age vs. charges: OLS Regression Results ============================================================================== Dep. Variable: charges R-squared: 0.089 Model: OLS Adj. R-squared: 0.089 Method: Least Squares F-statistic: 131.2 Date: Tue, 17 Nov 2020 Prob (F-statistic): 4.89e-29 Time: 18:34:33 Log-Likelihood: -14415. No. Observations: 1338 AIC: 2.883e+04 Df Residuals: 1336 BIC: 2.884e+04 Df Model: 1 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ const 3165.8850 937.149 3.378 0.001 1327.440 5004.330 age 257.7226 22.502 11.453 0.000 213.579 301.866 ============================================================================== Omnibus: 399.600 Durbin-Watson: 2.033 Prob(Omnibus): 0.000 Jarque-Bera (JB): 864.239 Skew: 1.733 Prob(JB): 2.15e-188 Kurtosis: 4.869 Cond. No. 124. ============================================================================== Notes: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. ********************************************** ********************************************** ********************************************** P-Values: const 7.506030e-04 age 4.886693e-29 dtype: float64 sex vs. charges: OLS Regression Results ============================================================================== Dep. Variable: charges R-squared: 0.003 Model: OLS Adj. R-squared: 0.003 Method: Least Squares F-statistic: 4.400 Date: Tue, 17 Nov 2020 Prob (F-statistic): 0.0361 Time: 18:34:33 Log-Likelihood: -14475. No. Observations: 1338 AIC: 2.895e+04 Df Residuals: 1336 BIC: 2.897e+04 Df Model: 1 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ const 1.257e+04 470.072 26.740 0.000 1.16e+04 1.35e+04 sex 1387.1723 661.331 2.098 0.036 89.812 2684.532 ============================================================================== Omnibus: 331.451 Durbin-Watson: 2.011 Prob(Omnibus): 0.000 Jarque-Bera (JB): 636.534 Skew: 1.496 Prob(JB): 6.00e-139 Kurtosis: 4.572 Cond. No. 2.63 ============================================================================== Notes: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. ********************************************** ********************************************** ********************************************** P-Values: const 1.626108e-126 sex 3.613272e-02 dtype: float64 bmi vs. charges: OLS Regression Results ============================================================================== Dep. Variable: charges R-squared: 0.039 Model: OLS Adj. R-squared: 0.039 Method: Least Squares F-statistic: 54.71 Date: Tue, 17 Nov 2020 Prob (F-statistic): 2.46e-13 Time: 18:34:33 Log-Likelihood: -14451. No. Observations: 1338 AIC: 2.891e+04 Df Residuals: 1336 BIC: 2.892e+04 Df Model: 1 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ const 1192.9372 1664.802 0.717 0.474 -2072.974 4458.849 bmi 393.8730 53.251 7.397 0.000 289.409 498.337 ============================================================================== Omnibus: 261.030 Durbin-Watson: 1.983 Prob(Omnibus): 0.000 Jarque-Bera (JB): 431.091 Skew: 1.297 Prob(JB): 2.45e-94 Kurtosis: 4.004 Cond. No. 160. ============================================================================== Notes: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. ********************************************** ********************************************** ********************************************** P-Values: const 4.737685e-01 bmi 2.459086e-13 dtype: float64 children vs. charges: OLS Regression Results ============================================================================== Dep. Variable: charges R-squared: 0.005 Model: OLS Adj. R-squared: 0.004 Method: Least Squares F-statistic: 6.206 Date: Tue, 17 Nov 2020 Prob (F-statistic): 0.0129 Time: 18:34:33 Log-Likelihood: -14475. No. Observations: 1338 AIC: 2.895e+04 Df Residuals: 1336 BIC: 2.896e+04 Df Model: 1 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ const 1.252e+04 446.450 28.049 0.000 1.16e+04 1.34e+04 children 683.0894 274.202 2.491 0.013 145.176 1221.002 ============================================================================== Omnibus: 341.103 Durbin-Watson: 2.003 Prob(Omnibus): 0.000 Jarque-Bera (JB): 666.755 Skew: 1.528 Prob(JB): 1.64e-145 Kurtosis: 4.619 Cond. No. 2.65 ============================================================================== Notes: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. ********************************************** ********************************************** ********************************************** P-Values: const 1.676518e-136 children 1.285213e-02 dtype: float64 smoker vs. charges: OLS Regression Results ============================================================================== Dep. Variable: charges R-squared: 0.620 Model: OLS Adj. R-squared: 0.619 Method: Least Squares F-statistic: 2178. Date: Tue, 17 Nov 2020 Prob (F-statistic): 8.27e-283 Time: 18:34:33 Log-Likelihood: -13831. No. Observations: 1338 AIC: 2.767e+04 Df Residuals: 1336 BIC: 2.768e+04 Df Model: 1 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ const 8434.2683 229.014 36.829 0.000 7985.002 8883.535 smoker 2.362e+04 506.075 46.665 0.000 2.26e+04 2.46e+04 ============================================================================== Omnibus: 135.996 Durbin-Watson: 2.025 Prob(Omnibus): 0.000 Jarque-Bera (JB): 212.201 Skew: 0.727 Prob(JB): 8.34e-47 Kurtosis: 4.300 Cond. No. 2.60 ============================================================================== Notes: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. ********************************************** ********************************************** ********************************************** P-Values: const 1.581020e-205 smoker 8.271436e-283 dtype: float64 region vs. charges: OLS Regression Results ============================================================================== Dep. Variable: charges R-squared: 0.000 Model: OLS Adj. R-squared: -0.001 Method: Least Squares F-statistic: 0.05149 Date: Tue, 17 Nov 2020 Prob (F-statistic): 0.821 Time: 18:34:33 Log-Likelihood: -14478. No. Observations: 1338 AIC: 2.896e+04 Df Residuals: 1336 BIC: 2.897e+04 Df Model: 1 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ const 1.337e+04 562.359 23.781 0.000 1.23e+04 1.45e+04 region -68.0449 299.858 -0.227 0.821 -656.289 520.199 ============================================================================== Omnibus: 337.427 Durbin-Watson: 2.003 Prob(Omnibus): 0.000 Jarque-Bera (JB): 655.098 Skew: 1.516 Prob(JB): 5.59e-143 Kurtosis: 4.600 Cond. No. 3.83 ============================================================================== Notes: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. ********************************************** ********************************************** ********************************************** P-Values: const 1.574658e-104 region 8.205178e-01 dtype: float64