2023-2024/labs/lab05/AI-lab05-linRegressionLS.ipynb

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    "\r\n",
    "# Probleme de regresie <img src=\"images/regression.png\" width=\"200\">\r\n",
    "\r\n",
    "## Obiective\r\n",
    "* rezolvarea unor probleme de regresie/predictie \r\n",
    "* diferentierea intre regresie univariata, bivariata si multi-variata\r\n",
    "* folosirea unor algoritmi liniari bazati pe metoda celor mai mici patrate \r\n",
    "\r\n",
    "## Cuvinte cheie:\r\n",
    "* date de antrenare si date de testare \r\n",
    "* atribute/catacteristici ale datelor\r\n",
    "* model de regresie\r\n",
    "* eroarea de predictie\r\n"
   ],
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   "cell_type": "markdown",
   "source": [
    "## Aspecte teoretice"
   ],
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   "source": [
    "Problemele de regresie identifica relatia de dependenta intre datele de iesire si datele de intrare ale unui probleme, adica pe baza unor caracteristici a datelor se doreste prezicearea unor valori asociate acestor date. Valorile prezise sunt de tip continu. "
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    "\r\n",
    "\r\n",
    "<details>\r\n",
    "  <summary>Remember the theory behind regression</summary>\r\n",
    " \r\n",
    "\r\n",
    "Relatia de dependenta poate fi:\r\n",
    "- liniara (tema abordata in acest laborator)\r\n",
    "- ne-liniara (tema abordata in alt laborator)\r\n",
    "\r\n",
    "### Exemple de probleme de regresie:\r\n",
    "- predictia actiunilor la bursa in functie de anumiti indicatori economici \r\n",
    "- predictia consumului de inghetata in functie de temperatura si de numarul de copii dintr-o tabara\r\n",
    "\r\n",
    "### Formalizare problema de regresie liniara:\r\n",
    "\r\n",
    "Regresia liniara este un model liniar (un model care presupune ca exista o dependenta liniara intre variabilele de input X si variabila de output Y). Mai specific, variabila de iesire paote fi calculata  ca o combinatie a variabilelor de intrare. \r\n",
    "\r\n",
    "- datele se caracterizeaza prin $atribute$ ($x = (x_1, x_2, ..., x_3)$) si $output$ (atat atributele, cat si outputul sunt valori numerice continue)\r\n",
    "- modelul (liniar) de predictie (regresorul): $y = f(x, w) = w_0 + w_1 * x_1 + w_2 * x_2 + ...$ \r\n",
    "\r\n",
    "### Metodologia rezolvarii unei probleme de regresie (liniara)\r\n",
    "\r\n",
    "**Antrenare** \r\n",
    "\r\n",
    "> Input: un set de exemple etichetate $(x^i, y^i)$, cu $i \\in \\{1, 2, ..., trainDataSize\\}$, $x^i$ - vectorul de atribute asociate unui exemplu, $y^i$ etichetata asociata exemplului $x^i$ (valoare numerica reala/float)\r\n",
    "\r\n",
    "> Output: un model de regresie = regresor (adica valorile optime ale coeficientilor $w$ din ecuatia de regresie $f(x, w) = w_0 + w_1 * x_1 + w_2 * x_2 + ...$)\r\n",
    "\r\n",
    "> Algoritm: \r\n",
    "- metoda celor mai mici patrate ($Least Square$) - in laboratorul de azi :)\r\n",
    "- $Gradient Descent$ - in alt laborator :)\r\n",
    "\r\n",
    "**Testare** \r\n",
    "\r\n",
    "> Input: un exemplu ne-etichetat $(x_{new})$, cu $x_{new}$ - vectorul de atribute asociate acelui exemplu\r\n",
    "\r\n",
    "> Output: valoarea prezisa pentru exemplul $x_{new}$\r\n",
    "\r\n",
    "> Algoritm:\r\n",
    "Folosirea regresorului invatat (a coeficientilor) pentru a calcula valoarea outputului\r\n",
    "$$y_{new} = f(x_{new}, w)$$\r\n",
    "\r\n",
    "**Metoda celor mai mici patrate**\r\n",
    "\r\n",
    "Presupunem cazul unei regresii univariate (un exemplu are un singur atribut, deci $f(x,w) = w_0 + w_1 * x_1$. \r\n",
    "Se doreste identificarea valorilor optime pentru coeficientii **w**=$[w_0, w_1]$ stiindu-se un set de $n$ exemple de antrenament de forma $(x^i, y^i)$, cu $i = 1, 2, ..., n$, $x^i = (x^i_1)$.\r\n",
    "\r\n",
    "Se defineste o functie de cost: $cost(x) = \\sum_{i=1}^{n}(y^i_{computed} - y^i)^2$. Se identifica punctul de minim al acestei functii, care duce la valorile optime pt **w**.\r\n",
    "\r\n",
    "$$w_1 = \\frac{n \\sum_{i=1}^{n}(x^i * y^i) -\\sum_{i=1}^{n}x^i * \\sum_{i=1}^{n}y^i}{n \\sum_{i=1}^{n}(x^i)^2 - (\\sum_{i=1}^{n}x^i)^2} $$\r\n",
    "\r\n",
    "$$w_0 = \\frac{\\sum_{i=1}^{n}y^i - w_1 \\sum_{i=1}^{n}x^i}{n}$$\r\n",
    "\r\n",
    "Pentru cazul unei regresii multi-variate ($m$ atribute): $f(x,w) = w_0 + w_1 * x_1 + w_2 * x_2 + ... w_m * x_m$) si un set de date cu $n$ exemple:\r\n",
    "\r\n",
    "$\\boldsymbol{w} = (X^{T}X)^{-1}X^{T}{Y}$,\r\n",
    "unde $X = (x^i_{j})$, $Y = (y^i)$, $i = 1, 2, ..., n$, $j = 1, 2, ..., m$.\r\n",
    "\r\n",
    "\r\n",
    "\r\n",
    "\r\n",
    "\r\n",
    "### Evaluarea performantei regresorului (a se vedea materialele din laboratorul 6)\r\n",
    "\r\n",
    "- the absolute difference  (this is $L_1$ distance):\r\n",
    "$$Error = \\frac{1}{n} \\times \\sum_{i=1}^{n} |y^i - y^i_{computed}| = Mean Absolute Error (MAE)$$\r\n",
    "- the square difference (this is the $L_2$ distance):\r\n",
    "$$Error = \\sqrt{\\frac{1}{n} \\times \\sum_{i=1}^{n} (y^i - y^i_{computed}) ^ 2} = Root Mean Square Error (RMSE)$$ \r\n",
    "\r\n",
    "</details>"
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   "cell_type": "code",
   "execution_count": null,
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   "cell_type": "markdown",
   "source": [
    "## Exemple"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Demo1\r\n"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Problemă: Ce îi poate face pe oameni fericiți?\r\n",
    "\r\n",
    "Se consideră problema predicției gradului de fericire a populației globului folosind informații despre diferite caracteristici a bunăstării respectivei populații precum Produsul intern brut al țării în care locuiesc (gross domestic product – GBP), gradul de fericire, etc.  Folsind datele aferente anului 2017 [here](https://www.kaggle.com/unsdsn/world-happiness#2017.csv), să se realizeze o predicție a gradului de fericire în funcție de Produsul intern brut. \r\n",
    "\r\n",
    "Deci avem o problema de regresie univariata $y = w_0 + w_1 * x$, unde:\r\n",
    "- o variabila dependenta – y (gradul de fericire) si \r\n",
    "- o variabila independenta – x (PIB-ul).\r\n",
    "\r\n",
    "Pasi in rezolvare:\r\n",
    "* plot pt distributia datelor & plot pt “verificarea” liniaritatii (daca legatura intre y si x e una liniara)\r\n",
    "* impartire date pe train si test\r\n",
    "* invatare model (cu tool generic si cu tool de least square)\r\n",
    "* plot rezultate\r\n",
    "* calcul metrici de performanta (eroarea)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "# prerequisites \r\n",
    "import csv\r\n",
    "import os\r\n",
    "import matplotlib.pyplot as plt\r\n",
    "import numpy as np  \r\n",
    "from sklearn import linear_model"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Pasul 1 - plot pt distributia datelor & plot pt “verificarea” liniaritatii (daca legatura intre y si x e una liniara)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "# load data and consider a single feature (Economy..GDP.per.capita) and the output to be estimated (happiness)\r\n",
    "\r\n",
    "def loadData(fileName, inputVariabName, outputVariabName):\r\n",
    "    data = []\r\n",
    "    dataNames = []\r\n",
    "    with open(fileName) as csv_file:\r\n",
    "        csv_reader = csv.reader(csv_file, delimiter=',')\r\n",
    "        line_count = 0\r\n",
    "        for row in csv_reader:\r\n",
    "            if line_count == 0:\r\n",
    "                dataNames = row\r\n",
    "            else:\r\n",
    "                data.append(row)\r\n",
    "            line_count += 1\r\n",
    "    selectedVariable = dataNames.index(inputVariabName)\r\n",
    "    inputs = [float(data[i][selectedVariable]) for i in range(len(data))]\r\n",
    "    selectedOutput = dataNames.index(outputVariabName)\r\n",
    "    outputs = [float(data[i][selectedOutput]) for i in range(len(data))]\r\n",
    "    \r\n",
    "    return inputs, outputs\r\n",
    "\r\n",
    "crtDir =  os.getcwd()\r\n",
    "filePath = os.path.join(crtDir, 'data', 'world-happiness-report-2017.csv')\r\n",
    "\r\n",
    "inputs, outputs = loadData(filePath, 'Economy..GDP.per.Capita.', 'Happiness.Score')\r\n",
    "print('in:  ', inputs[:5])\r\n",
    "print('out: ', outputs[:5])"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "in:   [1.61646318435669, 1.48238301277161, 1.480633020401, 1.56497955322266, 1.44357192516327]\n",
      "out:  [7.53700017929077, 7.52199983596802, 7.50400018692017, 7.49399995803833, 7.4689998626709]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "# see how the data looks (plot the histograms associated to input data - GDP feature - and output data - happiness)\r\n",
    "\r\n",
    "def plotDataHistogram(x, variableName):\r\n",
    "    n, bins, patches = plt.hist(x, 10)\r\n",
    "    plt.title('Histogram of ' + variableName)\r\n",
    "    plt.show()\r\n",
    "\r\n",
    "plotDataHistogram(inputs, 'capita GDP')\r\n",
    "plotDataHistogram(outputs, 'Happiness score')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "# check the liniarity (to check that a linear relationship exists between the dependent variable (y = happiness) and the independent variable (x = capita).)\r\n",
    "\r\n",
    "plt.plot(inputs, outputs, 'ro') \r\n",
    "plt.xlabel('GDP capita')\r\n",
    "plt.ylabel('happiness')\r\n",
    "plt.title('GDP capita vs. happiness')\r\n",
    "plt.show()\r\n"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Pasul 2 - impartire date pe train si validation"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "# Split the Data Into Training and Test Subsets\r\n",
    "# In this step we will split our dataset into training and testing subsets (in proportion 80/20%).\r\n",
    "\r\n",
    "# Training data set is used for learning the linear model. Testing dataset is used for validating of the model. All data from testing dataset will be new to model and we may check how accurate are model predictions.\r\n",
    "\r\n",
    "np.random.seed(5)\r\n",
    "indexes = [i for i in range(len(inputs))]\r\n",
    "trainSample = np.random.choice(indexes, int(0.8 * len(inputs)), replace = False)\r\n",
    "validationSample = [i for i in indexes  if not i in trainSample]\r\n",
    "\r\n",
    "trainInputs = [inputs[i] for i in trainSample]\r\n",
    "trainOutputs = [outputs[i] for i in trainSample]\r\n",
    "\r\n",
    "validationInputs = [inputs[i] for i in validationSample]\r\n",
    "validationOutputs = [outputs[i] for i in validationSample]\r\n",
    "\r\n",
    "plt.plot(trainInputs, trainOutputs, 'ro', label = 'training data')   #train data are plotted by red and circle sign\r\n",
    "plt.plot(validationInputs, validationOutputs, 'g^', label = 'validation data')     #test data are plotted by green and a triangle sign\r\n",
    "plt.title('train and validation data')\r\n",
    "plt.xlabel('GDP capita')\r\n",
    "plt.ylabel('happiness')\r\n",
    "plt.legend()\r\n",
    "plt.show()\r\n"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Pasul 3 - invatare model (cu tool generic si cu tool de least square)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "# learning step: init and train a linear regression model y = f(x) = w0 + w1 * x\r\n",
    "# Prediction step: used the trained model to estimate the output for a new input\r\n",
    "\r\n",
    "# using sklearn \r\n",
    "# training data preparation (the sklearn linear model requires as input training data as noSamples x noFeatures array; in the current case, the input must be a matrix of len(trainInputs) lineas and one columns (a single feature is used in this problem))\r\n",
    "xx = [[el] for el in trainInputs]\r\n",
    "\r\n",
    "# model initialisation\r\n",
    "regressor = linear_model.LinearRegression()\r\n",
    "# training the model by using the training inputs and known training outputs\r\n",
    "regressor.fit(xx, trainOutputs)\r\n",
    "# save the model parameters\r\n",
    "w0, w1 = regressor.intercept_, regressor.coef_[0]\r\n",
    "print('the learnt model: f(x) = ', w0, ' + ', w1, ' * x')\r\n",
    "\r\n",
    "# # using developed code\r\n",
    "# from myRegression import MyLinearUnivariateRegression\r\n",
    "\r\n",
    "# # model initialisation\r\n",
    "# regressor = MyLinearUnivariateRegression()\r\n",
    "# # training the model by using the training inputs and known training outputs\r\n",
    "# regressor.fit(trainInputs, trainOutputs)\r\n",
    "# # save the model parameters\r\n",
    "# w0, w1 = regressor.intercept_, regressor.coef_\r\n",
    "# print('the learnt model: f(x) = ', w0, ' + ', w1, ' * x')\r\n"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "d:\\_Work\\School\\_2021-2022\\sem2\\AI\\labs\\lab07\n",
      "the learnt model: f(x) =  3.2007686227262897  +  2.1503460960730023  * x\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Pasul 4 - plot rezultate (model invatat, predictii)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "source": [
    "\r\n",
    "# plot the learnt model\r\n",
    "# prepare some synthetic data (inputs are random, while the outputs are computed by the learnt model)\r\n",
    "noOfPoints = 1000\r\n",
    "xref = []\r\n",
    "val = min(trainInputs)\r\n",
    "step = (max(trainInputs) - min(trainInputs)) / noOfPoints\r\n",
    "for i in range(1, noOfPoints):\r\n",
    "    xref.append(val)\r\n",
    "    val += step\r\n",
    "yref = [w0 + w1 * el for el in xref] \r\n",
    "\r\n",
    "plt.plot(trainInputs, trainOutputs, 'ro', label = 'training data')  #train data are plotted by red and circle sign\r\n",
    "plt.plot(xref, yref, 'b-', label = 'learnt model')                  #model is plotted by a blue line\r\n",
    "plt.title('train data and the learnt model')\r\n",
    "plt.xlabel('GDP capita')\r\n",
    "plt.ylabel('happiness')\r\n",
    "plt.legend()\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "source": [
    "# use the trained model to predict new inputs\r\n",
    "\r\n",
    "# makes predictions for test data (manual)\r\n",
    "# computedTestOutputs = [w0 + w1 * el for el in testInputs]\r\n",
    "\r\n",
    "# makes predictions for test data (by tool)\r\n",
    "computedValidationOutputs = regressor.predict([[x] for x in validationInputs])\r\n",
    "\r\n",
    "# plot the computed outputs (see how far they are from the real outputs)\r\n",
    "plt.plot(validationInputs, computedValidationOutputs, 'yo', label = 'computed test data')  #computed test data are plotted yellow red and circle sign\r\n",
    "plt.plot(validationInputs, validationOutputs, 'g^', label = 'real test data')  #real test data are plotted by green triangles\r\n",
    "plt.title('computed validation and real validation data')\r\n",
    "plt.xlabel('GDP capita')\r\n",
    "plt.ylabel('happiness')\r\n",
    "plt.legend()\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Pasul 5 - calcul metrici de performanta (eroarea)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "source": [
    "# compute the differences between the predictions and real outputs\r\n",
    "# \"manual\" computation\r\n",
    "error = 0.0\r\n",
    "for t1, t2 in zip(computedValidationOutputs, validationOutputs):\r\n",
    "    error += (t1 - t2) ** 2\r\n",
    "error = error / len(validationOutputs)\r\n",
    "print('prediction error (manual): ', error)\r\n",
    "\r\n",
    "# by using sklearn \r\n",
    "from sklearn.metrics import mean_squared_error\r\n",
    "\r\n",
    "error = mean_squared_error(validationOutputs, computedValidationOutputs)\r\n",
    "print('prediction error (tool):  ', error)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "prediction error (manual):  0.4142120438026716\n",
      "prediction error (tool):   0.4142120438026716\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Toti pasii impreuna"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "source": [
    "# put all steps togheter\r\n",
    "\r\n",
    "# using sklearn \r\n",
    "\r\n",
    "def plotData(x1, y1, x2 = None, y2 = None, x3 = None, y3 = None, title = None):\r\n",
    "    plt.plot(x1, y1, 'ro', label = 'train data')\r\n",
    "    if (x2):\r\n",
    "        plt.plot(x2, y2, 'b-', label = 'learnt model')\r\n",
    "    if (x3):\r\n",
    "        plt.plot(x3, y3, 'g^', label = 'test data')\r\n",
    "    plt.title(title)\r\n",
    "    plt.legend()\r\n",
    "    plt.show()\r\n",
    "\r\n",
    "crtDir =  os.getcwd()\r\n",
    "filePath = os.path.join(crtDir, 'data', 'world-happiness-report-2017.csv')\r\n",
    "\r\n",
    "inputs, outputs = loadData(filePath, 'Economy..GDP.per.Capita.', 'Happiness.Score')\r\n",
    "\r\n",
    "plotDataHistogram(inputs, 'capita GDP')\r\n",
    "plotDataHistogram(outputs, 'Happiness score')\r\n",
    "\r\n",
    "# check the liniarity (to check that a linear relationship exists between the dependent variable (y = happiness) and the independent variable (x = capita).)\r\n",
    "plotData(inputs, outputs, [], [], [], [], 'capita vs. hapiness')\r\n",
    "\r\n",
    "# split data into training data (80%) and testing data (20%)\r\n",
    "np.random.seed(5)\r\n",
    "indexes = [i for i in range(len(inputs))]\r\n",
    "trainSample = np.random.choice(indexes, int(0.8 * len(inputs)), replace = False)\r\n",
    "validationSample = [i for i in indexes  if not i in trainSample]\r\n",
    "trainInputs = [inputs[i] for i in trainSample]\r\n",
    "trainOutputs = [outputs[i] for i in trainSample]\r\n",
    "validationInputs = [inputs[i] for i in validationSample]\r\n",
    "validationOutputs = [outputs[i] for i in validationSample]\r\n",
    "\r\n",
    "plotData(trainInputs, trainOutputs, [], [], validationInputs, validationOutputs, \"train and test data\")\r\n",
    "\r\n",
    "# training step\r\n",
    "xx = [[el] for el in trainInputs]\r\n",
    "regressor = linear_model.LinearRegression()\r\n",
    "# regressor = linear_model.SGDRegressor(max_iter =  10000)\r\n",
    "regressor.fit(xx, trainOutputs)\r\n",
    "w0, w1 = regressor.intercept_, regressor.coef_\r\n",
    "\r\n",
    "# plot the model\r\n",
    "noOfPoints = 1000\r\n",
    "xref = []\r\n",
    "val = min(trainInputs)\r\n",
    "step = (max(trainInputs) - min(trainInputs)) / noOfPoints\r\n",
    "for i in range(1, noOfPoints):\r\n",
    "    xref.append(val)\r\n",
    "    val += step\r\n",
    "yref = [w0 + w1 * el for el in xref] \r\n",
    "plotData(trainInputs, trainOutputs, xref, yref, [], [], title = \"train data and model\")\r\n",
    "\r\n",
    "#makes predictions for test data\r\n",
    "# computedTestOutputs = [w0 + w1 * el for el in testInputs]\r\n",
    "#makes predictions for test data (by tool)\r\n",
    "computedValidationOutputs = regressor.predict([[x] for x in validationInputs])\r\n",
    "plotData([], [], validationInputs, computedValidationOutputs, validationInputs, validationOutputs, \"predictions vs real test data\")\r\n",
    "\r\n",
    "#compute the differences between the predictions and real outputs\r\n",
    "error = 0.0\r\n",
    "for t1, t2 in zip(computedValidationOutputs, validationOutputs):\r\n",
    "    error += (t1 - t2) ** 2\r\n",
    "error = error / len(validationOutputs)\r\n",
    "print(\"prediction error (manual): \", error)\r\n",
    "\r\n",
    "error = mean_squared_error(validationOutputs, computedValidationOutputs)\r\n",
    "print(\"prediction error (tool): \", error)\r\n"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "prediction error (manual):  0.41421204380267185\n",
      "prediction error (tool):  0.41421204380267185\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Tema "
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "**Ce îi poate face pe oameni fericiți?** \r\n",
    "Se consideră problema predicției gradului de fericire a populației globului folosind informații despre diferite caracteristici a bunăstării respectivei populații precum Produsul intern brut al țării în care locuiesc (gross domestic product – GBP), gradul de fericire, etc. \r\n",
    "\r\n",
    "Folsind datele aferente anului 2017 [link](https://www.kaggle.com/unsdsn/world-happiness#2017.csv), să se realizeze o predicție a gradului de fericire în funcție de Produsul intern brut si de gradul de libertate.\r\n",
    "\r\n",
    "Concret, trebuie rezolvata o problema de regresie bivariata $y = w_0 + w_1 * x_1 + w_2 * x_2$, unde \r\n",
    "- o variabila dependenta – $y$ (gradul de fericire)\r\n",
    "- 2 variabile independente – $x_1$ (PIB), $x_2$ (gradul de libertate).\r\n",
    "\r\n",
    "Se respecta aceeasi metodologie ca si la partea live/demo (doar ca trebuie sa se foloseasca 2 features). \r\n",
    "\r\n",
    "Algoritmul de regresie prin metoda celor mai mici patrate poate fi:\r\n",
    "\r\n",
    "- preluat dintr-un tool/API\r\n",
    "- dezvoltat pe cont propriu. "
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [],
   "metadata": {}
  }
 ]
}