update book

This commit is contained in:
Morten Hjorth-Jensen
2025-08-18 09:18:31 +02:00
parent 6fe1e82698
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"source": [
"Welcome to FYS-STK3155/4155!\n",
"\n",
"In this first week will focus on getting you set up with the programs you are going to be using throughout this course. We expect that many of you will encounter some trouble with setting these programs up, as they can be extremely finnicky and prone to not working the same on all machines, so we strongly encourage you to not get discouraged, and to show up to the group-sessions where we can help you along. The group sessions are also the best place to find group partners for the projects and to be challenged on your understanding of the material, which are both essential to doing well in this course.\n",
"In this first week will focus on getting you set up with the programs you are going to be using throughout this course. We expect that many of you will encounter some trouble with setting these programs up, as they can be extremely finnicky and prone to not working the same on all machines, so we strongly encourage you to not get discouraged, and to show up to the group-sessions where we can help you along. The group sessions are also the best place to find group partners for the projects and to be challenged on your understanding of the material, which are both essential to doing well in this course. We strongly encourage you to form groups of 2-3 participants. \n",
"\n",
"If you are unable to complete this weeks exercises, don't worry, this will likely be the most frustrating week for many of you. You have time to get back on track next week, especially if you come to the group-sessions!"
"If you are unable to complete this weekss exercises, don't worry, this will likely be the most frustrating week for many of you. You have time to get back on track next week, especially if you come to the group-sessions! Note also that this week's set of exercises does not count for the additional score. The deadline for the weekly exercises is set to Fridays, at midnight."
]
},
{
@@ -121,11 +121,11 @@
"id": "b5a4818a",
"metadata": {},
"source": [
"Following the theme of the previous exercises, another way of improving the reproducibility of your results and shareability of your code is having a good handle on which python packages you are using.\n",
"Following the themes from the previous exercises, another way of improving the reproducibility of your results and shareability of your code is having a good handle on which python packages you are using.\n",
"\n",
"There are many ways to manage your packages in Python, and you are free to use any approach you want, but in this course we encourage you to use something called a virtual environment. A virtual environemnt is a folder in your project which contains a Python runtime executable as well as all the packages you are using in the current project. In this way, each of your projects has its required set of packages installed in the same folder, so that if anything goes wrong while managing your packages it only affects the one project, and if multiple projects require different versions of the same package, you don't need to worry about messing up old projects. Also, it's easy to just delete the folder and start over if anything goes wrong.\n",
"\n",
"Virtual environments are typically created, activated, managed and updated using terminal commands, but for now we recommend that you let VS Code handle it for you to make the coding experience much easier. If you are familiar with another approach for virtual environments that works for you, feel free to keep doing it that way.\n"
"Virtual environments are typically created, activated, managed and updated using terminal commands, but for now we recommend that you let for example VS Code (a popular cross-paltform package) handle it for you to make the coding experience much easier. If you are familiar with another approach for virtual environments that works for you, feel free to keep doing it that way.\n"
]
},
{
@@ -169,9 +169,9 @@
"id": "d19ebd67",
"metadata": {},
"source": [
"Great job on getting through all of that! Now it's time to do some actual machine learning!\n",
"Great job on getting through all of that! Now it is time to do some actual machine learning!\n",
"\n",
"**a)** Complete the code below so that you fit a second order polynomial to the data. You will need to look up some skelarn documentation online (look at the imported functions for hints).\n",
"**a)** Complete the code below so that you fit a second order polynomial to the data. You will need to look up some scikit-learn documentation online (look at the imported functions for hints).\n",
"\n",
"**b)** Compute the mean square error for the line model and for the second degree polynomial model."
]
@@ -291,7 +291,7 @@
],
"metadata": {
"kernelspec": {
"display_name": ".venv",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
@@ -305,7 +305,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.0"
"version": "3.9.15"
}
},
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# Sphinx build info version 1
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
config: df0f44224508e73349e3c83eb15891ee
config: 73ce6691cda151d4aabc9466268ebbb7
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@@ -398,8 +398,8 @@ document.write(`
<section id="coding-setup-and-linear-regression">
<h2>Coding Setup and Linear Regression<a class="headerlink" href="#coding-setup-and-linear-regression" title="Link to this heading">#</a></h2>
<p>Welcome to FYS-STK3155/4155!</p>
<p>In this first week will focus on getting you set up with the programs you are going to be using throughout this course. We expect that many of you will encounter some trouble with setting these programs up, as they can be extremely finnicky and prone to not working the same on all machines, so we strongly encourage you to not get discouraged, and to show up to the group-sessions where we can help you along. The group sessions are also the best place to find group partners for the projects and to be challenged on your understanding of the material, which are both essential to doing well in this course.</p>
<p>If you are unable to complete this weeks exercises, dont worry, this will likely be the most frustrating week for many of you. You have time to get back on track next week, especially if you come to the group-sessions!</p>
<p>In this first week will focus on getting you set up with the programs you are going to be using throughout this course. We expect that many of you will encounter some trouble with setting these programs up, as they can be extremely finnicky and prone to not working the same on all machines, so we strongly encourage you to not get discouraged, and to show up to the group-sessions where we can help you along. The group sessions are also the best place to find group partners for the projects and to be challenged on your understanding of the material, which are both essential to doing well in this course. We strongly encourage you to form groups of 2-3 participants.</p>
<p>If you are unable to complete this weekss exercises, dont worry, this will likely be the most frustrating week for many of you. You have time to get back on track next week, especially if you come to the group-sessions! Note also that this weeks set of exercises does not count for the additional score. The deadline for the weekly exercises is set to Fridays, at midnight.</p>
<section id="learning-goals">
<h3>Learning goals<a class="headerlink" href="#learning-goals" title="Link to this heading">#</a></h3>
<p>After completing these exercises, you will know how to</p>
@@ -444,9 +444,9 @@ document.write(`
</section>
<section id="exercise-3-setting-up-a-python-virtual-environment">
<h2>Exercise 3 - Setting up a Python virtual environment<a class="headerlink" href="#exercise-3-setting-up-a-python-virtual-environment" title="Link to this heading">#</a></h2>
<p>Following the theme of the previous exercises, another way of improving the reproducibility of your results and shareability of your code is having a good handle on which python packages you are using.</p>
<p>Following the themes from the previous exercises, another way of improving the reproducibility of your results and shareability of your code is having a good handle on which python packages you are using.</p>
<p>There are many ways to manage your packages in Python, and you are free to use any approach you want, but in this course we encourage you to use something called a virtual environment. A virtual environemnt is a folder in your project which contains a Python runtime executable as well as all the packages you are using in the current project. In this way, each of your projects has its required set of packages installed in the same folder, so that if anything goes wrong while managing your packages it only affects the one project, and if multiple projects require different versions of the same package, you dont need to worry about messing up old projects. Also, its easy to just delete the folder and start over if anything goes wrong.</p>
<p>Virtual environments are typically created, activated, managed and updated using terminal commands, but for now we recommend that you let VS Code handle it for you to make the coding experience much easier. If you are familiar with another approach for virtual environments that works for you, feel free to keep doing it that way.</p>
<p>Virtual environments are typically created, activated, managed and updated using terminal commands, but for now we recommend that you let for example VS Code (a popular cross-paltform package) handle it for you to make the coding experience much easier. If you are familiar with another approach for virtual environments that works for you, feel free to keep doing it that way.</p>
<p><strong>a)</strong> Open this notebook in VS Code (<a class="reference external" href="https://code.visualstudio.com/Download">https://code.visualstudio.com/Download</a>). Download the Python and Jupyter extensions.</p>
<p><strong>b)</strong> Press ´Cmd + Shift + P´, then search and run ´Python: Create Environment…´</p>
<p><strong>c)</strong> Select ´Venv´</p>
@@ -461,16 +461,16 @@ document.write(`
</section>
<section id="exercise-3-fitting-an-ols-model-to-data">
<h2>Exercise 3 - Fitting an OLS model to data<a class="headerlink" href="#exercise-3-fitting-an-ols-model-to-data" title="Link to this heading">#</a></h2>
<p>Great job on getting through all of that! Now its time to do some actual machine learning!</p>
<p><strong>a)</strong> Complete the code below so that you fit a second order polynomial to the data. You will need to look up some skelarn documentation online (look at the imported functions for hints).</p>
<p>Great job on getting through all of that! Now it is time to do some actual machine learning!</p>
<p><strong>a)</strong> Complete the code below so that you fit a second order polynomial to the data. You will need to look up some scikit-learn documentation online (look at the imported functions for hints).</p>
<p><strong>b)</strong> Compute the mean square error for the line model and for the second degree polynomial model.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.preprocessing</span><span class="w"> </span><span class="kn">import</span> <span class="n">PolynomialFeatures</span> <span class="c1"># use the fit_transform method of the created object!</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.linear_model</span><span class="w"> </span><span class="kn">import</span> <span class="n">LinearRegression</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.metrics</span><span class="w"> </span><span class="kn">import</span> <span class="n">mean_squared_error</span>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">PolynomialFeatures</span> <span class="c1"># use the fit_transform method of the created object!</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LinearRegression</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">mean_squared_error</span>
</pre></div>
</div>
</div>
@@ -507,7 +507,7 @@ document.write(`
<p>Hopefully your model fit the data quite well, but to know how well the model actually generalizes to unseen data, which is most often what we care about, we need to split our data into training and testing data.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">train_test_split</span>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
</pre></div>
</div>
</div>
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<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
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<link rel="stylesheet" type="text/css" href="_static/styles/sphinx-book-theme.css?v=eba8b062" />
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<link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
@@ -502,7 +502,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
<p>We calculate the optimal intercept by including a feature with the constant value of 1 in our model, which is then multplied by some parameter <span class="math notranslate nohighlight">\(\beta_0\)</span> from the OLS method into the optimal intercept value (which will be <span class="math notranslate nohighlight">\(\beta_0\)</span>). In practice, we include the intercept in our model by adding a column of ones to the start of our feature matrix.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
</pre></div>
</div>
</div>
@@ -531,7 +531,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
<p><strong>b)</strong> Use the expression from <strong>3d)</strong> to find the optimal parameters <span class="math notranslate nohighlight">\(\boldsymbol{\hat{\beta}_{OLS}}\)</span> for predicting spending based on these features. Create a function for this operation, as you are going to need to use it a lot.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">OLS_parameters</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">OLS_parameters</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="k">return</span> <span class="o">...</span>
<span class="c1">#beta = OLS_parameters(X, y)</span>
@@ -556,7 +556,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
<p><strong>a)</strong> Create a feature matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> for the features <span class="math notranslate nohighlight">\(x, x^2, x^3, x^4, x^5\)</span>, including an intercept column of ones at the start. Make this into a function, as you will do this a lot over the next weeks.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">polynomial_features</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">polynomial_features</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="n">p</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
<span class="c1">#X[:, 0] = ...</span>
@@ -580,7 +580,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
<p><strong>c)</strong> Like in exercise 4 last week, split your feature matrix and target data into a training split and test split.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">train_test_split</span>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
<span class="c1">#X_train, X_test, y_train, y_test = ...</span>
</pre></div>
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@@ -17,9 +17,9 @@
"source": [
"Welcome to FYS-STK3155/4155!\n",
"\n",
"In this first week will focus on getting you set up with the programs you are going to be using throughout this course. We expect that many of you will encounter some trouble with setting these programs up, as they can be extremely finnicky and prone to not working the same on all machines, so we strongly encourage you to not get discouraged, and to show up to the group-sessions where we can help you along. The group sessions are also the best place to find group partners for the projects and to be challenged on your understanding of the material, which are both essential to doing well in this course.\n",
"In this first week will focus on getting you set up with the programs you are going to be using throughout this course. We expect that many of you will encounter some trouble with setting these programs up, as they can be extremely finnicky and prone to not working the same on all machines, so we strongly encourage you to not get discouraged, and to show up to the group-sessions where we can help you along. The group sessions are also the best place to find group partners for the projects and to be challenged on your understanding of the material, which are both essential to doing well in this course. We strongly encourage you to form groups of 2-3 participants. \n",
"\n",
"If you are unable to complete this weeks exercises, don't worry, this will likely be the most frustrating week for many of you. You have time to get back on track next week, especially if you come to the group-sessions!"
"If you are unable to complete this weekss exercises, don't worry, this will likely be the most frustrating week for many of you. You have time to get back on track next week, especially if you come to the group-sessions! Note also that this week's set of exercises does not count for the additional score. The deadline for the weekly exercises is set to Fridays, at midnight."
]
},
{
@@ -121,11 +121,11 @@
"id": "b5a4818a",
"metadata": {},
"source": [
"Following the theme of the previous exercises, another way of improving the reproducibility of your results and shareability of your code is having a good handle on which python packages you are using.\n",
"Following the themes from the previous exercises, another way of improving the reproducibility of your results and shareability of your code is having a good handle on which python packages you are using.\n",
"\n",
"There are many ways to manage your packages in Python, and you are free to use any approach you want, but in this course we encourage you to use something called a virtual environment. A virtual environemnt is a folder in your project which contains a Python runtime executable as well as all the packages you are using in the current project. In this way, each of your projects has its required set of packages installed in the same folder, so that if anything goes wrong while managing your packages it only affects the one project, and if multiple projects require different versions of the same package, you don't need to worry about messing up old projects. Also, it's easy to just delete the folder and start over if anything goes wrong.\n",
"\n",
"Virtual environments are typically created, activated, managed and updated using terminal commands, but for now we recommend that you let VS Code handle it for you to make the coding experience much easier. If you are familiar with another approach for virtual environments that works for you, feel free to keep doing it that way.\n"
"Virtual environments are typically created, activated, managed and updated using terminal commands, but for now we recommend that you let for example VS Code (a popular cross-paltform package) handle it for you to make the coding experience much easier. If you are familiar with another approach for virtual environments that works for you, feel free to keep doing it that way.\n"
]
},
{
@@ -169,9 +169,9 @@
"id": "d19ebd67",
"metadata": {},
"source": [
"Great job on getting through all of that! Now it's time to do some actual machine learning!\n",
"Great job on getting through all of that! Now it is time to do some actual machine learning!\n",
"\n",
"**a)** Complete the code below so that you fit a second order polynomial to the data. You will need to look up some skelarn documentation online (look at the imported functions for hints).\n",
"**a)** Complete the code below so that you fit a second order polynomial to the data. You will need to look up some scikit-learn documentation online (look at the imported functions for hints).\n",
"\n",
"**b)** Compute the mean square error for the line model and for the second degree polynomial model."
]
@@ -291,7 +291,7 @@
],
"metadata": {
"kernelspec": {
"display_name": ".venv",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
@@ -305,7 +305,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.0"
"version": "3.9.15"
}
},
"nbformat": 4,
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@@ -6,11 +6,11 @@ html[data-theme="light"] .highlight span.linenos.special { color: #000000; backg
html[data-theme="light"] .highlight .hll { background-color: #fae4c2 }
html[data-theme="light"] .highlight { background: #fefefe; color: #080808 }
html[data-theme="light"] .highlight .c { color: #515151 } /* Comment */
html[data-theme="light"] .highlight .err { color: #A12236 } /* Error */
html[data-theme="light"] .highlight .k { color: #6730C5 } /* Keyword */
html[data-theme="light"] .highlight .l { color: #7F4707 } /* Literal */
html[data-theme="light"] .highlight .err { color: #a12236 } /* Error */
html[data-theme="light"] .highlight .k { color: #6730c5 } /* Keyword */
html[data-theme="light"] .highlight .l { color: #7f4707 } /* Literal */
html[data-theme="light"] .highlight .n { color: #080808 } /* Name */
html[data-theme="light"] .highlight .o { color: #00622F } /* Operator */
html[data-theme="light"] .highlight .o { color: #00622f } /* Operator */
html[data-theme="light"] .highlight .p { color: #080808 } /* Punctuation */
html[data-theme="light"] .highlight .ch { color: #515151 } /* Comment.Hashbang */
html[data-theme="light"] .highlight .cm { color: #515151 } /* Comment.Multiline */
@@ -18,135 +18,135 @@ html[data-theme="light"] .highlight .cp { color: #515151 } /* Comment.Preproc */
html[data-theme="light"] .highlight .cpf { color: #515151 } /* Comment.PreprocFile */
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"source": [
"Welcome to FYS-STK3155/4155!\n",
"\n",
"In this first week will focus on getting you set up with the programs you are going to be using throughout this course. We expect that many of you will encounter some trouble with setting these programs up, as they can be extremely finnicky and prone to not working the same on all machines, so we strongly encourage you to not get discouraged, and to show up to the group-sessions where we can help you along. The group sessions are also the best place to find group partners for the projects and to be challenged on your understanding of the material, which are both essential to doing well in this course.\n",
"In this first week will focus on getting you set up with the programs you are going to be using throughout this course. We expect that many of you will encounter some trouble with setting these programs up, as they can be extremely finnicky and prone to not working the same on all machines, so we strongly encourage you to not get discouraged, and to show up to the group-sessions where we can help you along. The group sessions are also the best place to find group partners for the projects and to be challenged on your understanding of the material, which are both essential to doing well in this course. We strongly encourage you to form groups of 2-3 participants. \n",
"\n",
"If you are unable to complete this weeks exercises, don't worry, this will likely be the most frustrating week for many of you. You have time to get back on track next week, especially if you come to the group-sessions!"
"If you are unable to complete this weekss exercises, don't worry, this will likely be the most frustrating week for many of you. You have time to get back on track next week, especially if you come to the group-sessions! Note also that this week's set of exercises does not count for the additional score. The deadline for the weekly exercises is set to Fridays, at midnight."
]
},
{
@@ -121,11 +121,11 @@
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"Following the theme of the previous exercises, another way of improving the reproducibility of your results and shareability of your code is having a good handle on which python packages you are using.\n",
"Following the themes from the previous exercises, another way of improving the reproducibility of your results and shareability of your code is having a good handle on which python packages you are using.\n",
"\n",
"There are many ways to manage your packages in Python, and you are free to use any approach you want, but in this course we encourage you to use something called a virtual environment. A virtual environemnt is a folder in your project which contains a Python runtime executable as well as all the packages you are using in the current project. In this way, each of your projects has its required set of packages installed in the same folder, so that if anything goes wrong while managing your packages it only affects the one project, and if multiple projects require different versions of the same package, you don't need to worry about messing up old projects. Also, it's easy to just delete the folder and start over if anything goes wrong.\n",
"\n",
"Virtual environments are typically created, activated, managed and updated using terminal commands, but for now we recommend that you let VS Code handle it for you to make the coding experience much easier. If you are familiar with another approach for virtual environments that works for you, feel free to keep doing it that way.\n"
"Virtual environments are typically created, activated, managed and updated using terminal commands, but for now we recommend that you let for example VS Code (a popular cross-paltform package) handle it for you to make the coding experience much easier. If you are familiar with another approach for virtual environments that works for you, feel free to keep doing it that way.\n"
]
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"Great job on getting through all of that! Now it's time to do some actual machine learning!\n",
"Great job on getting through all of that! Now it is time to do some actual machine learning!\n",
"\n",
"**a)** Complete the code below so that you fit a second order polynomial to the data. You will need to look up some skelarn documentation online (look at the imported functions for hints).\n",
"**a)** Complete the code below so that you fit a second order polynomial to the data. You will need to look up some scikit-learn documentation online (look at the imported functions for hints).\n",
"\n",
"**b)** Compute the mean square error for the line model and for the second degree polynomial model."
]
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