diff --git a/sqlglot/parsers/databricks.py b/sqlglot/parsers/databricks.py
index 2805c1d933..345f5fc310 100644
--- a/sqlglot/parsers/databricks.py
+++ b/sqlglot/parsers/databricks.py
@@ -31,6 +31,16 @@ class DatabricksParser(SparkParser):
         "CURDATE": lambda self: self._parse_curdate(),
     }
 
+    FUNCTION_PARSERS = {
+        **SparkParser.FUNCTION_PARSERS,
+        "REGR_AVGX": lambda self: self._parse_regr(exp.RegrAvgx),
+        "REGR_AVGY": lambda self: self._parse_regr(exp.RegrAvgy),
+        "REGR_COUNT": lambda self: self._parse_regr(exp.RegrCount),
+        "REGR_INTERCEPT": lambda self: self._parse_regr(exp.RegrIntercept),
+        "REGR_R2": lambda self: self._parse_regr(exp.RegrR2),
+        "REGR_SLOPE": lambda self: self._parse_regr(exp.RegrSlope),
+    }
+
     FACTOR = {
         **SparkParser.FACTOR,
         TokenType.COLON: exp.JSONExtract,
@@ -59,3 +69,13 @@ def _parse_cluster_property(self):
         if self._match_texts(("AUTO", "NONE")):
             return self.expression(exp.ClusterProperty(this=self._prev.text.upper()))
         return super()._parse_cluster_property()
+
+    def _parse_regr(self, expr_type: type[exp.AggFunc]) -> exp.AggFunc:
+        args: list[exp.Expr] = []
+        if self._match(TokenType.DISTINCT):
+            args.append(self.expression(exp.Distinct(expressions=[self._parse_lambda()])))
+            self._match(TokenType.COMMA)
+        else:
+            self._match(TokenType.ALL)
+        args.extend(self._parse_function_args())
+        return self.expression(expr_type(this=seq_get(args, 0), expression=seq_get(args, 1)))
diff --git a/sqlglot/typing/databricks.py b/sqlglot/typing/databricks.py
index aa0f35147d..77b6c3e181 100644
--- a/sqlglot/typing/databricks.py
+++ b/sqlglot/typing/databricks.py
@@ -5,12 +5,23 @@
 
 EXPRESSION_METADATA = {
     **EXPRESSION_METADATA,
+    **{
+        exp_type: {"returns": exp.DType.DOUBLE}
+        for exp_type in {
+            exp.RegrAvgx,
+            exp.RegrAvgy,
+            exp.RegrIntercept,
+            exp.RegrR2,
+            exp.RegrSlope,
+        }
+    },
     **{
         exp_type: {"returns": exp.DType.INT}
         for exp_type in {
             exp.RegexpCount,
         }
     },
+    exp.RegrCount: {"returns": exp.DType.BIGINT},
     exp.RegexpExtractAll: {
         "annotator": lambda self, e: self._set_type(
             e, exp.DataType.from_str("ARRAY<STRING>", dialect="databricks")
diff --git a/tests/fixtures/optimizer/annotate_functions.sql b/tests/fixtures/optimizer/annotate_functions.sql
index 271d8fff9e..88d7b3349b 100644
--- a/tests/fixtures/optimizer/annotate_functions.sql
+++ b/tests/fixtures/optimizer/annotate_functions.sql
@@ -4219,6 +4219,10 @@ DOUBLE;
 REGR_AVGX(tbl.decfloat_col, tbl.decfloat_col);
 DECFLOAT;
 
+# dialect: databricks
+REGR_AVGX(DISTINCT tbl.double_col, tbl.double_col);
+DOUBLE;
+
 # dialect: snowflake
 REGR_AVGY(tbl.double_col, tbl.double_col);
 DOUBLE;
@@ -4231,6 +4235,26 @@ DOUBLE;
 REGR_AVGY(tbl.decfloat_col, tbl.decfloat_col);
 DECFLOAT;
 
+# dialect: databricks
+REGR_AVGY(tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_AVGY(tbl.int_col, tbl.int_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_AVGY(ALL tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_AVGY(DISTINCT tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_AVGY(tbl.double_col, tbl.double_col) OVER (PARTITION BY 1);
+DOUBLE;
+
 # dialect: snowflake
 REGR_COUNT(tbl.double_col, tbl.double_col);
 DOUBLE;
@@ -4247,6 +4271,26 @@ DOUBLE;
 REGR_COUNT(tbl.decfloat_col, tbl.decfloat_col);
 DECFLOAT;
 
+# dialect: databricks
+REGR_COUNT(tbl.double_col, tbl.double_col);
+BIGINT;
+
+# dialect: databricks
+REGR_COUNT(tbl.int_col, tbl.int_col);
+BIGINT;
+
+# dialect: databricks
+REGR_COUNT(ALL tbl.double_col, tbl.double_col);
+BIGINT;
+
+# dialect: databricks
+REGR_COUNT(DISTINCT tbl.double_col, tbl.double_col);
+BIGINT;
+
+# dialect: databricks
+REGR_COUNT(tbl.double_col, tbl.double_col) OVER (PARTITION BY 1);
+BIGINT;
+
 # dialect: snowflake
 REGR_INTERCEPT(tbl.double_col, tbl.double_col);
 DOUBLE;
@@ -4263,6 +4307,26 @@ DOUBLE;
 REGR_INTERCEPT(tbl.decfloat_col, tbl.decfloat_col);
 DECFLOAT;
 
+# dialect: databricks
+REGR_INTERCEPT(tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_INTERCEPT(tbl.int_col, tbl.int_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_INTERCEPT(ALL tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_INTERCEPT(DISTINCT tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_INTERCEPT(tbl.double_col, tbl.double_col) OVER (PARTITION BY 1);
+DOUBLE;
+
 # dialect: snowflake
 REGR_R2(tbl.double_col, tbl.double_col);
 DOUBLE;
@@ -4279,6 +4343,26 @@ DOUBLE;
 REGR_R2(tbl.decfloat_col, tbl.decfloat_col);
 DECFLOAT;
 
+# dialect: databricks
+REGR_R2(tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_R2(tbl.int_col, tbl.int_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_R2(ALL tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_R2(DISTINCT tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_R2(tbl.double_col, tbl.double_col) OVER (PARTITION BY 1);
+DOUBLE;
+
 # dialect: snowflake
 REGR_SXX(tbl.double_col, tbl.double_col);
 DOUBLE;
@@ -4343,6 +4427,26 @@ DOUBLE;
 REGR_SLOPE(tbl.decfloat_col, tbl.decfloat_col);
 DECFLOAT;
 
+# dialect: databricks
+REGR_SLOPE(tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_SLOPE(tbl.int_col, tbl.int_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_SLOPE(ALL tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_SLOPE(DISTINCT tbl.double_col, tbl.double_col);
+DOUBLE;
+
+# dialect: databricks
+REGR_SLOPE(tbl.double_col, tbl.double_col) OVER (PARTITION BY 1);
+DOUBLE;
+
 # dialect: snowflake
 REGR_VALX(NULL, 2.0);
 DOUBLE;