Fix default values for simulation runs and typo related to alpha (#842)

* fix: significance_level
https://github.com/py-why/dowhy/issues/809

Signed-off-by: Michael Klesel <michael@klesel.info>

* fix: default number of simulations for CI
https://github.com/py-why/dowhy/issues/841

Signed-off-by: Michael Klesel <michael@klesel.info>

* fix: significance_level
https://github.com/py-why/dowhy/issues/809

Signed-off-by: Michael Klesel <michael@klesel.info>

* fix: default number of simulations for CI
https://github.com/py-why/dowhy/issues/841

Signed-off-by: Michael Klesel <michael@klesel.info>

* remove: self._linear_model (not used in class)
Signed-off-by: Michael Klesel <michael@klesel.info>

---------

Signed-off-by: Michael Klesel <michael@klesel.info>

dowhy/causal_estimator.py

@@ -26,7 +26,9 @@ class CausalEstimator:
     # The default number of simulations for statistical testing
     DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000
     # The default number of simulations to obtain confidence intervals
-    DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100
+    # This should be at least 399 for a 5% error rate:
+    # https://www.econstor.eu/bitstream/10419/67820/1/587473266.pdf
+    DEFAULT_NUMBER_OF_SIMULATIONS_CI = 399
     # The portion of the total size that should be taken each time to find the confidence intervals
     # 1 is the recommended value
     # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf

dowhy/causal_estimators/linear_regression_estimator.py

@@ -68,7 +68,6 @@ class LinearRegressionEstimator(RegressionEstimator):
             **kwargs,
         )
         self.logger.info("INFO: Using Linear Regression Estimator")
-        self._linear_model = self.model
 
     def fit(
         self,

dowhy/causal_refuter.py

@@ -173,7 +173,7 @@ def test_significance(
     estimate,
     simulations: List,
     test_type: SignificanceTestType = SignificanceTestType.AUTO,
-    significance_level: float = 0.85,
+    significance_level: float = 0.95,
 ):
     """Tests the statistical significance of the estimate obtained to the simulations produced by a refuter.