small.csvX1,X2,YS,-0.1,19.19S,2.53,22.74S,4.86,23.91M,0.26,7.07M,2.55,7.93M,4.87,8.93L,0.08,20.63L,2...

Question

small.csvX1,X2,YS,-0.1,19.19S,2.53,22.74S,4.86,23.91M,0.26,7.07M,2.55,7.93M,4.87,8.93L,0.08,20.63L,2.62,23.46L,5.09,25.75__MACOSX/._small.csvpart2.csvMonth,Year,salesJanuary,2012,Feuary,2012,March,2012,April,2012,May,2012,June,2012,July,2012,August,2012,September,2012,1.71October,2012,1.9November,2012,2.74December,2012,4.2January,2013,1.45Feuary,2013,1.8March,2013,2.03April,2013,1.99May,2013,2.32June,2013,2.2July,2013,2.13August,2013,2.43September,2013,1.9October,2013,2.13November,2013,2.56December,2013,4.16January,2014,2.31Feuary,2014,1.89March,2014,2.02April,2014,2.23May,2014,2.39June,2014,2.14July,2014,2.27August,2014,2.21September,2014,1.89October,2014,2.29November,2014,2.83December,2014,4.04January,2015,2.31Feuary,2015,1.99March,2015,2.42April,2015,2.45May,2015,2.57June,2015,2.42July,2015,2.4August,2015,2.5September,2015,2.09October,2015,2.54November,2015,2.97December,2015,4.35January,2016,2.56Feuary,2016,2.28March,2016,2.69April,2016,2.48May,2016,2.73June,2016,2.37July,2016,2.31August,2016,2.23September,2016,October,2016,November,2016,December,2016,__MACOSX/._part2.csvcategoricals.pptxCATEGORICAL VARIABLES-ENCODING-1We will use data visualization To understand the results of regression models with a categorical variableAnd to show the model performanceEXAMPLESExample 1EXAMPLESConsider the following datasetNumerical Categorical Predictors – EXAMPLE        X1        X2        Y        S        -0.10        19.19        S        2.53        22.74        S        4.86        23.91        M        0.26        7.07        M        2.55        7.93        M        4.87        8.93        L        0.08        20.63        L        2.62        23.46        L        5.09        25.75Increase size of table numbers4Consider the following dataset         XXXXXXXXXXLABEL ENCODING        X1        X2        Y        S        -0.10        19.19        S        2.53        22.74        S        4.86        23.91        M        0.26        7.07        M        2.55        7.93        M        4.87        8.93        L        0.08        20.63        L        2.62        23.46        L        5.09        25.75        X1        X2        Y        0        -0.10        19.19        0        2.53        22.74        0        4.86        23.91        1        0.26        7.07        1        2.55        7.93        1        4.87        8.93        2        0.08        20.63        2        2.62        23.46        2        5.09        25.75Numerical Categorical Predictors – EXAMPLE5X1 and X2 in the model as continuous variablesR2 is close to 0.05, the explained variation of the response about the fitted equation is negligibleThe Adjusted R-squared is negative and equal to XXXXXXXXXXBoth predictors X1 and X2 seem not to be useful for predicting Y.Coefficients:          Estimate Std. Eor t value Pr(>|t|)(Intercept XXXXXXXXXX XXXXXXXXXX037 *x XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXx XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX Residual standard eor: 8.505 on 6 degrees of freedomMultiple R-squared: XXXXXXXXXX,   Adjusted R-squared: XXXXXXXXXXF-statistic: XXXXXXXXXXon 2 and 6 DF,  p-value: 0.8504Numerical Categorical Predictors – EXAMPLEX1 and X2 in the model as continuous variablesCoefficients:          Estimate Std. Eor t value Pr(>|t|)(Intercept XXXXXXXXXX XXXXXXXXXX037 *x XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXx XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX Residual standard eor: 8.505 on 6 degrees of freedomMultiple R-squared: XXXXXXXXXX,   Adjusted R-squared: XXXXXXXXXXF-statistic: XXXXXXXXXXon 2 and 6 DF,  p-value: 0.8504Numerical Categorical Predictors – EXAMPLE7X1 and X2 in the model as continuous variablesCoefficients:          Estimate Std. Eor t value Pr(>|t|)(Intercept XXXXXXXXXX XXXXXXXXXX037 *x XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXx XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX Residual standard eor: 8.505 on 6 degrees of freedomMultiple R-squared: XXXXXXXXXX,   Adjusted R-squared: XXXXXXXXXXF-statistic: XXXXXXXXXXon 2 and 6 DF,  p-value: 0.8504Numerical Categorical Predictors – EXAMPLE8The fitted plane is0.7769 X2Numerical Categorical Predictors – EXAMPLEReplace X1 with binary variables X11 and X12      XXXXXXXXXXONE-HOT ENCODING        X11        X12        X2        Y        0        0        -0.10        19.19        0        0        2.53        22.74        0        0        4.86        23.91        1        0        0.26        7.07        1        0        2.55        7.93        1        0        4.87        8.93        0        1        0.08        20.63        0        1        2.62        23.46        0        1        5.09        25.75        X1        X2        Y        S        -0.10        19.19        S        2.53        22.74        S        4.86        23.91        M        0.26        7.07        M        2.55        7.93        M        4.87        8.93        L        0.08        20.63        L        2.62        23.46        L        5.09        25.75Numerical Categorical Predictors – EXAMPLE10.Coefficients:          Estimate Std. Eor t value Pr(>|t|)(Intercept XXXXXXXXXX XXXXXXXXXX90e-07 ***x XXXXXXXXXX XXXXXXXXXX4.54e-06 ***x XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXx XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX **Residual standard eor: XXXXXXXXXXon 5 degrees of freedomMultiple R-squared: XXXXXXXXXX,   Adjusted R-squared: XXXXXXXXXXF-statistic: 225 on 3 and 5 DF,  p-value: 9.416e-06Numerical Categorical Predictors – EXAMPLECoefficients:          Estimate Std. Eor t value Pr(>|t|)(Intercept XXXXXXXXXX XXXXXXXXXX90e-07 ***x XXXXXXXXXX XXXXXXXXXX4.54e-06 ***x XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXx XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX **Residual standard eor: XXXXXXXXXXon 5 degrees of freedomMultiple R-squared: XXXXXXXXXX,   Adjusted R-squared: XXXXXXXXXXF-statistic: 225 on 3 and 5 DF,  p-value: 9.416e-06Numerical Categorical Predictors – EXAMPLEThe fitted equations for each level areNumerical Categorical Predictors – EXAMPLEWhat encoding is better?Numerical Categorical Predictors – EXAMPLE     XXXXXXXXXXLABEL ENCODING                    XXXXXXXXXXONE-HOT ENCODING        X11        X12        X2        Y        0        0        -0.10        19.19        0        0        2.53        22.74        0        0        4.86        23.91        1        0        0.26        7.07        1        0        2.55        7.93        1        0        4.87        8.93        0        1        0.08        20.63        0        1        2.62        23.46        0        1        5.09        25.75        X1        X2        Y        0        -0.10        19.19        0        2.53        22.74        0        4.86        23.91        1        0.26        7.07        1        2.55        7.93        1        4.87        8.93        2        0.08        20.63        2        2.62        23.46        2        5.09        25.75Numerical Categorical Predictors – EXAMPLE15                  LABEL             ONE-HOT                     ENCODING        ENCODINGR-squared            0.05259        0.9926Adjusted R-squared: XXXXXXXXXX        0.9882Numerical Categorical Predictors – EXAMPLE16Why are the models different?Numerical Categorical Predictors – EXAMPLELabel encoding prediction equation 0.7769 X2One-hot encoding prediction equationsNumerical Categorical Predictors – EXAMPLElabel encoding results in a regression planeone-hot encoding results in a set of regression lines (one for each category of the categorical variable)Numerical Categorical Predictors – EXAMPLEIf the observations are close to a plane then label encoding and one-hot encoding results are goodNumerical Categorical Predictors – EXAMPLEWith a large number of variables in the model it is not possible to have a display like thisWe may relay on R2 or cross-validation eor to choose the best modelNumerical Categorical Predictors – EXAMPLEExample 2ForecastingConsider the following demand dataEXAMPLE 2Increase size of table numbers23Consider the following demand dataEXAMPLE 2Increase size of table numbers24Wide format to long formatEXAMPLE 2Increase size of table numbers25Model 1Linear RegressionUse linear regression                predict sales using time as predictoEXAMPLE 2Increase size of table numbers27EXAMPLE 2 – LINEAR REGRESION MODEL 1Increase size of table numbers28        sales vs PeriodEXAMPLE 2 – LINEAR REGRESION MODEL 1Increase size of table numbers29Model 2Categorical variableand label encodingpredict sales using Year and MonthEXAMPLE 2 – MODEL 2Increase size of table numbers31predict sales using Year and Monthlabel encode MonthEXAMPLE 2 – MODEL 2Increase size of table numbers32predict sales using Year and Monthlabel encode MonthEXAMPLE 2 – MODEL 2Increase size of table numbers33predict sales using Year and Monthlabel encode MonthEXAMPLE 2 – MODEL 2Increase size of table numbers34predict sales using Year and Monthlabel encode Monthmodel sales using Year and Period         XXXXXXXXXXboth numeric)EXAMPLE 2 – MODEL 2Increase size of table numbers35EXAMPLE 2 – MODEL 2Increase size of table numbers36          sales vs Year and PeriodEXAMPLE 2 – MODEL 2Increase size of table numbers37Model 3Categorical variableand one-hot encodingpredict sales using Year and Monthone-hot encode MonthEXAMPLE 2 – MODEL 3Increase size of table numbers39EXAMPLE 2 – MODEL 3Increase size of table numbers40    sales vs Year and MonthEXAMPLE 2 – MODEL 3Increase size of table numbers41__MACOSX/._categoricals.pptxDay 6.docxDay 6: Assignment Submit Assignment· Submitting a file upload· File Types pdf, doc, and docxInstructionsWrite and run the code developed in class to predict the total sales from file sales.csvand submit the jupyter notebook in pdf format.SubmissionClick on the blue button in the top right corner to submit your assignment.  Click Next (below) to progress through the course.RuicAssignment Ruic        Assignment Ruic        Criteria        Ratings        Pts        This criterion is linked to a Learning OutcomeCoding                60.0 to >30.0 ptsFull MarksNo coding eors        30.0 to >20.0 ptsNo MarksMore than three coding eors        20.0 to >0 ptsPartial MarksOne to three coding eors        60.0 pts        This criterion is linked to a Learning OutcomeFormat & Editing                40.0 to >20.0 ptsFull MarksCode is clear and easy to follow. Plots display effective visualization.

Kshitij · Accepted Answer

day-6archive-qu3zg0my-gk010hyi/.ipynb_checkpoints/Day6-checkpoint.ipynb
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    "# importing libraires 
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    "import pandas as pd
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    "import numpy as np
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    "from matplotlib import pyplot as plt"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1"
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       "  X1    X2      Y
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       "0  S -0.10  19.19
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       "1  S  2.53  22.74
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       "2  S  4.86  23.91
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       "3  M  0.26   7.07
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       "4  M  2.55   7.93"
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     "execution_count": 2,
     "metadata": {},
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   "source": [
    "#loading small data
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    "df = pd.read_csv('small.csv')
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    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "# loading the statsmodel library 
",
    "import statsmodels.formula.api as smf
",
    "import statsmodels.api as sm
",
    "from sklearn.preprocessing import LabelEncoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sklearn's label encoder
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    "labelencoder = LabelEncoder()"
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       "   X1    X2      Y
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       "0   2 -0.10  19.19
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       "2   2  4.86  23.91
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       "3   1  0.26   7.07
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    "# encoding of labels
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    "df['X1'] = labelencoder.fit_transform(df['X1'])
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    "df"
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   "execution_count": 6,
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    "X = df[['X1', 'X2']] 
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    "y = df['Y']"
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     "text": [
      "c:\users\kaush\appdata\local\programs\python\python36\lib\site-packages\numpy\core\fromnumeric.py:2542: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.
",
      "  return ptp(axis=axis, out=out, **kwargs)
",
      "c:\users\kaush\appdata\local\programs\python\python36\lib\site-packages\scipy\stats\stats.py:1535: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=9
",
      "  "anyway, n=%i" % int(n))
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       "
",
       "OLS Regression Results
",
       "
",
       "  Dep. Variable:            Y          R-squared:             0.053
",
       "
",
       "
",
       "  Model:                   OLS         Adj. R-squared:       -0.263
",
       "
",
       "
",
       "  Method:             Least Squares    F-statistic:          0.1665
",
       "
",
       "
",
       "  Date:             Thu, 28 May 2020   Prob (F-statistic):   0.850 
",
       "
",
       "
",
       "  Time:                 05:12:53       Log-Likelihood:      -30.212
",
       "
",
       "
",
       "  No. Observations:           9        AIC:                   66.42
",
       "
",
       "
",
       "  Df Residuals:               6        BIC:                   67.02
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       "
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       "
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       "  Df Model:                   2                                    
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       "
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       "
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       "  Covariance Type:      nonrobust                                  
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       "
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       "
",
       "           coef     std err      t      P>|t|  [0.025    0.975]  
",
       "
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       "
",
       "  const    16.3716     5.831     2.808  0.031     2.104    30.639
",
       "
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       "
",
       "  X1       -0.6019     3.474    -0.173  0.868    -9.103     7.899
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       "
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       "
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       "  X2        0.7769     1.428     0.544  0.606    -2.716     4.270
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       "
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       "
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       "
",
       "  Omnibus:        3.603   Durbin-Watson:         0.961
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       "
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       "
",
       "  Prob(Omnibus):  0.165   Jarque-Bera (JB):      1.553
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       "
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       "
",
       "  Skew:          -0.704   Prob(JB):              0.460
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       "
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       "
",
       "  Kurtosis:       1.530   Cond. No.               7.65
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       "
",
       "Warnings:[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
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       """"
",
       "                            OLS Regression Results                            
",
       "==============================================================================
",
       "Dep. Variable:                      Y   R-squared:                       0.053
",
       "Model:                            OLS   Adj. R-squared:                 -0.263
",
       "Method:                 Least Squares   F-statistic:                    0.1665
",
       "Date:                Thu, 28 May 2020   Prob (F-statistic):              0.850
",
       "Time:                        05:12:53   Log-Likelihood:                -30.212
",
       "No. Observations:                   9   AIC:                             66.42
",
       "Df Residuals:                       6   BIC:                             67.02
",
       "Df Model:                           2                                         
",
       "Covariance Type:            nonrobust                                         
",
       "==============================================================================
",
       "                 coef    std err          t      P>|t|      [0.025      0.975]
",
       "------------------------------------------------------------------------------
",
       "const         16.3716      5.831      2.808      0.031       2.104      30.639
",
       "X1            -0.6019      3.474     -0.173      0.868      -9.103       7.899
",
       "X2             0.7769      1.428      0.544      0.606      -2.716       4.270
",
       "==============================================================================
",
       "Omnibus:                        3.603   Durbin-Watson:                   0.961
",
       "Prob(Omnibus):                  0.165   Jarque-Bera (JB):                1.553
",
       "Skew:                          -0.704   Prob(JB):                        0.460
",
       "Kurtosis:                       1.530   Cond. No.                         7.65
",
       "==============================================================================
",
       "
",
       "Warnings:
",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
",
       """""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# fitting our model and printing the summery.
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    "X = sm.add_constant(X)
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    "model = sm.OLS(y, X).fit()
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    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# part 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# one hot coding for our labels
",
    "df = pd.concat([df,pd.get_dummies(df['X1'], prefix='X1',drop_first=True)],axis=1).drop(['X1'],axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
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       "        text-align: right;
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       "    }
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       "
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       "
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       "  
",
       "    
",
       "      
",
       "      X2
",
       "      Y
",
       "      X1_1
",
       "      X1_2
",
       "    
",
       "  
",
       "  
",
       "    
",
       "      0
",
       "      -0.10
",
       "      19.19
",
       "      0
",
       "      1
",
       "    
",
       "    
",
       "      1
",
       "      2.53
",
       "      22.74
",
       "      0
",
       "      1
",
       "    
",
       "    
",
       "      2
",
       "      4.86
",
       "      23.91
",
       "      0
",
       "      1
",
       "    
",
       "    
",
       "      3
",
       "      0.26
",
       "      7.07
",
       "      1
",
       "      0
",
       "    
",
       "    
",
       "      4
",
       "      2.55
",
       "      7.93
",
       "      1
",
       "      0
",
       "    
",
       "    
",
       "      5
",
       "      4.87
",
       "      8.93
",
       "      1
",
       "      0
",
       "    
",
       "    
",
       "      6
",
       "      0.08
",
       "      20.63
",
       "      0
",
       "      0
",
       "    
",
       "    
",
       "      7
",
       "      2.62
",
       "      23.46
",
       "      0
",
       "      0
",
       "    
",
       "    
",
       "      8
",
       "      5.09
",
       "      25.75
",
       "      0
",
       "      0
",
       "    
",
       "  
",
       "
",
       ""
      ],
      "text/plain": [
       "     X2      Y  X1_1  X1_2
",
       "0 -0.10  19.19     0     1
",
       "1  2.53  22.74     0     1
",
       "2  4.86  23.91     0     1
",
       "3  0.26   7.07     1     0
",
       "4  2.55   7.93     1     0
",
       "5  4.87   8.93     1     0
",
       "6  0.08  20.63     0     0
",
       "7  2.62  23.46     0     0
",
       "8  5.09  25.75     0     0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[['X1_1', 'X1_2','X2']] 
",
    "y = df['Y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "
",
       "OLS Regression Results
",
       "
",
       "  Dep. Variable:            Y          R-squared:             0.993
",
       "
",
       "
",
       "  Model:                   OLS         Adj. R-squared:        0.988
",
       "
",
       "
",
       "  Method:             Least Squares    F-statistic:           225.0
",
       "
",
       "
",
       "  Date:             Thu, 28 May 2020   Prob (F-statistic): 9.42e-06
",
       "
",
       "
",
       "  Time:                 05:12:53       Log-Likelihood:      -8.3472
",
       "
",
       "
",
       "  No. Observations:           9        AIC:                   24.69
",
       "
",
       "
",
       "  Df Residuals:               5        BIC:                   25.48
",
       "
",
       "
",
       "  Df Model:                   3                                    
",
       "
",
       "
",
       "  Covariance Type:      nonrobust                                  
",
       "
",
       "
",
       "
",
       "
",
       "           coef     std err      t      P>|t|  [0.025    0.975]  
",
       "
",
       "
",
       "  const    21.1624     0.594    35.645  0.000    19.636    22.689
",
       "
",
       "
",
       "  X1_1    -15.2734     0.670   -22.792  0.000   -16.996   -13.551
",
       "
",
       "
",
       "  X1_2     -1.1974     0.671    -1.786  0.134    -2.921     0.526
",
       "
",
       "
",
       "  X2        0.8155     0.138     5.920  0.002     0.461     1.170
",
       "
",
       "
",
       "
",
       "
",
       "  Omnibus:        0.672   Durbin-Watson:         1.798
",
       "
",
       "
",
       "  Prob(Omnibus):  0.715   Jarque-Bera (JB):      0.529
",
       "
",
       "
",
       "  Skew:           0.003   Prob(JB):              0.768
",
       "
",
       "
",
       "  Kurtosis:       1.812   Cond. No.               11.4
",
       "
",
       "Warnings:[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "
",
       """"
",
       "                            OLS Regression Results                            
",
       "==============================================================================
",
       "Dep. Variable:                      Y   R-squared:                       0.993
",
       "Model:                            OLS   Adj. R-squared:                  0.988
",
       "Method:                 Least Squares   F-statistic:                     225.0
",
       "Date:                Thu, 28 May 2020   Prob (F-statistic):           9.42e-06
",
       "Time:                        05:12:53   Log-Likelihood:                -8.3472
",
       "No. Observations:                   9   AIC:                             24.69
",
       "Df Residuals:                       5   BIC:                             25.48
",
       "Df Model:                           3                                         
",
       "Covariance Type:            nonrobust                                         
",
       "==============================================================================
",
       "                 coef    std err          t      P>|t|      [0.025      0.975]
",
       "------------------------------------------------------------------------------
",
       "const         21.1624      0.594     35.645      0.000      19.636      22.689
",
       "X1_1         -15.2734      0.670    -22.792      0.000     -16.996     -13.551
",
       "X1_2          -1.1974      0.671     -1.786      0.134      -2.921       0.526
",
       "X2             0.8155      0.138      5.920      0.002       0.461       1.170
",
       "==============================================================================
",
       "Omnibus:                        0.672   Durbin-Watson:                   1.798
",
       "Prob(Omnibus):                  0.715   Jarque-Bera (JB):                0.529
",
       "Skew:                           0.003   Prob(JB):                        0.768
",
       "Kurtosis:                       1.812   Cond. No.                         11.4
",
       "==============================================================================
",
       "
",
       "Warnings:
",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
",
       """""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# again fiting data but with one hot coded labels
",
    "X = sm.add_constant(X)
",
    "model2 = sm.OLS(y, X).fit()
",
    "model2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "
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       "
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       "  
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       "    
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       "      
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       "      Month
",
       "      Year
",
       "      sales
",
       "    
",
       "  
",
       "  
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       "    
",
       "      0
",
       "      January
",
       "      2012
",
       "      NaN
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       "    
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       "    
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       "      1
",
       "      February
",
       "      2012
",
       "      NaN
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       "    
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       "    
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       "      2
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       "      March
",
       "      2012
",
       "      NaN
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       "    
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       "      3
",
       "      April
",
       "      2012
",
       "      NaN
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       "    
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       "    
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       "      4
",
       "      May
",
       "      2012
",
       "      NaN
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       "    
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       "  
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       "
",
       ""
      ],
      "text/plain": [
       "      Month  Year  sales
",
       "0   January  2012    NaN
",
       "1  February  2012    NaN
",
       "2     March  2012    NaN
",
       "3     April  2012    NaN
",
       "4       May  2012    NaN"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# loading data for second part
",
    "df = pd.read_csv('part2.csv')
",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "# gnearting period data 
",
    "k=list(range(1, len(df.Month)+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  
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       "      
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       "      Month
",
       "      Year
",
       "      sales
",
       "      Period
",
       "    
",
       "  
",
       "  
",
       "    
",
       "      0
",
       "      January
",
       "      2012
",
       "      NaN
",
       "      1
",
       "    
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       "    
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       "      1
",
       "      February
",
       "      2012
",
       "      NaN
",
       "      2
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       "    
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       "    
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       "      2
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       "      March
",
       "      2012
",
       "      NaN
",
       "      3
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       "    
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       "    
",
       "      3
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       "      April
",
       "      2012
",
       "      NaN
",
       "      4
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       "      4
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       "      May
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       "      2012
",
       "      NaN
",
       "      5
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       "  
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       ""
      ],
      "text/plain": [
       "      Month  Year  sales  Period
",
       "0   January  2012    NaN       1
",
       "1  February  2012    NaN       2
",
       "2     March  2012    NaN       3
",
       "3     April  2012    NaN       4
",
       "4       May  2012    NaN       5"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df["Period"]=k
",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "# formulating our model based on data frame column names 
",
    "mod = smf.ols(formula='sales ~ Period', data=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fitting our model
",
    "res = mod.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "
",
       "OLS Regression Results
",
       "
",
       "  Dep. Variable:          sales        R-squared:             0.044
",
       "
",
       "
",
       "  Model:                   OLS         Adj. R-squared:        0.023
",
       "
",
       "
",
       "  Method:             Least Squares    F-statistic:           2.121
",
       "
",
       "
",
       "  Date:             Thu, 28 May 2020   Prob (F-statistic):   0.152 
",
       "
",
       "
",
       "  Time:                 05:32:38       Log-Likelihood:      -42.960
",
       "
",
       "
",
       "  No. Observations:          48        AIC:                   89.92
",
       "
",
       "
",
       "  Df Residuals:              46        BIC:                   93.66
",
       "
",
       "
",
       "  Df Model:                   1                                    
",
       "
",
       "
",
       "  Covariance Type:      nonrobust                                  
",
       "
",
       "
",
       "
",
       "
",
       "               coef     std err      t      P>|t|  [0.025    0.975]  
",
       "
",
       "
",
       "  Intercept     2.1355     0.223     9.590  0.000     1.687     2.584
",
       "
",
       "
",
       "  Period        0.0092     0.006     1.456  0.152    -0.004     0.022
",
       "
",
       "
",
       "
",
       "
",
       "  Omnibus:       34.103   Durbin-Watson:         1.733
",
       "
",
       "
",
       "  Prob(Omnibus):  0.000   Jarque-Bera (JB):     71.518
",
       "
",
       "
",
       "  Skew:           2.147   Prob(JB):           2.95e-16
",
       "
",
       "
",
       "  Kurtosis:       7.161   Cond. No.               90.2
",
       "
",
       "Warnings:[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "
",
       """"
",
       "                            OLS Regression Results                            
",
       "==============================================================================
",
       "Dep. Variable:                  sales   R-squared:                       0.044
",
       "Model:                            OLS   Adj. R-squared:                  0.023
",
       "Method:                 Least Squares   F-statistic:                     2.121
",
       "Date:                Thu, 28 May 2020   Prob (F-statistic):              0.152
",
       "Time:                        05:32:38   Log-Likelihood:                -42.960
",
       "No. Observations:                  48   AIC:                             89.92
",
       "Df Residuals:                      46   BIC:                             93.66
",
       "Df Model:                           1                                         
",
       "Covariance Type:            nonrobust                                         
",
       "==============================================================================
",
       "                 coef    std err          t      P>|t|      [0.025      0.975]
",
       "------------------------------------------------------------------------------
",
       "Intercept      2.1355      0.223      9.590      0.000       1.687       2.584
",
       "Period         0.0092      0.006      1.456      0.152      -0.004       0.022
",
       "==============================================================================
",
       "Omnibus:                       34.103   Durbin-Watson:                   1.733
",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               71.518
",
       "Skew:                           2.147   Prob(JB):                     2.95e-16
",
       "Kurtosis:                       7.161   Cond. No.                         90.2
",
       "==============================================================================
",
       "
",
       "Warnings:
",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
",
       """""
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# summery
",
    "res.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "# predicting our sales based on period
",
    "prediction = res.predict(df['Period'])
",
    "df['Prediction']=prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
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       "    
",
       "  
",
       "  
",
       "    
",
       "      0
",
       "      January
",
       "      2012
",
       "      NaN
",
       "      1
",
       "      2.144635
",
       "    
",
       "    
",
       "      1
",
       "      February
",
       "      2012
",
       "      NaN
",
       "      2
",
       "      2.153814
",
       "    
",
       "    
",
       "      2
",
       "      March
",
       "      2012
",
       "      NaN
",
       "      3
",
       "      2.162992
",
       "    
",
       "    
",
       "      3
",
       "      April
",
       "      2012
",
       "      NaN
",
       "      4
",
       "      2.172170
",
       "    
",
       "    
",
       "      4
",
       "      May
",
       "      2012
",
       "      NaN
",
       "      5
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       "      2.181348
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       "    
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       "  
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       "
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       ""
      ],
      "text/plain": [
       "      Month  Year  sales  Period  Prediction
",
       "0   January  2012    NaN       1    2.144635
",
       "1  February  2012    NaN       2    2.153814
",
       "2     March  2012    NaN       3    2.162992
",
       "3     April  2012    NaN       4    2.172170
",
       "4       May  2012    NaN       5    2.181348"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ""
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     "execution_count": 74,
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
",
      "text/plain": [
       ""
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ploting the prediction and sales with respect to year. 
",
    "df.plot(x='Year', y=['sales', 'Prediction'], figsize=(10,5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# model using year and period "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "# now formulating our model on period and year as predictors and sales as target
",
    "mod = smf.ols(formula='sales ~ Period + Year', data=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fitting our model
",
    "res = mod.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "
",
       "OLS Regression Results
",
       "
",
       "  Dep. Variable:          sales        R-squared:             0.343
",
       "
",
       "
",
       "  Model:                   OLS         Adj. R-squared:        0.314
",
       "
",
       "
",
       "  Method:             Least Squares    F-statistic:           11.75
",
       "
",
       "
",
       "  Date:             Thu, 28 May 2020   Prob (F-statistic): 7.86e-05
",
       "
",
       "
",
       "  Time:                 05:42:34       Log-Likelihood:      -33.960
",
       "
",
       "
",
       "  No. Observations:          48        AIC:                   73.92
",
       "
",
       "
",
       "  Df Residuals:              45        BIC:                   79.53
",
       "
",
       "
",
       "  Df Model:                   2                                    
",
       "
",
       "
",
       "  Covariance Type:      nonrobust                                  
",
       "
",
       "
",
       "
",
       "
",
       "               coef     std err      t      P>|t|  [0.025    0.975]  
",
       "
",
       "
",
       "  Intercept  2325.9544   513.588     4.529  0.000  1291.534  3360.374
",
       "
",
       "
",
       "  Period        0.1075     0.022     4.807  0.000     0.062     0.153
",
       "
",
       "
",
       "  Year         -1.1553     0.255    -4.525  0.000    -1.670    -0.641
",
       "
",
       "
",
       "
",
       "
",
       "  Omnibus:       12.873   Durbin-Watson:         1.313
",
       "
",
       "
",
       "  Prob(Omnibus):  0.002   Jarque-Bera (JB):     13.627
",
       "
",
       "
",
       "  Skew:           1.076   Prob(JB):            0.00110
",
       "
",
       "
",
       "  Kurtosis:       4.478   Cond. No.           1.41e+07
",
       "
",
       "Warnings:[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.[2] The condition number is large, 1.41e+07. This might indicate that there arestrong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "
",
       """"
",
       "                            OLS Regression Results                            
",
       "==============================================================================
",
       "Dep. Variable:                  sales   R-squared:                       0.343
",
       "Model:                            OLS   Adj. R-squared:                  0.314
",
       "Method:                 Least Squares   F-statistic:                     11.75
",
       "Date:                Thu, 28 May 2020   Prob (F-statistic):           7.86e-05
",
       "Time:                        05:42:34   Log-Likelihood:                -33.960
",
       "No. Observations:                  48   AIC:                             73.92
",
       "Df Residuals:                      45   BIC:                             79.53
",
       "Df Model:                           2                                         
",
       "Covariance Type:            nonrobust                                         
",
       "==============================================================================
",
       "                 coef    std err          t      P>|t|      [0.025      0.975]
",
       "------------------------------------------------------------------------------
",
       "Intercept   2325.9544    513.588      4.529      0.000    1291.534    3360.374
",
       "Period         0.1075      0.022      4.807      0.000       0.062       0.153
",
       "Year          -1.1553      0.255     -4.525      0.000      -1.670      -0.641
",
       "==============================================================================
",
       "Omnibus:                       12.873   Durbin-Watson:                   1.313
",
       "Prob(Omnibus):                  0.002   Jarque-Bera (JB):               13.627
",
       "Skew:                           1.076   Prob(JB):                      0.00110
",
       "Kurtosis:                       4.478   Cond. No.                     1.41e+07
",
       "==============================================================================
",
       "
",
       "Warnings:
",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
",
       "[2] The condition number is large, 1.41e+07. This might indicate that there are
",
       "strong multicollinearity or other numerical problems.
",
       """""
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# summery
",
    "res.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "# predicting the sales based on period and year. 
",
    "prediction2 = res.predict(df[['Period','Year']])
",
    "df['Prediction2']=prediction2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      Prediction2
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       "    
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       "  
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       "      1.550586
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       "      NaN
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",
       "      2.162992
",
       "      1.765593
",
       "    
",
       "    
",
       "      3
",
       "      April
",
       "      2012
",
       "      NaN
",
       "      4
",
       "      2.172170
",
       "      1.873097
",
       "    
",
       "    
",
       "      4
",
       "      May
",
       "      2012
",
       "      NaN
",
       "      5
",
       "      2.181348
",
       "      1.980600
",
       "    
",
       "  
",
       "
",
       ""
      ],
      "text/plain": [
       "      Month  Year  sales  Period  Prediction  Prediction2
",
       "0   January  2012    NaN       1    2.144635     1.550586
",
       "1  February  2012    NaN       2    2.153814     1.658089
",
       "2     March  2012    NaN       3    2.162992     1.765593
",
       "3     April  2012    NaN       4    2.172170     1.873097
",
       "4       May  2012    NaN       5    2.181348     1.980600"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ""
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png":

small.csv X1,X2,Y S,-0.1,19.19 S,2.53,22.74 S,4.86,23.91 M,0.26,7.07 M,2.55,7.93 M,4.87,8.93 L,0.08,20.63 L,2.62,23.46 L,5.09,25.75 __MACOSX/._small.csv part2.csv Month,Year,sales January,2012,...

Solution