Replacing \( y_i \) with \( y_i - \beta_0 = y_i - \overline{\boldsymbol{y}} \) in the cost function will give us (in vector-matrix disguise) diff --git a/doc/pub/week38/html/._week38-bs013.html b/doc/pub/week38/html/._week38-bs013.html index de10148b5..659ea337e 100644 --- a/doc/pub/week38/html/._week38-bs013.html +++ b/doc/pub/week38/html/._week38-bs013.html @@ -443,7 +443,7 @@ y = np.e Maxpolydegree = 20 X = np.zeros((n,Maxpolydegree)) -We include explicitely the intercpt column +#We include explicitely the intercept column X[:,0] = 1.0 for degree in range(Maxpolydegree): diff --git a/doc/pub/week38/html/week38-reveal.html b/doc/pub/week38/html/week38-reveal.html index c2f081444..77dfcb1bd 100644 --- a/doc/pub/week38/html/week38-reveal.html +++ b/doc/pub/week38/html/week38-reveal.html @@ -649,7 +649,7 @@ the sum \( \sum_{i=0}^{n-1} X_{ij} \) can be rewritten as
$$
-\sum_{i=0}^{n-1} \left(X_{ij} - \frac{1}{n}\sum_{i=0}^{n-1} X_{ij}) = \sum_{i=0}^{n-1} X_{ij} - \sum_{i=0}^{n-1} \frac{1}{n} \sum_{i=0}^{n-1}X_{ij},
+\sum_{i=0}^{n-1} \left(X_{ij} - \frac{1}{n}\sum_{i=0}^{n-1} X_{ij}\right) = \sum_{i=0}^{n-1} X_{ij} - \sum_{i=0}^{n-1} \frac{1}{n} \sum_{i=0}^{n-1}X_{ij},
$$
@@ -675,7 +675,7 @@ $$
$$
-the average value of \( \boldsymbol{y] \).
+the average value of \( \boldsymbol{y} \).
Replacing \( y_i \) with \( y_i - \beta_0 = y_i - \overline{\boldsymbol{y}} \) in the cost function will give us (in vector-matrix disguise) @@ -725,7 +725,7 @@ y = np.exp(-x**2) + 20 X = np.zeros((n,Maxpolydegree)) -We include explicitely the intercpt column +#We include explicitely the intercept column X[:,0] = 1.0 for degree in range(Maxpolydegree): diff --git a/doc/pub/week38/html/week38-solarized.html b/doc/pub/week38/html/week38-solarized.html index 748ba6002..65b61ff31 100644 --- a/doc/pub/week38/html/week38-solarized.html +++ b/doc/pub/week38/html/week38-solarized.html @@ -799,7 +799,7 @@ If we assume that every column of \( \boldsymbol{X} \) is centered, which we can the sum \( \sum_{i=0}^{n-1} X_{ij} \) can be rewritten as $$ -\sum_{i=0}^{n-1} \left(X_{ij} - \frac{1}{n}\sum_{i=0}^{n-1} X_{ij}) = \sum_{i=0}^{n-1} X_{ij} - \sum_{i=0}^{n-1} \frac{1}{n} \sum_{i=0}^{n-1}X_{ij}, +\sum_{i=0}^{n-1} \left(X_{ij} - \frac{1}{n}\sum_{i=0}^{n-1} X_{ij}\right) = \sum_{i=0}^{n-1} X_{ij} - \sum_{i=0}^{n-1} \frac{1}{n} \sum_{i=0}^{n-1}X_{ij}, $$ resulting in @@ -818,7 +818,7 @@ $$ \beta_0 = \frac{1}{n}\sum_{i=0}^{n-1} y_i = \overline{\boldsymbol{y}}, $$ -the average value of \( \boldsymbol{y] \). +the average value of \( \boldsymbol{y} \).
Replacing \( y_i \) with \( y_i - \beta_0 = y_i - \overline{\boldsymbol{y}} \) in the cost function will give us (in vector-matrix disguise) @@ -866,7 +866,7 @@ y = np.exp(-x**2) + 20 X = np.zeros((n,Maxpolydegree)) -We include explicitely the intercpt column +#We include explicitely the intercept column X[:,0] = 1.0 for degree in range(Maxpolydegree): diff --git a/doc/pub/week38/html/week38.html b/doc/pub/week38/html/week38.html index d229b1d1c..04534cf80 100644 --- a/doc/pub/week38/html/week38.html +++ b/doc/pub/week38/html/week38.html @@ -804,7 +804,7 @@ If we assume that every column of \( \boldsymbol{X} \) is centered, which we can the sum \( \sum_{i=0}^{n-1} X_{ij} \) can be rewritten as $$ -\sum_{i=0}^{n-1} \left(X_{ij} - \frac{1}{n}\sum_{i=0}^{n-1} X_{ij}) = \sum_{i=0}^{n-1} X_{ij} - \sum_{i=0}^{n-1} \frac{1}{n} \sum_{i=0}^{n-1}X_{ij}, +\sum_{i=0}^{n-1} \left(X_{ij} - \frac{1}{n}\sum_{i=0}^{n-1} X_{ij}\right) = \sum_{i=0}^{n-1} X_{ij} - \sum_{i=0}^{n-1} \frac{1}{n} \sum_{i=0}^{n-1}X_{ij}, $$ resulting in @@ -823,7 +823,7 @@ $$ \beta_0 = \frac{1}{n}\sum_{i=0}^{n-1} y_i = \overline{\boldsymbol{y}}, $$ -the average value of \( \boldsymbol{y] \). +the average value of \( \boldsymbol{y} \).
Replacing \( y_i \) with \( y_i - \beta_0 = y_i - \overline{\boldsymbol{y}} \) in the cost function will give us (in vector-matrix disguise) @@ -871,7 +871,7 @@ y = np.e Maxpolydegree = 20 X = np.zeros((n,Maxpolydegree)) -We include explicitely the intercpt column +#We include explicitely the intercept column X[:,0] = 1.0 for degree in range(Maxpolydegree): diff --git a/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz b/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz index ebfa58c4b..bce3b2666 100644 Binary files a/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz and b/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz differ diff --git a/doc/pub/week38/ipynb/week38.ipynb b/doc/pub/week38/ipynb/week38.ipynb index 573e0db46..665c54c68 100644 --- a/doc/pub/week38/ipynb/week38.ipynb +++ b/doc/pub/week38/ipynb/week38.ipynb @@ -628,7 +628,7 @@ "metadata": {}, "source": [ "$$\n", - "\\sum_{i=0}^{n-1} \\left(X_{ij} - \\frac{1}{n}\\sum_{i=0}^{n-1} X_{ij}) = \\sum_{i=0}^{n-1} X_{ij} - \\sum_{i=0}^{n-1} \\frac{1}{n} \\sum_{i=0}^{n-1}X_{ij},\n", + "\\sum_{i=0}^{n-1} \\left(X_{ij} - \\frac{1}{n}\\sum_{i=0}^{n-1} X_{ij}\\right) = \\sum_{i=0}^{n-1} X_{ij} - \\sum_{i=0}^{n-1} \\frac{1}{n} \\sum_{i=0}^{n-1}X_{ij},\n", "$$" ] }, @@ -684,7 +684,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "the average value of $\\boldsymbol{y]$.\n", + "the average value of $\\boldsymbol{y}$.\n", "\n", "Replacing $y_i$ with $y_i - \\beta_0 = y_i - \\overline{\\boldsymbol{y}}$ in the cost function will give us (in vector-matrix disguise)" ] @@ -743,7 +743,7 @@ "\n", "Maxpolydegree = 20\n", "X = np.zeros((n,Maxpolydegree))\n", - "We include explicitely the intercpt column\n", + "#We include explicitely the intercept column\n", "X[:,0] = 1.0\n", "\n", "for degree in range(Maxpolydegree):\n", diff --git a/doc/src/week38/week38.do.txt b/doc/src/week38/week38.do.txt index 4f0c87ecf..ed3924b19 100644 --- a/doc/src/week38/week38.do.txt +++ b/doc/src/week38/week38.do.txt @@ -441,7 +441,7 @@ the sum $\sum_{i=0}^{n-1} X_{ij}$ can be rewritten as !bt \[ -\sum_{i=0}^{n-1} \left(X_{ij} - \frac{1}{n}\sum_{i=0}^{n-1} X_{ij}) = \sum_{i=0}^{n-1} X_{ij} - \sum_{i=0}^{n-1} \frac{1}{n} \sum_{i=0}^{n-1}X_{ij}, +\sum_{i=0}^{n-1} \left(X_{ij} - \frac{1}{n}\sum_{i=0}^{n-1} X_{ij}\right) = \sum_{i=0}^{n-1} X_{ij} - \sum_{i=0}^{n-1} \frac{1}{n} \sum_{i=0}^{n-1}X_{ij}, \] !et resulting in @@ -464,7 +464,7 @@ or \beta_0 = \frac{1}{n}\sum_{i=0}^{n-1} y_i = \overline{\bm{y}}, \] !et -the average value of $\bm{y]$. +the average value of $\bm{y}$. Replacing $y_i$ with $y_i - \beta_0 = y_i - \overline{\bm{y}}$ in the cost function will give us (in vector-matrix disguise) !bt @@ -506,7 +506,7 @@ y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2) Maxpolydegree = 20 X = np.zeros((n,Maxpolydegree)) -We include explicitely the intercpt column +#We include explicitely the intercept column X[:,0] = 1.0 for degree in range(Maxpolydegree):