updated relationship-between-coefficient-of-determination-and-pearson…

…-correlation-coefficient.ipynb
zyxue · Jan 3, 2021 · a845977 · a845977
1 parent 542927a
commit a845977
Showing 1 changed file with 21 additions and 26 deletions.
diff --git a/...lationship-between-coefficient-of-determination-and-pearson-correlation-coefficient.ipynb b/...lationship-between-coefficient-of-determination-and-pearson-correlation-coefficient.ipynb
@@ -10,7 +10,9 @@
     "import matplotlib.pyplot as plt\n",
     "import pandas as pd\n",
     "import statsmodels.api as sm\n",
-    "import statsmodels.formula.api as smf"
+    "import statsmodels.formula.api as smf\n",
+    "\n",
+    "np.random.seed(123)"
    ]
   },
   {
@@ -45,7 +47,7 @@
     {
      "data": {
       "text/plain": [
-       "<matplotlib.axes._subplots.AxesSubplot at 0x11e4cda30>"
+       "<AxesSubplot:xlabel='x', ylabel='y'>"
       ]
      },
      "execution_count": 4,
@@ -54,7 +56,7 @@
     },
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -123,12 +125,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "var_y=59.17, var_y_hat=58.53, r_squared=0.9892, 0.9892\n"
+      "var_y=47.42, var_y_hat=46.22, r_squared=0.9747, ρ_squared=0.9747\n"
      ]
     }
    ],
    "source": [
-    "print(f'{var_y=:.2f}, {var_y_hat=:.2f}, {r_squared=:.4f}, {ρ_squared:.4f}')"
+    "print(f'{var_y=:.2f}, {var_y_hat=:.2f}, {r_squared=:.4f}, {ρ_squared=:.4f}')"
    ]
   },
   {
@@ -176,25 +178,25 @@
      "text": [
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
-      "Dep. Variable:                      y   R-squared:                       0.989\n",
-      "Model:                            OLS   Adj. R-squared:                  0.989\n",
-      "Method:                 Least Squares   F-statistic:                     1644.\n",
-      "Date:                Sun, 15 Mar 2020   Prob (F-statistic):           3.82e-19\n",
-      "Time:                        11:55:29   Log-Likelihood:                -23.929\n",
-      "No. Observations:                  20   AIC:                             51.86\n",
-      "Df Residuals:                      18   BIC:                             53.85\n",
+      "Dep. Variable:                      y   R-squared:                       0.975\n",
+      "Model:                            OLS   Adj. R-squared:                  0.973\n",
+      "Method:                 Least Squares   F-statistic:                     693.1\n",
+      "Date:                Sat, 02 Jan 2021   Prob (F-statistic):           8.00e-16\n",
+      "Time:                        20:57:08   Log-Likelihood:                -30.204\n",
+      "No. Observations:                  20   AIC:                             64.41\n",
+      "Df Residuals:                      18   BIC:                             66.40\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
-      "Intercept      0.8229      0.438      1.878      0.077      -0.097       1.743\n",
-      "x              2.8368      0.070     40.547      0.000       2.690       2.984\n",
+      "Intercept     -0.1367      0.602     -0.227      0.823      -1.401       1.128\n",
+      "x              2.9906      0.114     26.327      0.000       2.752       3.229\n",
       "==============================================================================\n",
-      "Omnibus:                        0.529   Durbin-Watson:                   2.322\n",
-      "Prob(Omnibus):                  0.767   Jarque-Bera (JB):                0.624\n",
-      "Skew:                          -0.261   Prob(JB):                        0.732\n",
-      "Kurtosis:                       2.310   Cond. No.                         14.8\n",
+      "Omnibus:                        1.344   Durbin-Watson:                   1.699\n",
+      "Prob(Omnibus):                  0.511   Jarque-Bera (JB):                0.972\n",
+      "Skew:                          -0.519   Prob(JB):                        0.615\n",
+      "Kurtosis:                       2.706   Cond. No.                         12.7\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
@@ -205,13 +207,6 @@
    "source": [
     "print(results.summary())"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
@@ -230,7 +225,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.1"
+   "version": "3.8.2"
   }
  },
  "nbformat": 4,