Module 2 Exercise 5

module2/exo5/exo5_python_en.org

@@ -74,28 +74,43 @@ temperature (in Fahrenheit) and pressure (in psi), and finally the
 number of identified malfunctions.
 
 * Graphical inspection
-Flights without incidents do not provide any information
-on the influence of temperature or pressure on malfunction.
-We thus focus on the experiments in which at least one O-ring was defective.
+Flights without incidents do not provide any information on the influence of temperature or pressure on malfunction. We thus focus on the experiments in which at least one O-ring was defective.
 
+(Note: this approximation is not correct, as flights without incidents does provide information regarding the failure probability).
 #+begin_src python :results value :session *python* :exports both
-data = data[data.Malfunction>0]
+#data = data[data.Malfunction>0]
 data
 #+end_src
 
 #+RESULTS:
-:         Date  Count  Temperature  Pressure  Malfunction
-: 1   11/12/81      6           70        50            1
-: 8    2/03/84      6           57       200            1
-: 9    4/06/84      6           63       200            1
-: 10   8/30/84      6           70       200            1
-: 13   1/24/85      6           53       200            2
-: 20  10/30/85      6           75       200            2
-: 22   1/12/86      6           58       200            1
-
-We have a high temperature variability but
-the pressure is almost always 200, which should
-simplify the analysis.
+#+begin_example
+        Date  Count  Temperature  Pressure  Malfunction
+0    4/12/81      6           66        50            0
+1   11/12/81      6           70        50            1
+2    3/22/82      6           69        50            0
+3   11/11/82      6           68        50            0
+4    4/04/83      6           67        50            0
+5    6/18/82      6           72        50            0
+6    8/30/83      6           73       100            0
+7   11/28/83      6           70       100            0
+8    2/03/84      6           57       200            1
+9    4/06/84      6           63       200            1
+10   8/30/84      6           70       200            1
+11  10/05/84      6           78       200            0
+12  11/08/84      6           67       200            0
+13   1/24/85      6           53       200            2
+14   4/12/85      6           67       200            0
+15   4/29/85      6           75       200            0
+16   6/17/85      6           70       200            0
+17   7/29/85      6           81       200            0
+18   8/27/85      6           76       200            0
+19  10/03/85      6           79       200            0
+20  10/30/85      6           75       200            2
+21  11/26/85      6           76       200            0
+22   1/12/86      6           58       200            1
+#+end_example
+
+We have a high temperature variability but the pressure is almost always 200, which should simplify the analysis.
 
 How does the frequency of failure vary with temperature?
 #+begin_src python :results output file :var matplot_lib_filename="freq_temp_python.png" :exports both :session *python*
@@ -142,20 +157,21 @@ logmodel.summary()
 #+RESULTS:
 #+begin_example
                   Generalized Linear Model Regression Results                  
-==============================================================================
-Dep. Variable:              Frequency   No. Observations:                    7
-Model:                            GLM   Df Residuals:                        5
+===============================================================================
+Dep. Variable:               Frequency   No. Observations:                   23
+Model:                             GLM   Df Residuals:                       21
 Model Family:                 Binomial   Df Model:                            1
-Link Function:                  logit   Scale:                             1.0
-Method:                          IRLS   Log-Likelihood:                -3.6370
-Date:                Fri, 20 Jul 2018   Deviance:                       3.3763
-Time:                        16:56:08   Pearson chi2:                    0.236
-No. Iterations:                     5                                         
+Link Function:                   logit   Scale:                          1.0000
+Method:                           IRLS   Log-Likelihood:                -3.9210
+Date:              mer., 16 sept. 2020   Deviance:                       3.0144
+Time:                         00:01:54   Pearson chi2:                     5.00
+No. Iterations:                      6                                         
+Covariance Type:             nonrobust                                         
 ===============================================================================
                   coef    std err          z      P>|z|      [0.025      0.975]
 -------------------------------------------------------------------------------
-Intercept      -1.3895      7.828     -0.178      0.859     -16.732      13.953
-Temperature     0.0014      0.122      0.012      0.991      -0.238       0.240
+Intercept       5.0850      7.477      0.680      0.496      -9.570      19.740
+Temperature    -0.1156      0.115     -1.004      0.316      -0.341       0.110
 ===============================================================================
 #+end_example