diff --git a/module2/exo5/exo5_python_en.org b/module2/exo5/exo5_python_en.org index 39a203bed10eed51f00f5222dee62329bf13ec72..abae0f131707ed7212b3aa180331e4f7b11f1eab 100644 --- a/module2/exo5/exo5_python_en.org +++ b/module2/exo5/exo5_python_en.org @@ -42,30 +42,30 @@ data #+RESULTS: #+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 + 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 The data set shows us the date of each test, the number of O-rings @@ -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* @@ -141,21 +156,22 @@ logmodel.summary() #+RESULTS: #+begin_example - Generalized Linear Model Regression Results -============================================================================== -Dep. Variable: Frequency No. Observations: 7 -Model: GLM Df Residuals: 5 -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 + Generalized Linear Model Regression Results +=============================================================================== +Dep. Variable: Frequency No. Observations: 23 +Model: GLM Df Residuals: 21 +Model Family: Binomial Df Model: 1 +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 diff --git a/module2/exo5/freq_temp_python.png b/module2/exo5/freq_temp_python.png index 93cb9e626441d23f6dff59ed252d7b14eb37abdb..b8104a660edea589efb8d667808c638292ac1641 100644 Binary files a/module2/exo5/freq_temp_python.png and b/module2/exo5/freq_temp_python.png differ diff --git a/module2/exo5/proba_estimate_python.png b/module2/exo5/proba_estimate_python.png index 77fc4b275dd8815b1ab91cd3b67b1beb93e00748..80dd87da41652c72e18af352484a1d809f7d2623 100644 Binary files a/module2/exo5/proba_estimate_python.png and b/module2/exo5/proba_estimate_python.png differ