Merge pull request #3 from agustinaliagac/fix-typos

Fix formula typo in exercise 3 and other typos in exercise 5

Author: MitchMG2

Exercise3/exercise3.ipynb

@@ -373,7 +373,7 @@
     "$$\n",
     "\\begin{align*}\n",
     "& \\frac{\\partial J(\\theta)}{\\partial \\theta_0} = \\frac{1}{m} \\sum_{i=1}^m \\left( h_\\theta\\left( x^{(i)} \\right) - y^{(i)} \\right) x_j^{(i)}  & \\text{for } j = 0 \\\\\n",
-    "& \\frac{\\partial J(\\theta)}{\\partial \\theta_0} = \\left( \\frac{1}{m} \\sum_{i=1}^m \\left( h_\\theta\\left( x^{(i)} \\right) - y^{(i)} \\right) x_j^{(i)} \\right) + \\frac{\\lambda}{m} \\theta_j & \\text{for } j  \\ge 1\n",
+    "& \\frac{\\partial J(\\theta)}{\\partial \\theta_j} = \\left( \\frac{1}{m} \\sum_{i=1}^m \\left( h_\\theta\\left( x^{(i)} \\right) - y^{(i)} \\right) x_j^{(i)} \\right) + \\frac{\\lambda}{m} \\theta_j & \\text{for } j  \\ge 1\n",
     "\\end{align*}\n",
     "$$\n",
     "\n",

Exercise5/exercise5.ipynb

@@ -687,9 +687,9 @@
     "\n",
     "### 3.2 Optional (ungraded) exercise: Adjusting the regularization parameter\n",
     "\n",
-    "In this section, you will get to observe how the regularization parameter affects the bias-variance of regularized polynomial regression. You should now modify the the lambda parameter and try $\\lambda = 1, 100$. For each of these values, the script should generate a polynomial fit to the data and also a learning curve.\n",
+    "In this section, you will get to observe how the regularization parameter affects the bias-variance of regularized polynomial regression. You should now modify the lambda parameter and try $\\lambda = 1, 100$. For each of these values, the script should generate a polynomial fit to the data and also a learning curve.\n",
     "\n",
-    "For $\\lambda = 1$, the generated plots should look like the the figure below. You should see a polynomial fit that follows the data trend well (left) and a learning curve (right) showing that both the cross validation and training error converge to a relatively low value. This shows the $\\lambda = 1$ regularized polynomial regression model does not have the high-bias or high-variance problems. In effect, it achieves a good trade-off between bias and variance.\n",
+    "For $\\lambda = 1$, the generated plots should look like the figure below. You should see a polynomial fit that follows the data trend well (left) and a learning curve (right) showing that both the cross validation and training error converge to a relatively low value. This shows the $\\lambda = 1$ regularized polynomial regression model does not have the high-bias or high-variance problems. In effect, it achieves a good trade-off between bias and variance.\n",
     "\n",
     "<table>\n",
     "    <tr>\n",