improvements to reg1 error vert lines plot; minor clarification reg2

Author: trevorcampbell

source/regression1.md

@@ -476,8 +476,8 @@ us the smallest RMSPE.
 from sklearn.neighbors import KNeighborsRegressor
 
 # (synthetic) new prediction points
-pts = pd.DataFrame({"sqft": [1250, 1850, 2250], "price": [250000, 200000, 500000]})
-finegrid = pd.DataFrame({"sqft": np.arange(900, 3901, 10)})
+pts = pd.DataFrame({"sqft": [1200, 1850, 2250], "price": [300000, 200000, 500000]})
+finegrid = pd.DataFrame({"sqft": np.arange(600, 3901, 10)})
 
 # preprocess the data, make the pipeline
 sacr_preprocessor = make_column_transformer((StandardScaler(), ["sqft"]))
@@ -495,22 +495,22 @@ sacr_full_preds_hid = pd.concat(
 )
 
 sacr_new_preds_hid = pd.concat(
-    (pts, pd.DataFrame(sacr_pipeline.predict(pts), columns=["predicted"])),
+    (small_sacramento[["sqft", "price"]].reset_index(), pd.DataFrame(sacr_pipeline.predict(small_sacramento[["sqft", "price"]]), columns=["predicted"])),
     axis=1,
-)
+).drop(columns=["index"])
 
 # to make altair mark_line works, need to create separate dataframes for each vertical error line
-sacr_new_preds_melted_df = sacr_new_preds_hid.melt(id_vars=["sqft"])
 errors_plot = (
     small_plot
     + alt.Chart(sacr_full_preds_hid).mark_line(color="#ff7f0e").encode(x="sqft", y="predicted")
     + alt.Chart(sacr_new_preds_hid)
     .mark_circle(opacity=1)
     .encode(x="sqft", y="price")
 )
+sacr_new_preds_melted_df = sacr_new_preds_hid.melt(id_vars=["sqft"])
 v_lines = []
-for i in pts["sqft"]:
-    line_df = sacr_new_preds_melted_df.query("sqft == @i")
+for i in sacr_new_preds_hid["sqft"]:
+    line_df = sacr_new_preds_melted_df.query(f"sqft == {i}")
     v_lines.append(alt.Chart(line_df).mark_line(color="black").encode(x="sqft", y="value"))
 
 errors_plot = alt.layer(*v_lines, errors_plot)
@@ -526,7 +526,7 @@ glue("fig:07-verticalerrors", errors_plot, display=False)
 :::{glue:figure} fig:07-verticalerrors
 :name: fig:07-verticalerrors
 
-Scatter plot of price (USD) versus house size (square feet) with example predictions (orange line) and the error in those predictions compared with true response values for three selected observations (vertical lines).
+Scatter plot of price (USD) versus house size (square feet) with example predictions (orange line) and the error in those predictions compared with true response values (vertical lines).
 :::
 
 +++

source/regression2.md

@@ -313,7 +313,7 @@ Scatter plot of sale price versus size with many possible lines that could be dr
 
 Simple linear regression chooses the straight line of best fit by choosing
 the line that minimizes the **average squared vertical distance** between itself and
-each of the observed data points in the training data. {numref}`fig:08-verticalDistToMin` illustrates
+each of the observed data points in the training data (equivalent to minimizing the RMSE). {numref}`fig:08-verticalDistToMin` illustrates
 these vertical distances as lines. Finally, to assess the predictive
 accuracy of a simple linear regression model,
 we use RMSPE—the same measure of predictive performance we used with K-NN regression.