diff --git a/constant_model_loss_transformations/loss_transformations.qmd b/constant_model_loss_transformations/loss_transformations.qmd index 8525d70b..feb9fb3a 100644 --- a/constant_model_loss_transformations/loss_transformations.qmd +++ b/constant_model_loss_transformations/loss_transformations.qmd @@ -822,11 +822,11 @@ In this calculation, we use the fact that the **sum of deviations from the mean Let's quickly walk through the proof for this: $$\sum_{i=1}^{n} (y_i - \bar{y}) = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n} \bar{y}$$ -$$ = \sum\_{i=1}^{n} y_i - n\bar{y}$$ +$$ = \sum_{i=1}^{n} y_i - n\bar{y}$$ -$$ = \sum*{i=1}^{n} y_i - n\frac{1}{n}\sum*{i=1}^{n}y$$ +$$ = \sum_{i=1}^{n} y_i - n\frac{1}{n}\sum_{i=1}^{n}y$$ -$$ = \sum*{i=1}^{n} y_i - \sum*{i=1}^{n}y_i$$ +$$ = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n}y_i$$ In our calculations, we'll also be using the definition of the variance as a sample. As a refresher: diff --git a/docs/constant_model_loss_transformations/loss_transformations.html b/docs/constant_model_loss_transformations/loss_transformations.html index 0179cd5e..2f527ac2 100644 --- a/docs/constant_model_loss_transformations/loss_transformations.html +++ b/docs/constant_model_loss_transformations/loss_transformations.html @@ -1180,9 +1180,9 @@

\(\sum_{i=1}^{n} (y_i - \bar{y}) = 0\).

Let’s quickly walk through the proof for this: \[\sum_{i=1}^{n} (y_i - \bar{y}) = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n} \bar{y}\]

-

\[ = \sum\_{i=1}^{n} y_i - n\bar{y}\]

-

\[ = \sum*{i=1}^{n} y_i - n\frac{1}{n}\sum*{i=1}^{n}y\]

-

\[ = \sum*{i=1}^{n} y_i - \sum*{i=1}^{n}y_i\]

+

\[ = \sum_{i=1}^{n} y_i - n\bar{y}\]

+

\[ = \sum_{i=1}^{n} y_i - n\frac{1}{n}\sum_{i=1}^{n}y\]

+

\[ = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n}y_i\]

In our calculations, we’ll also be using the definition of the variance as a sample. As a refresher:

\[\sigma_y^2 = \frac{1}{n}\sum_{i=1}^{n} (y_i - \bar{y})^2\]

Getting into our calculation for MSE minimization:

@@ -2333,11 +2333,11 @@

Let's quickly walk through the proof for this: $$\sum_{i=1}^{n} (y_i - \bar{y}) = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n} \bar{y}$$ -$$ = \sum\_{i=1}^{n} y_i - n\bar{y}$$ +$$ = \sum_{i=1}^{n} y_i - n\bar{y}$$ -$$ = \sum*{i=1}^{n} y_i - n\frac{1}{n}\sum*{i=1}^{n}y$$ +$$ = \sum_{i=1}^{n} y_i - n\frac{1}{n}\sum_{i=1}^{n}y$$ -$$ = \sum*{i=1}^{n} y_i - \sum*{i=1}^{n}y_i$$ +$$ = \sum_{i=1}^{n} y_i - \sum_{i=1}^{n}y_i$$ In our calculations, we'll also be using the definition of the variance as a sample. As a refresher: diff --git a/docs/intro_to_modeling/intro_to_modeling_files/figure-html/cell-2-output-1.png b/docs/intro_to_modeling/intro_to_modeling_files/figure-html/cell-2-output-1.png index aa0030c3..68b17604 100644 Binary files a/docs/intro_to_modeling/intro_to_modeling_files/figure-html/cell-2-output-1.png and b/docs/intro_to_modeling/intro_to_modeling_files/figure-html/cell-2-output-1.png differ diff --git a/docs/pandas_2/pandas_2.html b/docs/pandas_2/pandas_2.html index d9715319..a43bb36d 100644 --- a/docs/pandas_2/pandas_2.html +++ b/docs/pandas_2/pandas_2.html @@ -1602,12 +1602,12 @@

-328525 +384635 CA M -1994 -Refugio -17 +2015 +August +177 @@ -1634,34 +1634,34 @@

-337557 -1998 -Ryan -2432 +229975 +2020 +Alyana +17 -353111 -2004 -Rylan -72 +50602 +1964 +Joanie +9 -274384 -1962 -Gerhard -8 +332277 +1995 +Antonino +5 -251406 -1935 -Lester -41 +89092 +1982 +Doris +44 -48869 -1963 -Terilyn -8 +7620 +1925 +Hiroko +6 @@ -1687,27 +1687,27 @@

-343302 +149281 2000 -Timmy -21 +Jada +193 -151635 +342595 2000 -Victor -8 +Israel +374 -150822 +344601 2000 -Ankita -12 +Zayd +6 -152044 +152062 2000 -Hania +Jaileen 6 diff --git a/docs/pandas_3/pandas_3.html b/docs/pandas_3/pandas_3.html index 8a9ca9f1..4a435c7e 100644 --- a/docs/pandas_3/pandas_3.html +++ b/docs/pandas_3/pandas_3.html @@ -894,7 +894,7 @@ 

babynames.groupby("Year")
-
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x105e8db20>
+
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x105d49400>

What does this strange output mean? Calling .groupby (documentation) has generated a GroupBy object. You can imagine this as a set of “mini” sub-DataFrames, where each subframe contains all of the rows from babynames that correspond to a particular year.

@@ -1429,9 +1429,9 @@

-