2 deleted 10 characters in body edited Aug 3 '15 at 12:46 dsaxton 10.2k11 gold badge1717 silver badges3939 bronze badges There's some chance you're overfitting the data with this sample size (the $$R^2$$ value seems suspiciously high), but more to the point there's nothing inconsistent between a high $$R^2$$ and lots of "insignificant" predictors. This is simply because the coefficient of determination never decreases when you add variables to the model, so if you start with a high $$R^2$$ then you'll end up with one as long as you don't drop any variables. Below are some simple simulations that demonstrate this idea. Here I generated data according to the model $$Y_i = x_{1i} + \epsilon_i$$ where $$\epsilon_i \sim$$ normal$$(0, \sigma^2)$$ and then fit a regression only involving $$x_{1i}$$ along with another that included nine extra noise predictors $$x_{2i}, x_{3i}, \ldots, x_{10i}$$ that bore no relation to $$Y_i$$. We can see that the second model has a larger $$R^2$$ even though the added variables are obviously not important. There's some chance you're overfitting the data with this sample size (the $$R^2$$ value seems suspiciously high), but more to the point there's nothing inconsistent between a high $$R^2$$ and lots of "insignificant" predictors. This is simply because the coefficient of determination never decreases when you add variables to the model, so if you start with a high $$R^2$$ then you'll end up with one as long as you don't drop any variables. Below are some simple simulations that demonstrate this idea. Here I generated data according to the model $$Y_i = x_{1i} + \epsilon_i$$ where $$\epsilon_i \sim$$ normal$$(0, \sigma^2)$$ and then fit a regression only involving $$x_{1i}$$ along with another that included nine extra noise predictors $$x_{2i}, x_{3i}, \ldots, x_{10i}$$ that bore no relation to $$Y_i$$. We can see that the second model has a larger $$R^2$$ even though the added variables are obviously not important. There's some chance you're overfitting the data with this sample size (the $$R^2$$ value seems suspiciously high), but more to the point there's nothing inconsistent between a high $$R^2$$ and lots of "insignificant" predictors. This is simply because the coefficient of determination never decreases when you add variables to the model, so if you start with a high $$R^2$$ then you'll end up with one as long as you don't drop any variables. Below are some simple simulations that demonstrate this idea. Here I generated data according to the model $$Y_i = x_{1i} + \epsilon_i$$ where $$\epsilon_i \sim$$ normal$$(0, \sigma^2)$$ and then fit a regression only involving $$x_{1i}$$ along with another that included nine extra noise predictors $$x_{2i}, x_{3i}, \ldots, x_{10i}$$ that bore no relation to $$Y_i$$. We can see that the second model has a larger $$R^2$$ even though the added variables are not important. 1 answered Aug 3 '15 at 3:14 dsaxton 10.2k11 gold badge1717 silver badges3939 bronze badges There's some chance you're overfitting the data with this sample size (the $$R^2$$ value seems suspiciously high), but more to the point there's nothing inconsistent between a high $$R^2$$ and lots of "insignificant" predictors. This is simply because the coefficient of determination never decreases when you add variables to the model, so if you start with a high $$R^2$$ then you'll end up with one as long as you don't drop any variables. Below are some simple simulations that demonstrate this idea. Here I generated data according to the model $$Y_i = x_{1i} + \epsilon_i$$ where $$\epsilon_i \sim$$ normal$$(0, \sigma^2)$$ and then fit a regression only involving $$x_{1i}$$ along with another that included nine extra noise predictors $$x_{2i}, x_{3i}, \ldots, x_{10i}$$ that bore no relation to $$Y_i$$. We can see that the second model has a larger $$R^2$$ even though the added variables are obviously not important. Model 1:  OLS Regression Results ============================================================================== Dep. Variable: y R-squared: 0.935 Model: OLS Adj. R-squared: 0.934 Method: Least Squares F-statistic: 1424. Date: Sun, 02 Aug 2015 Prob (F-statistic): 1.44e-60 Time: 22:37:24 Log-Likelihood: -4.2454 No. Observations: 100 AIC: 10.49 Df Residuals: 99 BIC: 13.10 Df Model: 1 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [95.0% Conf. Int.] ------------------------------------------------------------------------------ var_1 0.9865 0.026 37.734 0.000 0.935 1.038 ============================================================================== Omnibus: 7.358 Durbin-Watson: 1.957 Prob(Omnibus): 0.025 Jarque-Bera (JB): 3.027 Skew: 0.016 Prob(JB): 0.220 Kurtosis: 2.148 Cond. No. 1.00 ==============================================================================  Model 2:  OLS Regression Results ============================================================================== Dep. Variable: y R-squared: 0.941 Model: OLS Adj. R-squared: 0.934 Method: Least Squares F-statistic: 143.2 Date: Sun, 02 Aug 2015 Prob (F-statistic): 9.08e-51 Time: 22:37:27 Log-Likelihood: 0.48280 No. Observations: 100 AIC: 19.03 Df Residuals: 90 BIC: 45.09 Df Model: 10 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [95.0% Conf. Int.] ------------------------------------------------------------------------------ var_1 0.9817 0.028 35.336 0.000 0.927 1.037 var_2 -0.0011 0.025 -0.043 0.966 -0.052 0.050 var_3 0.0098 0.025 0.393 0.695 -0.040 0.059 var_4 0.0253 0.030 0.856 0.394 -0.033 0.084 var_5 0.0160 0.027 0.596 0.553 -0.037 0.069 var_6 -0.0138 0.028 -0.486 0.628 -0.070 0.043 var_7 0.0100 0.024 0.418 0.677 -0.037 0.057 var_8 -0.0358 0.027 -1.335 0.185 -0.089 0.017 var_9 0.0180 0.026 0.707 0.482 -0.033 0.069 var_10 -0.0574 0.025 -2.288 0.024 -0.107 -0.008 ============================================================================== Omnibus: 5.760 Durbin-Watson: 1.815 Prob(Omnibus): 0.056 Jarque-Bera (JB): 2.903 Skew: -0.147 Prob(JB): 0.234 Kurtosis: 2.219 Cond. No. 1.72 ==============================================================================  This is one of the reasons why $$R^2$$ is rarely used when doing model selection.