFhmS8s6hEKDBIdWlu%2Frwkwzz797NOop9acFxXzf4yBhXhOKWbvxIP7w0Bx1aiHzdH%2BRlXVnb%2BXdxwYKLcXuGE7y4scE%2FAPPtJ8VIYXY3wC1HcHMqDG9xK1ZWlUXSrmIV9clVcFBBkPR3sKjw2n6F2BrF7Q2wWdBd2F38laNczU7bh0fJGPNs5vWUjIzsjr339h6b0Ov6zb%2Fv5PQL897auEuMQLbXleYWvkvxO6uPFF%2FC6%2BqNLFdfSL7nrgrgccXSPZpbmgaFd2%2FCjr7jrULJUd4zYeyfVBk%2BvfiUrnwo3vRmGcFuLeXAsI4oJ3qfhX1%2FSmZXg%2BdqE85%2Bs%2FfP2HttQmaV8WvnGGeusMz%2FCUyV0LZbJSX8Q3CKkRfCYgYxoqj2sV1oA0ZtTxyCxKIKtVl%2FjcGV%2FEaJP4XDEWQaSE7u7oGvmVv%2Fm1pfe6dVy3%2FS2JTFzPnF7n6n4S1FC5aHLDySp0cWEwr4NmVOriOg%2FfTVX5xTsWcdQ%2BtWV0i3W5TdnPWcPWQRE%2BhhiOgOGr%2FikuFCz5oDvJpu9DAtpiHXfbakUHKfjUV7DivsUfzw2FxkbTq0D%2BczSNomUUojZe5LVROW9JfTTIeDz7k9Uu1UI%2FopZC1cLfq%2BsjiJokkRXlSHjsBi54OSyVzGEhrlIIVOhwZxRkNbr%2FiaX3%2BnhCt%2F1lio6P%2FAKyLkw3A0ClKu%2BeChVBc2R1dHQDjwUeU%2BviVlVh4IsHUlV8lo9JCXgYR7YH34MkVK78w%2Bv98a2frJvCG%2BudFSNfnPlJRvdNwoz2X1j1QGb1b%2FfZwlGwSUTN%2Bn9Jsr5JP3z3JY6%2F96Uk23Icf%2BqPFwmlnrkZe5yfifTMRdTbTsS43Bt33pXzsnEYHXHpP9UD7eniRJ3YvX2tfQdvlS9g06OqQ1SxaQmdrPE8Uf1Se1x5WcfpxweK7xRGwZryURVKa2j7yvuc7a9eP1VzOtlFh%2F18HV3c1vxWA%2FIAFSlafEjdanNX9uHnAguRfOlIJ3981O5vkYL78j1kfIPfvGoggyPi%2BVTn%2Fw7aJZ9P4cgJVwj64SGgTiMex3fMMVtpf7xIKL3wU1a9%2Bdzmc6z6hZ%2FaWz3UyYiKgakY4zefs%2BeVMf8HyLO%2Bhf9UXUEgR9Tmj5vssv0zwJWlqkNUGNe7%2BWxSvd2VQ1Y5Uf0cXFYj3Jug8E4H3tOPavzLhzG1L%2B5zjmwAolKVz8kLJV5zMZOujm5V1WrGD6So%2BCy9eH3%2FhWaXtH9X9nxKdUvYGHf%2Bnq1wlO390OdTvbNtLPA8nII3Fg881gaP3%2F8KiIcEyLuv%2FxCdhdVbB8NSPCaUgKJw%2FQf3P7gf7wbJJ9vvLLDQmQWJ745czTsO7O%2FMBhbKNapiSCTkM8cjuBFRkzQDXOy44hn4X4HvpwcZ1z7IL6d5d%2BNPug2nckQNOakf7wSXF1lVRF3q4JgJzonD%2BqSiQHPK5ehd2cG%2FKydVYUx92%2FsMaIOacsxVsRXd3%2BcnN7o6urpzVXxrGylI%2BoBAp%2FThiPFo306%2BcR2eI3%2Fom8%2B1wTiM73mty63gWLLHz8WxI%2Fa2E3f92Qq0MSGV7Z2JxhdSJzfi52bIdePXkxu7sjCK%2Bb6%2F3XAWpCFXiLrDllcrTm3ZcLZco6qgmi2HaW9EJM8Ao%2BPyZ%2FrZoMuFJZ0l77zDkPhtyu1WgF2UzLGcmXLhdyqyylrefb%2F5eZsrE0y7Ck6%2B5G%2FndalqBdp9znh0h%2FSVk6KDKWxTn%2B90dXH1qNp4sfvS6W2gTgd5S8xVqgWgT25EYoNoZn3ra7w%2BzjYa3g%2BddcBmVO8l%2FpD4w8B7h%2FYUpiA88ZCuuAeS%2BtsObWoDvKRGzR9jwm1VvhvDr6vsCKH5Y9%2FyO7B3FYrtOJ6CQGRHuUZVQbX8Jo%2BpgiDJ5xrq0cs9bvBx1TVdaVC8iAj5fad6Duo6uWvivLaR3S28xMqTuwnOmmwqJ1Wbj3rjYXirV4W11A5G1mRaurh6VO2%2BBE5Sk3Mrkogjq%2Fn4HiB3A87AemdpOrewTUIHhMBx%2BL%2BedI36TdAN%2FGwjkKhe1idHmd%2BjjCpe2nTbe42c2NU9p3JF%2FbnqUpO6bp0OUfkkYWRKbMQwMiWfrlTail6KhNTdATzTfmenP9ZP82YqVdde88Y%2F%2FJw6rL1OooqelK4rm2%2B2W%2BBQvlXSc5J851GTu1InXedW8xotTClIDZ1Lv%2BSQng1tWcvVbrVcsb80fVmp61bTRL0LzmjJzfhS8Km66jtnogXVLan7JxCFM2HXoeZNqAxErWijfQcftDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxoz9%2F2u4KsiaNO1gTOYkgWLZCarynNZV6uyy6zRcFwRkdJzX1iee%2F64%2BhRBIyIR81S6W3CtZKy%2BHR53neZrO8zLFT0NXdhn%2BH9PyuTN2Gx0sqydraWHlz8rYyAyt9KVXs7%2BJjBQLTzbfr0X0PUh2BQokTLBsuXhJvoED6LqNFxsvhph9BYoOXl3o2vjRBNN4jJlcMxzU6Azmya41r%2BcgsAakBv9R0VQdJkfnOUHUeV6O%2BLav%2Bv9p5JV9T9zzWzXescZ3caU0LHMMSkrX1kkubXlF1F7rEyWIzRaWJ1YI8UJ%2BvWSB16%2BJzg594yoW%2Fmr3rSqHCX6ZyHUDwY9U5a5rhvWhGVxmhkvQrMwqtq5ZXZvA853ZX3YnSRLZ1suo5rrhFOt%2F9umRqTbSWAaaCJdv%2F%2Bcnn2omdQbN7Mmnbv9nGAX66FQFXZ1v7QXyhNqM%2FsY5lA6rqfNcKr53VkjTlr98EMwJxT6M%2FjryNUUQRvgnSgQNv4nLHP3JnWDutsQDqSHr8kGmr5jYw%2BquIMkKxNnnZX7Ax187qszwETXn17HPiqka%2B4zguOmVi21fJv5P97%2FGGatWadrF3es8FX0iq%2BmdjbrwsGhXOdZYsTb20EsYH1DGow1HhS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2Fy8vL6%2Bvqfn5%2Ft7e339%2Ff29vbo6Ojz8%2FP6%2Bvr19fX19fWmpqbLy8v6%2Bvr4%2BPjT09Pr6%2Bv6%2Bvrr6%2Buqqqrz8%2FPt7e2ioqLPz8%2Fa2trW1taioqLr6%2Bvi4uL5%2BflVVVXNzc3%2F%2F%2F%2FW1tbj4%2BPh4eHq6ur8%2FPz%2F%2F%2F%2F29vb7%2B%2Fvz8%2FP09PTMzMz%2F%2F%2F%2F%2F%2F%2F%2F5%2Bfn19fX%2F%2F%2F%2Fy8vL9%2Ff0AAADZ2dn8%2FPz7%2B%2Fv8%2FPzp6em%2Fv7%2F7%2B%2Fvq6urp6en%2B%2Fv7%2F%2F%2F%2F4ck%2FmAAAA8nRSTlMAGgDUzwIP8SMQ759fCgUvqfDGFeIYA78fbxNTt98%2FhsV%2FBhdD4Q1rRI%2Bvwo3ATxJTD18IoKWasozTETbQ4D40IX5hC6dAMR7RXydvEsRuotKLkZCATYahkzOxQlFqmbZwJiUhFWy1wyJYcXI7gB2XIEFbgjxgiWFtfTSFMy8wSYgEqFBDTSE2KCpnSyZZUaZHRFAsDuWBYJJ7AVZQpC0Z6njBKWjdN4dlMV30iN8bV7%2BzJJeHMRiDYsR6U9yVYxdP2c1dj8CKFZZVFjtaaTxOI9cMKQk4NnBW4PKUOmiNI%2FkwWoQYUdQOSk6GvkUURFSM3n71h14AAB4tSURBVHhe7J2HfyPHmaa%2FYicCDTQCQRAkQWgABpMcDSkOw3CGM5o8Gk2QRjlZOVjBsizbcs5pndb22r7d23ybc7zbdDnnnHPO%2Bd6%2F4FjdIGu6vmp280CtbF%2B%2Fkkn%2Fnip%2BaPSDDqA%2BFOm7J3ncIoDi0NAQkY3d2IaJSws2NNZZnCouduhAsrgf7o4BYy59O4fvn3ROJQKoREkBGKqYytAJCCEQWh220I81TPFIozLaNiCMH4PJr47WIooL1C1isUUsFSwpkMqPAMARDUIFjLcYpj5tGbmqw%2BP6bhz49jZwbZ9S9k8Kd20QQLDdzFbdIz%2FJJ0OFyJFaI6mOcZ6HGOzAGxdi0tN8JL063CmJwi9FviX34m4FUrlxl0PgaBgIbrXJJfVp08yTrbq2tt99bINtCj9p%2F2TiZMMigCzYGa0WxwBgrEjxCBUici56obyLjsF%2B%2Fez8KGLwUdxVJuq9HZcpljX16lgjlaeg8hTpmUVNqubcUjzNKnBbGIBbJS6pT8nMo5ilAms3kxsAbElvsP0DqP2Ttt9KsEYIoBELpWxWDyHMocSDdUiCYMYDvJmAl5sUE%2BcDgiaiLMd6FrTJUmskFaTyEah8JPZsiru8WGL8ouLpx2rfqshkVQix%2Bz%2FOoyRIte64GalXsb5%2FJFX7J4UfxsVI3EUcMyrVrbqAtbVVB1x96q39f4Yo0goYpBJ6EmhWa31nx3WrUmskFaTyJah8iVSofNrqY2umHOeNsyIQ457ksUTnlP0dq4NfVyuLrpTKLlHy0sUp1UASq%2F2Txr2ASAiiwJvNYrVzBLjUbJ4BjlS0qbdE%2F%2FStUgAExAMyWG2jI2EFDd3qujNsWcPOesxquY6d1OOSmiMbId4YCTT%2BBEq0xDjRKACM8mO1HwF2mYm%2BDnRdrRRht5hUmRPHAeD4CdL3jwBEBQ3OheC84VE%2FXi2L1Q9fB14kOgFc%2F%2BzeVgmgJKuVTnzsPSh2iFoncY82uVrw14aH1%2FxCNVbszO4heYa0vDPk30uc%2F%2BOxv2LgBAAGdjSM8R548OvqoxHiUl0bYWyX7R8h1P5J22%2BHUIlAxXSl5FYDeZS67hHgTO%2F%2F2aoPbWy12r9JqFVifFsqsLYGbGtlJyq%2BV2TuBRrA3WTgs%2FAY70S30519XFebg19X3520%2BbakctBO2j%2BZ%2BNt23qsdwduyWCWnjjB1h%2FZvdWkqhPxKVhi3gMamh2Ilhn304xeIaTVJpVlsTp9FLRt3F9DPgvtmX1czbf4FSeXghcT9k4WXLYxtg8oYrLJRKZNTC7XWa7R%2Fq1RDCDfq7RltpDwixPTcjIdii1R87MYnptUktdKYn6Pz89ZSJj6l6k8NcA%2Bc9bqavvmF6jbdHqwW0vYP5%2Fq9dLGo7qVTrY5OXKnXr0yM7m3V%2BFzIAs4S0crEckCmBDOedY1UCmI3%2BtN0LjUucan0yDOycjD8PZk4VJDCB3%2B%2FqmmtSqlc68g2dUYKlLJ%2FUrgzMl73Gu3xESfFqorzwO0OsXiI4kmrCe%2FSRoQ4T3slOK2ea0qa001Tgci0E2TiQkVk5tHooO9XnYJDWcP3TzovT4xOL5dJixDqXz29gHhGRZTRIRogzT2l5mk6b8F%2BG5KhtyB5%2Fj%2B2mie3mie3mlvNk1vNk1vNk1vNk1vNrZbouy65VR8%2BsST3UJbGpopjJYZdoNsFXGOptDrpfAn9LGWvU5xaLJFvmr9Ycu3kzstYuiHrUuaUFsfGFg%2FyQOFa%2BHaCIAeHMNTnPgA%2FwSrnrg3UPPD%2B1R8AHnwQ%2BIEUq7xONv4w%2Brk7ex2vBhRhng9ks%2BoyGAXU6XYrROTzXnTg4PrRW3EAIQQI8tueVn3I%2BGarnNuoz4%2BOztdZ%2F%2Bpl4KWXgMspVnmdbHwWIgxm91XHA7JxiJ1A64jHvJg0WS0CmBqzWf3NLSG2NmGTnopCOm8l8RZKpNsDSbG0l1UfUXyjVcZLqE8EoGCirj1cC%2F20Eq3yOgjrML6wwHgLFoWxUGHzicx1iB4CQJy7Iee7S4biAw4QUM9k1XhodzE%2B1yRqzo2zk3YXkPZaZODoEJl48avVU5pVQQjFJltVUgHfZJX9N%2FDDuJ3Cerdr%2FasvA5icBPByolVeB6yO5B2go%2FOXdzpJLuAVVseuGOv0%2F2M%2Bce6EnO0uIRO3elPbciars9UyhSlXZ%2FkJvoVSCS3OaeNRCTi%2F59j7UGFc0J7XVSWVad2hpv5VEO9fPQXgwx8GcMr4CRybTHWg6ijungJOuRo%2Fhp%2BgMD%2BBw4Y6Xb3OrOSG1BTPdKxCJZNVfJn6%2BbKhTnMcGG9yTv%2B5Zrb6CQT4LLtQEAkBIRKtFgR2IgpZrDa8aEzvX60AQBAAQIVi6bdzEa9jA7aso3FnGph2NA58ncJ8HTBsz5%2FQ69QkD1OM9TmNju7yYsqxmtFqI46fo36eg8HSzwM%2Fb7L3fR6RkYPwfTdzQVBtOklWuT1ulfevCiH0%2FtV7sZt7zd1ovM5F4KKqozgBpHMA6BB1AIDNb0yuGOvIVPAk8YT1BztW3fq5rXMb9fZjcexEEwEHpjPw%2BLjxDPwH2xHgvIIPMy5EBqtCiBSr6f2rswAaQjQAzCbsFVYn2NwMVB3FCWD1AeC9RO8FADb%2FmZ6az7fzcf15%2BWr7BzhWnYnV5irr1gPtWCX9swSbQHOrXN5qck61ByTgfPY9DzUC%2Fs6GICfsbVXCFKtp%2FatL%2FY9pHQKAJUOZyUnwOnNzYR3GhWAcKmDzHbU9GfpsvfcpPsh11ZhNZXVTG5qbt6hJ8l%2FOT%2FeITPyjX6l9kG8mqe0cwGp6%2F%2BrdAHCd6Lr%2BewKopNbh3Gx1kDoET%2FHBrqvGzCmrc6QlGFFA480k3jxdZpsJEoCgeE8lhfdQQ2JocjKj1fT%2B1RoAvJ%2Fo%2FQBQS7fK63CeZjW9TsOrM14dHW%2Br%2Ban6vF3qZbJKyurBpGnQQpicNDY0E4aAXnQC73%2BNh3XZsv5V1ow6RzQnv4%2FyMjJZ6nDO64jMdaZHJxgvUHnZND%2Bh%2FuguHdXmU0KEUF8PPpES0esZG5pJDAkxdDPOk%2FdC5Mmt5smt5smt5smt5lbz5Fbz5Fbz5Fbz5FZzq%2BYGw13usyHXNjcHKKrHZwuvpKWLinmDsECGlAwdND5R2vIg39VWq0atfV5Y14fs2ryIktVqjbUepmUW9zI2CUyes9AlnvJZtEfiaAEL%2B7OabBqJQ619rSnT4jwKiCHaRaD08MdFvVDnWhVXWpm9jFYrEf5AwoYQz1INNQZ7QG91GJfJkH%2BGBzSyghWyJoUAhJi0SIXRAaw292W1eSBWE4uI3YAIGAOYVsWl1sGsvhLhY3FahN6SqXLs0xZKxud5QurmeQee0xGIRnrRD%2FVGFE6iJKIQj0gdYsjI1RCzKhErnWrVj3Hy0Y3OwCDaqx2Ya92%2FVeBYhK8DbLplAbcC7MT2vh%2FEMZPVyhraZAjgMGRe9S2RQiWJg519D%2BoMnPi4e1n1oReZJXLHKtJqNUFrNaZ1EKuzIswstzp%2B6dK44Vm%2B3Ah%2BCmiZ9%2FsDxFNBnX6%2FrTYVHuwMvJBmdcFs1YdmtYp7yLVRdEFUSNBaiGsdwKqKxq0vAF%2BwuNVTn%2B68buH7uQqxdRYnXWL5XXxtYKtChfHEgcHPwKEeSixPJO3BZHVdt1oQc64NwEZM3zqpxPn6%2Bpth9fiLwIvHmdUOwswaVDTPb%2BB%2BYnkYP3dwx2rmu6XWQZyBhdgogHj5XYTChhCm%2BoWqZtXttn4EYW7Wpy%2Beqbi%2FXshk1dqy9mMVH9ja%2BgCY1YcsIcQW0DGp%2BGkcJpYbeGlfVktAaXCrzYM5A6%2FQ3lZpJWE7C9UYr0wBP4kwSh%2BTKrmSmsWqNdwctrhV0Q%2B3ipMnway6eF7usjYe4lZbpRpeIBbge%2FZlVZnI0nyXOjD4PTCHu8hk26tvh6gQ5ypKH5MacSWVW63G9VnDTriYLnNRhEyLdWSaWzLX8AU5%2Fkn98zpXwW6X1Mj%2F0NkCFhKOym0emVgYbKXag74HNtchGGyPTmyH2VbZ1adLVbykpGpW41xKJalV34qd30KwjkxjS2YX4WLXFfY%2BFmEakz3SYpt%2BH7lSXWFHJVud%2BvfXanNAqzxpj1vQpSpeLmQ7VUmpUivrTw9EmDJlyty25SD6oVHD404zqTQiMaOF3R%2FS%2BIboZ6Mw4PrDB3UGFpRchxTkSX3cwePQd0ZW2P8ZNHkvRJ7cap7cap7cam41T241T241T241T241t%2Bq2aOAs0rdVcquuXawYFrpdTF6%2Fl6eDJUqOu0SDxvdpH8mtus8eR9HUnQ3ftK4vANslPSdxisOlKcjZ8uc6jI9Ryzy%2FWKEuq%2BUn9KOHW5VA%2BVASn%2BrQAcR2wy%2FJvAWwoYjyuD4vFDnwTdi33ZhV1z55ybJYx0B9sw2UDOvrRqK0dAHcZ16C2xp2T1ywntO4d3aCcJXPH696M4EPm0s1aQWkISRQPpTEgcUWGQKAkLknBtIRlFbGm6yUokyeHDJyGLT6QKRVTcPJS8P6Wq%2F1ibnlNg4b1tcFwHR3jOunn8KmEGLkhG3fMeJofPR8yQcWXX1%2BuTAa%2BMAFTWpBAKLAtALSEBIoH0riAIrdwa1KEVA2OAfMQyZ5csjM14llHX2tahqOX2PLSr0%2F6kkwrK9r6ts%2BFcKaq1eZix7h%2BAnG%2B4uZr%2Bl8oUK%2B3p3hLiJURVhkjyANgQzUOJTEIWN3BrUqRSgbBs5KKcrlySHOE1tXIq1qGl8V1MPh0KJlWF%2FX0AVYQjuk9xuvb7CGTzB%2BP6w6UL1D4wsoLrLttrEbW7cRjpGR8iFXcaMl3x3UKmxlw8BZKUWZPF6IS%2BVauVSVNjDWHQMu8PWBI6u1%2BEFc%2FaTBNQE7Um3Gf3RrZMIbLzgaf6cHKTV%2Bgr%2BgrF4w2iAj5UNrGmeWpga2GmXNzHkpjbKXsc22v5HUutIAsDbEpao8gCg%2FxtcHJsn19XV%2F7kGE4VafkvVtMF5oEp0ul3QezHhSKvTXYfSpJ%2FY6BSylSKd86A7FjZaqzwxsNXqEOxI4K2WmI2InI3z7fTLGDx93KHxLY5ZKvQ3IbDYN6wMDgLa%2Brnf5i16C1Y%2BMb9cHGJdp%2BpwHMxsFAkjTGg3qUgkYlo7MlA85ihssWZMFZ1Cr1rA6TgycWzVTFcP2%2B4lSh50hoqfkWxopleddFoD6nGl9YAD6%2BrptrB2SuE6xNNClubLjdtFgfDtmHqworrRG72x0qQSEokzUOJTEw7daI71B75akTyXVwFkpTrlVrjVZ6hDRZZy8ZJZKzkUPjTNkWh%2FYsJL%2BxzzIeLfH8Z3YyZ0D8eS2ZSAUlUD5UBIH2qfPD%2F7ORvpUUg2clTJTocK33%2FzOpi91iFqwfvCaQ%2BYEM43H1FjKerzN01UPqJ4O4nj1XAMyjXOrA%2FHktmUgFJVE%2BZBELueNyeVmQk8mZW7dJ2nI5VIljwaZP0Z5uFZzU34kdYiubY2cdygpwbRylLoeb7MwKkSB7ZjVaSEzvToYT25bFkK1IXPKh0LkcD7dowNIVNkx8ugLO%2FY4TddqbsqPpA6R06TvvORxEnDeCzFo8l6IPLnVPLnVPLnV3Gqe3Gqe3Gqe3Gqe3Gpu1dzf%2B5Zx1ShxcPUHT2uqktR9uN%2F4ST9UWThIq65taI95S7gaAsyddTWPzc%2FCB85JnHT3ZdVuUULel2C1UsTCYK8at0XAUMsNrdqm9pi9uQd4%2B5kPq569Prk%2BgOISkaEPeXS%2BDns%2FfJzXJ2oplMnGAoC1fVlV28%2FkGVX529x750BW5YcvgEox7EYrAYAQrL835ICJW09Xq09b5vkNGPi5kYl5jbPHVVmrjQMfqpWI9SE%2FQvTIRB0lnQdEgZlXarw%2BLRVBaTZ4o3opu9XOVQALCVK9%2BaqxkjcTDGT12RqKQBG1Z4eIDgMAEevvlVyGc2%2FYKRScYc8033pmHIxbq1crgZWxPrm4qwyc%2F1CN9D7kCnwfldtxTOPRRxc4j3biuOLqyKOEmGy0apCptTJa7RYRxnTc3yvlFYxWpdRBrDZnPIQvjuYQUQ0QgkgIredTchnOo5PRGufWZH3Y%2BVmPceDUZ12Ac1ld5zt%2FBF1G60MOqkA1CLxZjdPVlo01zkOpM%2BU4b9kpa5oxGyf7%2FGQ2qz5UCyrLyoaSp1V6KKVtKfvirkNEDWCH1khlL74u8Trnl3oTTqXIOXBnbw0mTgSdQ6bXg4zeh7wePrZX0%2FjVsF%2BS8UhqoPEppFhlNkaEAKA3cJJtvi3oYCfWY4a73BUu1Q%2Bri8JBWj0UjbP%2BXsllOPfCRtc7PJ3L%2B8RKMXsd8%2BOKKzgngMmqJ4TWh1xBtSq%2FHtL4j1uyC4vxUiRV449ZKVa5DfNBecmDjHcpjh9FYyM81VSHg5S7XHZXPJBVMe9J2JgXQ0Rvi8ZZf2%2FIARO3Xd93bc5hd4rmOkIYuSASOienWisBf7J2F%2Bl9yMF8oTAfHNHrHHGGq8MOMY5Qqs6D4SqApHUDlY1Uq803IPNGM46xOb3S60F9JIHd5Wa7K%2B5vjcj8B%2Bdbxei9SbE1FPb3yrD%2B3r14ESgmzR%2BUE93xaQC1u8q8D1neA4%2FxOmO%2FUHAqBo67AmKcnMK4B0qIspFqlVY3AGysanRzTgJrppx2l8vvige7W7pmeTPAjGddG%2Br394L19751nJzCFeDpsrEPucjmZ%2BdK%2BIxFhjAbKVZpxYK1osO56MGDlLtcdlc8sFVn%2BHQABKdl735Cf%2B9bwtUQwOBB1g%2BGiYfZSLVKFxuXyBwn5S6X3RUPbpWcJgkx1JS9%2Bwn9vW8lZ82xB1%2BfiU4ZEOYNCqablDXqLlfXGuz1M3kvRJ7vZKt5cqu51Ty51Ty51Ty51Ty51Ty51dxqntyqe5W%2BrZP3A3dhd4g6NrpkSqc7BibV%2FgjtM4twDXRsjIyxYXMI9dUcn7Lk1VdfVd%2FexFSAA18nOXs%2F8GGrhoUF1KzDxOyVbAAvMKv34RNkSGdxbGyxY%2Bb%2F%2Bs84xFKCefnoFoCUngEebT3LoppfjM265ZZb1Lc3Ma94IgbcItsUxlPWSWZWk%2Fty8fyMBXgzzzN5lSkAaH%2BNDdTwx2jM1aC7iDCLrpE%2F0XLZ86kBNZd4mvuwiv5f%2FAwt2sb5yGrV9d3kA8b3GfUN9Yus0YdvTzrn6ySbrZYAWEJYAEqs6tGjkDG8iBrjj8Mj1oh1N71g8xZ6dTLg%2FHvvk1w75Ot13JexOUCoMNvFViQVFzJYnZubU9%2F44svmAyb6ptNCFWHM%2FVvvT9p%2BkdFqtE4y36DIqi%2BtHo6a%2FGp6X64AgNtuAwBBsawB3tnpf6e%2F6Ih%2BE8DCC9p1%2BAjaaABAFUdM%2FE%2F9Zcm1C8%2FHPw5UiMUF4GY8VoWY96zXZfuIQLWQwSoA9S198WX3BqRAH8AN7TBadAv8L36%2Fhp28lO1YbTDbKuaO1cgq%2FKFIJ1yXrwGrrLLzrHX661PsRbfUbQKsTBfWu%2FHRNoAfs9Dl%2FI87KxZ7HWwCm8o1270Zr6vB6T8ddRkqqZmtmhdf5qsJTmktOoVJQCw7hl3%2F09jJV7JZ%2FWAJKsUUq%2FrfgG4AwFNP8fV%2Bj27nttvkV%2F1Qsi4egcwXY%2FzyjxKssFqLVB7Edae%2B9gBQb17Hgzfz49v8d%2FAXiUKuUkLjV4FfbaBkasYDipUYhdj9h7T8QhHe2%2F820TrtzyqX2kjSyhYX7QHmXf%2Bz6KfRzGS1UT4FlXtSra6ryevJ%2Fbp0224ols96zxchU9c3bwrX7wSA10llro7umXcA9TNd1Odi3Jf8E%2BTHOLk1fMZpt53PoObqUtsA2kpryrFakVJPFivqHjijVSa1Ol2VWolpZVKJkqwGHqI8SZmsfrADFXzRZJWvnyyDaoH166afgXuHEMY7wzfvhVUA6N2Mz1i4f0KIiadgndH4kY9b6HU1fh%2FaPXr8ceq1tcWwi965ZQDL57xilmM1%2BszJb9b023sPO9Hu9uqA36n4QDum7gLkbipUgQvEtTKpBCTcqI6KMN4ns1ktPwqVapNb5Vqj62q1wPqB0626dv%2Fm52mHLeiOBypyRHvqbUwtLEyhPezEeRXAn22hGuMdeB%2BLtvpjHjqx%2BqdXZfXK6ul20rHK%2B2%2FDjxTFhIwKwLoiZEbJ2Nb%2BOFvnVH3TtUYbzy35ScveVvCJbFZbUMGXs7yzKURWC0OsHzjdqn18a1rMzwvWDP2xBsZ7D7GVyclZnnzyHe94cnLZ0Xhh8vfwR1%2FU1s4%2BiSj880rLTYrelzeXsxyr0lpAFIyyNd1hXuS6XEeYepmvc6q%2B6c%2BBVYLSKqVyTc9ls3ofVKxeyjrJrBeC9c2mWD0%2B3CQKAmJpPrNVJlisDlFveWJiuUfE%2BGv4B804ryCWCsXSmBfzjf3%2Fbiku1Y2k8pzZ8ABv4wwNFBGlwF4HTYFtDuFks1qDyvNp6yRzq6pvlm%2Fe6ip7uzTs7NFlTGKkTNmzIgKNBCIWbXg6oGA6bclrngJbG9gYZ2VUiNEVh96sCCmdwYQnMCpUmJtC4YB7IRz67kneC5Ent5ont5ont5ont5pbzZNbzZNbzZNbzZNbXZhaiIPcagtRii5ljQsYJy%2B4rnn3dlGkNzH4KFomHIbz0liR9T8fKF%2BcmlqUnMcdA7qUKXt0xNqAbZgeWu3%2FwFfRz4%2BQKa2rLUOTAYoV0%2FK0tg1qceFu7SzMi58i4Ul2i6a9VUzYIWiimdnqm7%2Fu8amv3XPna5LzHEFjck6C9P7kvZrRhICBhVZFNPYw%2BnmYWNzSGH7lGjR6yrhW47OwJbfxLOm53%2FspZhX4w8AFcXTDcJh1pn7jDRAL3viNqY7RK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<h1 class="title">Practical Machine Learning Project</h1>
<h4 class="author"><em>Stefano Biffani</em></h4>
<h4 class="date"><em>Tuesday, December 16, 2014</em></h4>
</div>
<div id="introduction" class="section level1">
<h1>Introduction</h1>
<p>Data for the present study were obtained from the Weight Lifting Exercises Dataset. Six young health participants were asked to perform one set of 10 repetitions of the Unilateral Dumbbell Biceps Curl in five different fashions: exactly according to the specification (Class A), throwing the elbows to the front (Class B), lifting the dumbbell only halfway (Class C), lowering the dumbbell only halfway (Class D) and throwing the hips to the front (Class E). The objective of this project was to predict “how (well)” an activity was performed by the wearer based on a set of features recorded by sensors located on the belt, forearm, arm, and dumbell of the 6 participants.</p>
</div>
<div id="material-and-methods" class="section level1">
<h1>Material and Methods</h1>
<p>The MLE dataset comprised 19622 record and 160 variables. Some variables (n=100) had a large number of missing values. Those variables were statistics estimated from measures obtained within the same time-window and within the same participant. If the variable <em>new_window</em> had value =<strong>yes</strong>, the complete row was deleted.</p>
<p>Eventually 52 variables were retained. Correlation between variables ranged from -0.992 to 1 with an average of 0.021. A graphical visualitation of the correlations within variables can be observed in the following figure</p>
<p><img src="data:image/png;base64,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" title="plot of chunk step2" alt="plot of chunk step2" width="672" /></p>
<p>Data were divided into a training and a testing dataset (proportion 80/20). Training data was used to train 3 different algorithms which were used predict the <em>classe</em> variable. The 3 selected algorithms were: 1. A Linear Discriminant Analysis with PCA pre-processing 2. A Linear Discriminant Analysis without PCA pre-processing 3. A boosting algorithm</p>
<p>The 3 algorithms were selected based on data structure. Some predictors are highly correlated and reducing the number of predictors might be a good solution (method 1). Moreover <strong>LDA</strong> is a very powerful approach when the response variable is multi-class (method 2). On the other side a method which weight and add all the predictors (especially when these are weak) might be more useful than reducing the number of predictors (method 3).</p>
<p>As regards cross-validation, because of the data size and following what suggested by Kim (Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap, Computational Statistics & Data Analysis, Volume 53, Issue 11, 1 September 2009, Pages 37353745), a 10-fold CV scheme repeated 3 times was used.</p>
</div>
<div id="results---training" class="section level1">
<h1>Results - Training</h1>
<p>The percentage of the 5 different classes in the training dataset can be observed in the following figure. <img 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" title="plot of chunk torta" alt="plot of chunk torta" width="672" /> Class A (i.e., exercise correctly executed) is the most frequent, with nearly a 30 % frequency.</p>
<p>The accuracy obtained by the CV process was 0.5249, 0.7175 and 0.9667 for the Linear Discriminant Analysis with PCA pre-processing, the Linear Discriminant Analysis without PCA pre-processing and the boosting algorithm, respectively.</p>
<p>The latter algorithm showed the best results over all parameters</p>
<pre class="r"><code>cm.GBM</code></pre>
<pre><code>## Confusion Matrix and Statistics
##
## Reference
## Prediction A B C D E
## A 1075 14 4 0 1
## B 26 700 16 1 0
## C 0 18 646 4 2
## D 0 3 14 606 6
## E 0 6 5 8 686
##
## Overall Statistics
##
## Accuracy : 0.967
## 95% CI : (0.961, 0.972)
## No Information Rate : 0.287
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.958
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: A Class: B Class: C Class: D Class: E
## Sensitivity 0.976 0.945 0.943 0.979 0.987
## Specificity 0.993 0.986 0.992 0.993 0.994
## Pos Pred Value 0.983 0.942 0.964 0.963 0.973
## Neg Pred Value 0.991 0.987 0.988 0.996 0.997
## Prevalence 0.287 0.193 0.178 0.161 0.181
## Detection Rate 0.280 0.182 0.168 0.158 0.179
## Detection Prevalence 0.285 0.193 0.174 0.164 0.184
## Balanced Accuracy 0.985 0.965 0.968 0.986 0.991</code></pre>
</div>
<div id="testing" class="section level1">
<h1>Testing</h1>
Estimates obtained from boosting algorithm were used to predict 20 unknown records. Results are as follows: <!-- html table generated in R 3.0.3 by xtable 1.7-4 package --> <!-- Tue Dec 16 22:28:32 2014 -->
<table border="1">
<tr> <th> </th> <th>
X
</th> <th>
user_name
</th> <th>
pred_classe
</th> </tr>
<tr> <td align="right">
1
</td> <td align="right">
1
</td> <td>
pedro
</td> <td>
B
</td> </tr>
<tr> <td align="right">
2
</td> <td align="right">
2
</td> <td>
jeremy
</td> <td>
A
</td> </tr>
<tr> <td align="right">
3
</td> <td align="right">
3
</td> <td>
jeremy
</td> <td>
B
</td> </tr>
<tr> <td align="right">
4
</td> <td align="right">
4
</td> <td>
adelmo
</td> <td>
A
</td> </tr>
<tr> <td align="right">
5
</td> <td align="right">
5
</td> <td>
eurico
</td> <td>
A
</td> </tr>
<tr> <td align="right">
6
</td> <td align="right">
6
</td> <td>
jeremy
</td> <td>
E
</td> </tr>
<tr> <td align="right">
7
</td> <td align="right">
7
</td> <td>
jeremy
</td> <td>
D
</td> </tr>
<tr> <td align="right">
8
</td> <td align="right">
8
</td> <td>
jeremy
</td> <td>
B
</td> </tr>
<tr> <td align="right">
9
</td> <td align="right">
9
</td> <td>
carlitos
</td> <td>
A
</td> </tr>
<tr> <td align="right">
10
</td> <td align="right">
10
</td> <td>
charles
</td> <td>
A
</td> </tr>
<tr> <td align="right">
11
</td> <td align="right">
11
</td> <td>
carlitos
</td> <td>
B
</td> </tr>
<tr> <td align="right">
12
</td> <td align="right">
12
</td> <td>
jeremy
</td> <td>
C
</td> </tr>
<tr> <td align="right">
13
</td> <td align="right">
13
</td> <td>
eurico
</td> <td>
B
</td> </tr>
<tr> <td align="right">
14
</td> <td align="right">
14
</td> <td>
jeremy
</td> <td>
A
</td> </tr>
<tr> <td align="right">
15
</td> <td align="right">
15
</td> <td>
jeremy
</td> <td>
E
</td> </tr>
<tr> <td align="right">
16
</td> <td align="right">
16
</td> <td>
eurico
</td> <td>
E
</td> </tr>
<tr> <td align="right">
17
</td> <td align="right">
17
</td> <td>
pedro
</td> <td>
A
</td> </tr>
<tr> <td align="right">
18
</td> <td align="right">
18
</td> <td>
carlitos
</td> <td>
B
</td> </tr>
<tr> <td align="right">
19
</td> <td align="right">
19
</td> <td>
pedro
</td> <td>
B
</td> </tr>
<tr> <td align="right">
20
</td> <td align="right">
20
</td> <td>
eurico
</td> <td>
B
</td> </tr>
</table>
</div>
</div>
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