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UNI-PROG3-CW2-MLWP/Q1.ipynb
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bobbert afc0105d5e PART 1F
2026-04-25 16:25:54 +01:00

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"cell_type": "markdown",
"source": [
"## This is the Q1 Notebook!\n",
"\n",
"It's tracked via GitHub! hence the need for this line for the init commit"
],
"id": "193cc36275a60171"
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"cell_type": "code",
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns"
],
"id": "edaea0c939a83b79",
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"cell_type": "code",
"source": "df = pd.read_csv('data/googleplaystore_new.csv')",
"id": "e657e9baacc13e6b",
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"execution_count": 372
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{
"metadata": {},
"cell_type": "markdown",
"source": "## Part A\n",
"id": "751a6161e8e12bdd"
},
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"source": [
"df = df.dropna()\n",
"df = df.drop_duplicates()"
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"execution_count": 373
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"source": "df.head(10)",
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{
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" App Category Rating Reviews Size \\\n",
"0 Market Update Helper LIBRARIES_AND_DEMO 4.1 20145 11k \n",
"1 SuperLivePro BUSINESS 4.3 46353 21M \n",
"2 Wifi Connect Library LIBRARIES_AND_DEMO 3.9 58055 41k \n",
"3 Apk Installer LIBRARIES_AND_DEMO 3.8 7750 292k \n",
"4 English speaking texts EDUCATION 4.4 1619 3.0M \n",
"5 Eternal life LIBRARIES_AND_DEMO 5.0 26 2.5M \n",
"6 Dresses Ideas & Fashions +3000 BEAUTY 4.5 473 8.2M \n",
"7 GO Notifier COMMUNICATION 4.2 124346 695k \n",
"8 Prosperity EVENTS 5.0 16 2.3M \n",
"9 NSE Mobile Trading FINANCE 4.1 13868 1.4M \n",
"\n",
" Installs Type Price Content Rating Genres Android Ver \n",
"0 1,000,000+ Free 0 Everyone Libraries & Demo 1.5 and up \n",
"1 1,000,000+ Free 0 Everyone Business 1.5 and up \n",
"2 5,000,000+ Free 0 Everyone Libraries & Demo 1.5 and up \n",
"3 1,000,000+ Free 0 Everyone Libraries & Demo 1.6 and up \n",
"4 1,000,000+ Free 0 Everyone Education 1.6 and up \n",
"5 1,000+ Free 0 Everyone Libraries & Demo 1.6 and up \n",
"6 100,000+ Free 0 Mature 17+ Beauty 1.6 and up \n",
"7 10,000,000+ Free 0 Everyone Communication 2.0 and up \n",
"8 100+ Free 0 Everyone Events 2.0 and up \n",
"9 1,000,000+ Free 0 Everyone Finance 2.1 and up "
],
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"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>App</th>\n",
" <th>Category</th>\n",
" <th>Rating</th>\n",
" <th>Reviews</th>\n",
" <th>Size</th>\n",
" <th>Installs</th>\n",
" <th>Type</th>\n",
" <th>Price</th>\n",
" <th>Content Rating</th>\n",
" <th>Genres</th>\n",
" <th>Android Ver</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>Market Update Helper</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>4.1</td>\n",
" <td>20145</td>\n",
" <td>11k</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.5 and up</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>SuperLivePro</td>\n",
" <td>BUSINESS</td>\n",
" <td>4.3</td>\n",
" <td>46353</td>\n",
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" <td>Everyone</td>\n",
" <td>Business</td>\n",
" <td>1.5 and up</td>\n",
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" <tr>\n",
" <th>2</th>\n",
" <td>Wifi Connect Library</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>3.9</td>\n",
" <td>58055</td>\n",
" <td>41k</td>\n",
" <td>5,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.5 and up</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>Apk Installer</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>3.8</td>\n",
" <td>7750</td>\n",
" <td>292k</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.6 and up</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>English speaking texts</td>\n",
" <td>EDUCATION</td>\n",
" <td>4.4</td>\n",
" <td>1619</td>\n",
" <td>3.0M</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Education</td>\n",
" <td>1.6 and up</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>Eternal life</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>5.0</td>\n",
" <td>26</td>\n",
" <td>2.5M</td>\n",
" <td>1,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.6 and up</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>Dresses Ideas &amp; Fashions +3000</td>\n",
" <td>BEAUTY</td>\n",
" <td>4.5</td>\n",
" <td>473</td>\n",
" <td>8.2M</td>\n",
" <td>100,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Mature 17+</td>\n",
" <td>Beauty</td>\n",
" <td>1.6 and up</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>GO Notifier</td>\n",
" <td>COMMUNICATION</td>\n",
" <td>4.2</td>\n",
" <td>124346</td>\n",
" <td>695k</td>\n",
" <td>10,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Communication</td>\n",
" <td>2.0 and up</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>Prosperity</td>\n",
" <td>EVENTS</td>\n",
" <td>5.0</td>\n",
" <td>16</td>\n",
" <td>2.3M</td>\n",
" <td>100+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Events</td>\n",
" <td>2.0 and up</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>NSE Mobile Trading</td>\n",
" <td>FINANCE</td>\n",
" <td>4.1</td>\n",
" <td>13868</td>\n",
" <td>1.4M</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Finance</td>\n",
" <td>2.1 and up</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
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"metadata": {},
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],
"execution_count": 374
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},
"cell_type": "markdown",
"source": "## Part B",
"id": "5e0e0e76635904b6"
},
{
"metadata": {
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"cell_type": "code",
"source": [
"# Getting the column for size, checking if it's ending with an M or a k and converting the Mb to kb with 1024* and then again from kb to just b by another 1024*\n",
"def parse_size(size_str):\n",
" if isinstance(size_str, str):\n",
" if size_str.endswith('M'):\n",
" return float(size_str[:-1]) * 1024 * 1024\n",
" elif size_str.endswith('k'):\n",
" return float(size_str[:-1]) * 1024\n",
" return size_str"
],
"id": "c15cb7f9831e0f81",
"outputs": [],
"execution_count": 375
},
{
"metadata": {
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"end_time": "2026-04-25T14:53:58.334856400Z",
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"cell_type": "code",
"source": "df['Size in bytes'] = df['Size'].apply(parse_size)",
"id": "c76da70de24ddc72",
"outputs": [],
"execution_count": 376
},
{
"metadata": {
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"cell_type": "code",
"source": "df[['Size', 'Size in bytes']].head(10)",
"id": "73784ad66975e81f",
"outputs": [
{
"data": {
"text/plain": [
" Size Size in bytes\n",
"0 11k 11264.0\n",
"1 21M 22020096.0\n",
"2 41k 41984.0\n",
"3 292k 299008.0\n",
"4 3.0M 3145728.0\n",
"5 2.5M 2621440.0\n",
"6 8.2M 8598323.2\n",
"7 695k 711680.0\n",
"8 2.3M 2411724.8\n",
"9 1.4M 1468006.4"
],
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"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Size</th>\n",
" <th>Size in bytes</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>11k</td>\n",
" <td>11264.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>21M</td>\n",
" <td>22020096.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>41k</td>\n",
" <td>41984.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>292k</td>\n",
" <td>299008.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>3.0M</td>\n",
" <td>3145728.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>2.5M</td>\n",
" <td>2621440.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>8.2M</td>\n",
" <td>8598323.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>695k</td>\n",
" <td>711680.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>2.3M</td>\n",
" <td>2411724.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>1.4M</td>\n",
" <td>1468006.4</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
"execution_count": 377,
"metadata": {},
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}
],
"execution_count": 377
},
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"start_time": "2026-04-25T14:53:58.367405200Z"
}
},
"cell_type": "code",
"source": "print(11*1024) # Just checking the kb and mb conversion happened properly, by checking 2 of the values manually.",
"id": "7ac34d8bc88327a1",
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"11264\n"
]
}
],
"execution_count": 378
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.423348900Z",
"start_time": "2026-04-25T14:53:58.385473600Z"
}
},
"cell_type": "code",
"source": "print((21*1024)*1024) # Ideally this is the same as doing the calculation without the ( ) but just incase!",
"id": "f72b05042c5a16fa",
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"22020096\n"
]
}
],
"execution_count": 379
},
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"metadata": {
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},
"cell_type": "code",
"source": "print(1.4*1024*1024) # This one seemed odd... Checked on an online converted to double-check but turns out the 0.4 bytes shows up there too.",
"id": "dcaf54123ea0d75d",
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1468006.4\n"
]
}
],
"execution_count": 380
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{
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"cell_type": "code",
"source": "df.head(10)",
"id": "3e1112ae100d010c",
"outputs": [
{
"data": {
"text/plain": [
" App Category Rating Reviews Size \\\n",
"0 Market Update Helper LIBRARIES_AND_DEMO 4.1 20145 11k \n",
"1 SuperLivePro BUSINESS 4.3 46353 21M \n",
"2 Wifi Connect Library LIBRARIES_AND_DEMO 3.9 58055 41k \n",
"3 Apk Installer LIBRARIES_AND_DEMO 3.8 7750 292k \n",
"4 English speaking texts EDUCATION 4.4 1619 3.0M \n",
"5 Eternal life LIBRARIES_AND_DEMO 5.0 26 2.5M \n",
"6 Dresses Ideas & Fashions +3000 BEAUTY 4.5 473 8.2M \n",
"7 GO Notifier COMMUNICATION 4.2 124346 695k \n",
"8 Prosperity EVENTS 5.0 16 2.3M \n",
"9 NSE Mobile Trading FINANCE 4.1 13868 1.4M \n",
"\n",
" Installs Type Price Content Rating Genres Android Ver \\\n",
"0 1,000,000+ Free 0 Everyone Libraries & Demo 1.5 and up \n",
"1 1,000,000+ Free 0 Everyone Business 1.5 and up \n",
"2 5,000,000+ Free 0 Everyone Libraries & Demo 1.5 and up \n",
"3 1,000,000+ Free 0 Everyone Libraries & Demo 1.6 and up \n",
"4 1,000,000+ Free 0 Everyone Education 1.6 and up \n",
"5 1,000+ Free 0 Everyone Libraries & Demo 1.6 and up \n",
"6 100,000+ Free 0 Mature 17+ Beauty 1.6 and up \n",
"7 10,000,000+ Free 0 Everyone Communication 2.0 and up \n",
"8 100+ Free 0 Everyone Events 2.0 and up \n",
"9 1,000,000+ Free 0 Everyone Finance 2.1 and up \n",
"\n",
" Size in bytes \n",
"0 11264.0 \n",
"1 22020096.0 \n",
"2 41984.0 \n",
"3 299008.0 \n",
"4 3145728.0 \n",
"5 2621440.0 \n",
"6 8598323.2 \n",
"7 711680.0 \n",
"8 2411724.8 \n",
"9 1468006.4 "
],
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>App</th>\n",
" <th>Category</th>\n",
" <th>Rating</th>\n",
" <th>Reviews</th>\n",
" <th>Size</th>\n",
" <th>Installs</th>\n",
" <th>Type</th>\n",
" <th>Price</th>\n",
" <th>Content Rating</th>\n",
" <th>Genres</th>\n",
" <th>Android Ver</th>\n",
" <th>Size in bytes</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>Market Update Helper</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>4.1</td>\n",
" <td>20145</td>\n",
" <td>11k</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.5 and up</td>\n",
" <td>11264.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>SuperLivePro</td>\n",
" <td>BUSINESS</td>\n",
" <td>4.3</td>\n",
" <td>46353</td>\n",
" <td>21M</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Business</td>\n",
" <td>1.5 and up</td>\n",
" <td>22020096.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>Wifi Connect Library</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>3.9</td>\n",
" <td>58055</td>\n",
" <td>41k</td>\n",
" <td>5,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.5 and up</td>\n",
" <td>41984.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>Apk Installer</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>3.8</td>\n",
" <td>7750</td>\n",
" <td>292k</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.6 and up</td>\n",
" <td>299008.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>English speaking texts</td>\n",
" <td>EDUCATION</td>\n",
" <td>4.4</td>\n",
" <td>1619</td>\n",
" <td>3.0M</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Education</td>\n",
" <td>1.6 and up</td>\n",
" <td>3145728.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>Eternal life</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>5.0</td>\n",
" <td>26</td>\n",
" <td>2.5M</td>\n",
" <td>1,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.6 and up</td>\n",
" <td>2621440.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>Dresses Ideas &amp; Fashions +3000</td>\n",
" <td>BEAUTY</td>\n",
" <td>4.5</td>\n",
" <td>473</td>\n",
" <td>8.2M</td>\n",
" <td>100,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Mature 17+</td>\n",
" <td>Beauty</td>\n",
" <td>1.6 and up</td>\n",
" <td>8598323.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>GO Notifier</td>\n",
" <td>COMMUNICATION</td>\n",
" <td>4.2</td>\n",
" <td>124346</td>\n",
" <td>695k</td>\n",
" <td>10,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Communication</td>\n",
" <td>2.0 and up</td>\n",
" <td>711680.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>Prosperity</td>\n",
" <td>EVENTS</td>\n",
" <td>5.0</td>\n",
" <td>16</td>\n",
" <td>2.3M</td>\n",
" <td>100+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Events</td>\n",
" <td>2.0 and up</td>\n",
" <td>2411724.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>NSE Mobile Trading</td>\n",
" <td>FINANCE</td>\n",
" <td>4.1</td>\n",
" <td>13868</td>\n",
" <td>1.4M</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Finance</td>\n",
" <td>2.1 and up</td>\n",
" <td>1468006.4</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
"execution_count": 381,
"metadata": {},
"output_type": "execute_result"
}
],
"execution_count": 381
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T13:28:40.682532800Z",
"start_time": "2026-04-25T13:28:40.678521Z"
}
},
"cell_type": "markdown",
"source": "# Part C",
"id": "9883e69704d0a69e"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.503091400Z",
"start_time": "2026-04-25T14:53:58.483650900Z"
}
},
"cell_type": "code",
"source": "df['Numeric Installs'] = df['Installs'].str.replace('+', '').str.replace(',', '').astype(int)",
"id": "c8d4f46526918c20",
"outputs": [],
"execution_count": 382
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.525317500Z",
"start_time": "2026-04-25T14:53:58.504718Z"
}
},
"cell_type": "code",
"source": "df.head(10)",
"id": "cffd24a82d242352",
"outputs": [
{
"data": {
"text/plain": [
" App Category Rating Reviews Size \\\n",
"0 Market Update Helper LIBRARIES_AND_DEMO 4.1 20145 11k \n",
"1 SuperLivePro BUSINESS 4.3 46353 21M \n",
"2 Wifi Connect Library LIBRARIES_AND_DEMO 3.9 58055 41k \n",
"3 Apk Installer LIBRARIES_AND_DEMO 3.8 7750 292k \n",
"4 English speaking texts EDUCATION 4.4 1619 3.0M \n",
"5 Eternal life LIBRARIES_AND_DEMO 5.0 26 2.5M \n",
"6 Dresses Ideas & Fashions +3000 BEAUTY 4.5 473 8.2M \n",
"7 GO Notifier COMMUNICATION 4.2 124346 695k \n",
"8 Prosperity EVENTS 5.0 16 2.3M \n",
"9 NSE Mobile Trading FINANCE 4.1 13868 1.4M \n",
"\n",
" Installs Type Price Content Rating Genres Android Ver \\\n",
"0 1,000,000+ Free 0 Everyone Libraries & Demo 1.5 and up \n",
"1 1,000,000+ Free 0 Everyone Business 1.5 and up \n",
"2 5,000,000+ Free 0 Everyone Libraries & Demo 1.5 and up \n",
"3 1,000,000+ Free 0 Everyone Libraries & Demo 1.6 and up \n",
"4 1,000,000+ Free 0 Everyone Education 1.6 and up \n",
"5 1,000+ Free 0 Everyone Libraries & Demo 1.6 and up \n",
"6 100,000+ Free 0 Mature 17+ Beauty 1.6 and up \n",
"7 10,000,000+ Free 0 Everyone Communication 2.0 and up \n",
"8 100+ Free 0 Everyone Events 2.0 and up \n",
"9 1,000,000+ Free 0 Everyone Finance 2.1 and up \n",
"\n",
" Size in bytes Numeric Installs \n",
"0 11264.0 1000000 \n",
"1 22020096.0 1000000 \n",
"2 41984.0 5000000 \n",
"3 299008.0 1000000 \n",
"4 3145728.0 1000000 \n",
"5 2621440.0 1000 \n",
"6 8598323.2 100000 \n",
"7 711680.0 10000000 \n",
"8 2411724.8 100 \n",
"9 1468006.4 1000000 "
],
"text/html": [
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>App</th>\n",
" <th>Category</th>\n",
" <th>Rating</th>\n",
" <th>Reviews</th>\n",
" <th>Size</th>\n",
" <th>Installs</th>\n",
" <th>Type</th>\n",
" <th>Price</th>\n",
" <th>Content Rating</th>\n",
" <th>Genres</th>\n",
" <th>Android Ver</th>\n",
" <th>Size in bytes</th>\n",
" <th>Numeric Installs</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>Market Update Helper</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>4.1</td>\n",
" <td>20145</td>\n",
" <td>11k</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.5 and up</td>\n",
" <td>11264.0</td>\n",
" <td>1000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>SuperLivePro</td>\n",
" <td>BUSINESS</td>\n",
" <td>4.3</td>\n",
" <td>46353</td>\n",
" <td>21M</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Business</td>\n",
" <td>1.5 and up</td>\n",
" <td>22020096.0</td>\n",
" <td>1000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>Wifi Connect Library</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>3.9</td>\n",
" <td>58055</td>\n",
" <td>41k</td>\n",
" <td>5,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.5 and up</td>\n",
" <td>41984.0</td>\n",
" <td>5000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>Apk Installer</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>3.8</td>\n",
" <td>7750</td>\n",
" <td>292k</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.6 and up</td>\n",
" <td>299008.0</td>\n",
" <td>1000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>English speaking texts</td>\n",
" <td>EDUCATION</td>\n",
" <td>4.4</td>\n",
" <td>1619</td>\n",
" <td>3.0M</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Education</td>\n",
" <td>1.6 and up</td>\n",
" <td>3145728.0</td>\n",
" <td>1000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>Eternal life</td>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>5.0</td>\n",
" <td>26</td>\n",
" <td>2.5M</td>\n",
" <td>1,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Libraries &amp; Demo</td>\n",
" <td>1.6 and up</td>\n",
" <td>2621440.0</td>\n",
" <td>1000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>Dresses Ideas &amp; Fashions +3000</td>\n",
" <td>BEAUTY</td>\n",
" <td>4.5</td>\n",
" <td>473</td>\n",
" <td>8.2M</td>\n",
" <td>100,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Mature 17+</td>\n",
" <td>Beauty</td>\n",
" <td>1.6 and up</td>\n",
" <td>8598323.2</td>\n",
" <td>100000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>GO Notifier</td>\n",
" <td>COMMUNICATION</td>\n",
" <td>4.2</td>\n",
" <td>124346</td>\n",
" <td>695k</td>\n",
" <td>10,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Communication</td>\n",
" <td>2.0 and up</td>\n",
" <td>711680.0</td>\n",
" <td>10000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>Prosperity</td>\n",
" <td>EVENTS</td>\n",
" <td>5.0</td>\n",
" <td>16</td>\n",
" <td>2.3M</td>\n",
" <td>100+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Events</td>\n",
" <td>2.0 and up</td>\n",
" <td>2411724.8</td>\n",
" <td>100</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>NSE Mobile Trading</td>\n",
" <td>FINANCE</td>\n",
" <td>4.1</td>\n",
" <td>13868</td>\n",
" <td>1.4M</td>\n",
" <td>1,000,000+</td>\n",
" <td>Free</td>\n",
" <td>0</td>\n",
" <td>Everyone</td>\n",
" <td>Finance</td>\n",
" <td>2.1 and up</td>\n",
" <td>1468006.4</td>\n",
" <td>1000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
"execution_count": 383,
"metadata": {},
"output_type": "execute_result"
}
],
"execution_count": 383
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Part D",
"id": "1818d3183dae5398"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.573387900Z",
"start_time": "2026-04-25T14:53:58.546001500Z"
}
},
"cell_type": "code",
"source": "df.to_csv('data/googleplaystore_new_new.csv', index=False)",
"id": "5a99edb9f8b29b12",
"outputs": [],
"execution_count": 384
},
{
"metadata": {},
"cell_type": "markdown",
"source": "# Part E",
"id": "5372c799c0b2662"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.580316100Z",
"start_time": "2026-04-25T14:53:58.575389500Z"
}
},
"cell_type": "code",
"source": [
"from sklearn.model_selection import train_test_split\n",
"from sklearn.linear_model import LinearRegression, Ridge\n",
"from sklearn.preprocessing import PolynomialFeatures\n",
"from sklearn.metrics import mean_absolute_error, mean_squared_error"
],
"id": "8cc741d5b19eaa62",
"outputs": [],
"execution_count": 385
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.591629700Z",
"start_time": "2026-04-25T14:53:58.583316400Z"
}
},
"cell_type": "code",
"source": "df_new = pd.read_csv('data/googleplaystore_new_new.csv')",
"id": "bc158bb312aa3cd7",
"outputs": [],
"execution_count": 386
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.607120700Z",
"start_time": "2026-04-25T14:53:58.591629700Z"
}
},
"cell_type": "code",
"source": [
"columns_to_keep = ['Category', 'Reviews', 'Content Rating', 'Size in bytes', 'Numeric Installs', 'Rating']\n",
"df_min = df_new[columns_to_keep]"
],
"id": "585677f9cc3efc16",
"outputs": [],
"execution_count": 387
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.628153200Z",
"start_time": "2026-04-25T14:53:58.608117200Z"
}
},
"cell_type": "code",
"source": "df_min.head(20)",
"id": "76760facf2a6e8cb",
"outputs": [
{
"data": {
"text/plain": [
" Category Reviews Content Rating Size in bytes \\\n",
"0 LIBRARIES_AND_DEMO 20145 Everyone 11264.0 \n",
"1 BUSINESS 46353 Everyone 22020096.0 \n",
"2 LIBRARIES_AND_DEMO 58055 Everyone 41984.0 \n",
"3 LIBRARIES_AND_DEMO 7750 Everyone 299008.0 \n",
"4 EDUCATION 1619 Everyone 3145728.0 \n",
"5 LIBRARIES_AND_DEMO 26 Everyone 2621440.0 \n",
"6 BEAUTY 473 Mature 17+ 8598323.2 \n",
"7 COMMUNICATION 124346 Everyone 711680.0 \n",
"8 EVENTS 16 Everyone 2411724.8 \n",
"9 FINANCE 13868 Everyone 1468006.4 \n",
"10 COMMUNICATION 32254 Everyone 5767168.0 \n",
"11 COMMUNICATION 125232 Everyone 2831155.2 \n",
"12 EDUCATION 430 Everyone 538624.0 \n",
"13 EDUCATION 275 Everyone 2411724.8 \n",
"14 BOOKS_AND_REFERENCE 1778 Mature 17+ 5138022.4 \n",
"15 BUSINESS 2287 Everyone 1572864.0 \n",
"16 LIBRARIES_AND_DEMO 126862 Everyone 638976.0 \n",
"17 COMMUNICATION 255 Everyone 1677721.6 \n",
"18 LIFESTYLE 360 Everyone 4823449.6 \n",
"19 EDUCATION 656 Everyone 569344.0 \n",
"\n",
" Numeric Installs Rating \n",
"0 1000000 4.1 \n",
"1 1000000 4.3 \n",
"2 5000000 3.9 \n",
"3 1000000 3.8 \n",
"4 1000000 4.4 \n",
"5 1000 5.0 \n",
"6 100000 4.5 \n",
"7 10000000 4.2 \n",
"8 100 5.0 \n",
"9 1000000 4.1 \n",
"10 1000000 4.4 \n",
"11 10000000 4.2 \n",
"12 10000 4.0 \n",
"13 50000 4.0 \n",
"14 500000 3.9 \n",
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"18 10000 4.1 \n",
"19 10000 4.3 "
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" <th>Numeric Installs</th>\n",
" <th>Rating</th>\n",
" </tr>\n",
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" <td>11264.0</td>\n",
" <td>1000000</td>\n",
" <td>4.1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>BUSINESS</td>\n",
" <td>46353</td>\n",
" <td>Everyone</td>\n",
" <td>22020096.0</td>\n",
" <td>1000000</td>\n",
" <td>4.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>58055</td>\n",
" <td>Everyone</td>\n",
" <td>41984.0</td>\n",
" <td>5000000</td>\n",
" <td>3.9</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>7750</td>\n",
" <td>Everyone</td>\n",
" <td>299008.0</td>\n",
" <td>1000000</td>\n",
" <td>3.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>EDUCATION</td>\n",
" <td>1619</td>\n",
" <td>Everyone</td>\n",
" <td>3145728.0</td>\n",
" <td>1000000</td>\n",
" <td>4.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>26</td>\n",
" <td>Everyone</td>\n",
" <td>2621440.0</td>\n",
" <td>1000</td>\n",
" <td>5.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>BEAUTY</td>\n",
" <td>473</td>\n",
" <td>Mature 17+</td>\n",
" <td>8598323.2</td>\n",
" <td>100000</td>\n",
" <td>4.5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>COMMUNICATION</td>\n",
" <td>124346</td>\n",
" <td>Everyone</td>\n",
" <td>711680.0</td>\n",
" <td>10000000</td>\n",
" <td>4.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>EVENTS</td>\n",
" <td>16</td>\n",
" <td>Everyone</td>\n",
" <td>2411724.8</td>\n",
" <td>100</td>\n",
" <td>5.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>FINANCE</td>\n",
" <td>13868</td>\n",
" <td>Everyone</td>\n",
" <td>1468006.4</td>\n",
" <td>1000000</td>\n",
" <td>4.1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>COMMUNICATION</td>\n",
" <td>32254</td>\n",
" <td>Everyone</td>\n",
" <td>5767168.0</td>\n",
" <td>1000000</td>\n",
" <td>4.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>COMMUNICATION</td>\n",
" <td>125232</td>\n",
" <td>Everyone</td>\n",
" <td>2831155.2</td>\n",
" <td>10000000</td>\n",
" <td>4.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>EDUCATION</td>\n",
" <td>430</td>\n",
" <td>Everyone</td>\n",
" <td>538624.0</td>\n",
" <td>10000</td>\n",
" <td>4.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>EDUCATION</td>\n",
" <td>275</td>\n",
" <td>Everyone</td>\n",
" <td>2411724.8</td>\n",
" <td>50000</td>\n",
" <td>4.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>BOOKS_AND_REFERENCE</td>\n",
" <td>1778</td>\n",
" <td>Mature 17+</td>\n",
" <td>5138022.4</td>\n",
" <td>500000</td>\n",
" <td>3.9</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>BUSINESS</td>\n",
" <td>2287</td>\n",
" <td>Everyone</td>\n",
" <td>1572864.0</td>\n",
" <td>1000000</td>\n",
" <td>4.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>LIBRARIES_AND_DEMO</td>\n",
" <td>126862</td>\n",
" <td>Everyone</td>\n",
" <td>638976.0</td>\n",
" <td>10000000</td>\n",
" <td>3.5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>COMMUNICATION</td>\n",
" <td>255</td>\n",
" <td>Everyone</td>\n",
" <td>1677721.6</td>\n",
" <td>10000</td>\n",
" <td>4.1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>LIFESTYLE</td>\n",
" <td>360</td>\n",
" <td>Everyone</td>\n",
" <td>4823449.6</td>\n",
" <td>10000</td>\n",
" <td>4.1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>EDUCATION</td>\n",
" <td>656</td>\n",
" <td>Everyone</td>\n",
" <td>569344.0</td>\n",
" <td>10000</td>\n",
" <td>4.3</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
"execution_count": 388,
"metadata": {},
"output_type": "execute_result"
}
],
"execution_count": 388
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.644258400Z",
"start_time": "2026-04-25T14:53:58.629151300Z"
}
},
"cell_type": "code",
"source": "df_encoded = pd.get_dummies(df_min, columns=['Category', 'Content Rating'])",
"id": "8c4742ab98b8b6ca",
"outputs": [],
"execution_count": 389
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.650381200Z",
"start_time": "2026-04-25T14:53:58.645767200Z"
}
},
"cell_type": "code",
"source": [
"X = df_encoded.drop('Rating', axis=1)\n",
"y = df_encoded['Rating']"
],
"id": "7faed3f843076351",
"outputs": [],
"execution_count": 390
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.668155500Z",
"start_time": "2026-04-25T14:53:58.652896500Z"
}
},
"cell_type": "code",
"source": "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=101)",
"id": "8646df724923b0f5",
"outputs": [],
"execution_count": 391
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Trying Linear Regression",
"id": "e52a65f09530a141"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.677596300Z",
"start_time": "2026-04-25T14:53:58.670162100Z"
}
},
"cell_type": "code",
"source": [
"linear_model = LinearRegression()\n",
"linear_model.fit(X_train, y_train)\n",
"y_hat_linear = linear_model.predict(X_test)"
],
"id": "db88942671bdf26a",
"outputs": [],
"execution_count": 392
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:57:40.714273700Z",
"start_time": "2026-04-25T14:57:40.674040700Z"
}
},
"cell_type": "code",
"source": "X_test",
"id": "32a5d474cc8ed681",
"outputs": [
{
"data": {
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" Reviews Size in bytes Numeric Installs Category_ART_AND_DESIGN \\\n",
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"... ... ... ... \n",
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"\n",
" Category_COMMUNICATION ... Category_GAME Category_HEALTH_AND_FITNESS \\\n",
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"... ... ... \n",
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"\n",
" Category_LIFESTYLE Content Rating_Adults only 18+ \\\n",
"303 False False \n",
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"352 False False \n",
"952 True False \n",
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"... ... ... \n",
"1096 False False \n",
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"\n",
" Content Rating_Everyone Content Rating_Everyone 10+ \\\n",
"303 True False \n",
"805 True False \n",
"352 True False \n",
"952 True False \n",
"514 True False \n",
"... ... ... \n",
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"551 False False \n",
"660 True False \n",
"655 True False \n",
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"\n",
" Content Rating_Mature 17+ Content Rating_Teen \n",
"303 False False \n",
"805 False False \n",
"352 False False \n",
"952 False False \n",
"514 False False \n",
"... ... ... \n",
"1096 True False \n",
"551 True False \n",
"660 False False \n",
"655 False False \n",
"473 False False \n",
"\n",
"[333 rows x 26 columns]"
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" <td>False</td>\n",
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]
},
"execution_count": 401,
"metadata": {},
"output_type": "execute_result"
}
],
"execution_count": 401
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.695046Z",
"start_time": "2026-04-25T14:53:58.677596300Z"
}
},
"cell_type": "code",
"source": [
"print(f\"Mean absolute error = {mean_absolute_error(y_test, y_hat_linear)}\")\n",
"print(f\"Root mean squared error = {np.sqrt(mean_squared_error(y_test, y_hat_linear))}\")"
],
"id": "12af54f4b3a1a88d",
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean absolute error = 0.28061256731153783\n",
"Root mean squared error = 0.38671187333256235\n"
]
}
],
"execution_count": 393
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.773436200Z",
"start_time": "2026-04-25T14:53:58.696048500Z"
}
},
"cell_type": "code",
"source": [
"residual_error = y_test - y_hat_linear\n",
"\n",
"plt.figure(figsize=(8,5))\n",
"plt.scatter(y_test, residual_error, alpha=0.5)\n",
"plt.axhline(y=0, color='r', linestyle='--') # Adds a red line at 0 error for reference\n",
"plt.title(\"Residual Error Plot (Linear Regression)\")\n",
"plt.xlabel(\"True Rating Values (y)\")\n",
"plt.ylabel(\"Residual Error (y - y_hat)\")\n",
"plt.show()"
],
"id": "8c3be82a8033d876",
"outputs": [
{
"data": {
"text/plain": [
"<Figure size 800x500 with 1 Axes>"
],
"image/png": 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"
},
"metadata": {},
"output_type": "display_data",
"jetTransient": {
"display_id": null
}
}
],
"execution_count": 394
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Trying Polynomial Regression",
"id": "28a6926de3a1a2e7"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.782476500Z",
"start_time": "2026-04-25T14:53:58.774436300Z"
}
},
"cell_type": "code",
"source": [
"poly_converter = PolynomialFeatures(degree=2)\n",
"X_poly = poly_converter.fit_transform(X)"
],
"id": "b867289f4b8dd0ae",
"outputs": [],
"execution_count": 395
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.787833400Z",
"start_time": "2026-04-25T14:53:58.782476500Z"
}
},
"cell_type": "code",
"source": "X_train_p, X_test_p, y_train_p, y_test_p = train_test_split(X_poly, y, test_size=0.3, random_state=101)",
"id": "cf11946087afa62f",
"outputs": [],
"execution_count": 396
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.819419400Z",
"start_time": "2026-04-25T14:53:58.788835500Z"
}
},
"cell_type": "code",
"source": [
"poly_model = LinearRegression()\n",
"poly_model.fit(X_train_p, y_train_p)\n",
"y_hat_poly = poly_model.predict(X_test_p)"
],
"id": "61b135564e36f71d",
"outputs": [],
"execution_count": 397
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.835519700Z",
"start_time": "2026-04-25T14:53:58.820414Z"
}
},
"cell_type": "code",
"source": [
"print(f\"Mean absolute error = {mean_absolute_error(y_test_p, y_hat_poly)}\")\n",
"print(f\"Root mean squared error = {np.sqrt(mean_squared_error(y_test_p, y_hat_poly))}\")\n"
],
"id": "bfd534c1abda8530",
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean absolute error = 0.29501714163585174\n",
"Root mean squared error = 0.4157783198958284\n"
]
}
],
"execution_count": 398
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T14:53:58.840547200Z",
"start_time": "2026-04-25T14:53:58.836521600Z"
}
},
"cell_type": "markdown",
"source": [
"### Model Performance Results:\n",
"\n",
"Linear Regression: `MAE = 0.2806 | RMSE = 0.3867`\n",
"\n",
"Polynomial Regression: `MAE = 0.2950 | RMSE = 0.4158`\n",
"\n",
"This shows that the Linear Regression model performed better than the Polynomial Regression model in terms of both MAE and RMSE, indicating that the linear model is a better fit for this dataset. The residual error plot for the linear model also suggests that there are no clear patterns in the residuals, which is a good sign for the model's performance. This means that for this particular case, handling the rating predictions with a linear regression model would be better due to its lower error rate as compared to the polynomial regression model.\n"
],
"id": "eaefa3aed2214793"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Part F",
"id": "3c89e2f8ae31de3b"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T15:14:41.668654900Z",
"start_time": "2026-04-25T15:14:41.650113100Z"
}
},
"cell_type": "code",
"source": "features_to_test = ['Reviews', 'Size in bytes', 'Numeric Installs']",
"id": "ab09192a122e6e8f",
"outputs": [],
"execution_count": 404
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T15:15:26.186132400Z",
"start_time": "2026-04-25T15:15:26.176807100Z"
}
},
"cell_type": "code",
"source": [
"for feature in features_to_test:\n",
" X_single = df_encoded[[feature]]"
],
"id": "3f65e25b63cc8e93",
"outputs": [],
"execution_count": 407
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T15:15:37.813266600Z",
"start_time": "2026-04-25T15:15:37.797080500Z"
}
},
"cell_type": "code",
"source": "X_train_s, X_test_s, y_train_s, y_test_s = train_test_split(X_single, y, test_size=0.3, random_state=101)",
"id": "213bcc196f94054d",
"outputs": [],
"execution_count": 408
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T15:15:59.633576900Z",
"start_time": "2026-04-25T15:15:59.612227200Z"
}
},
"cell_type": "code",
"source": [
"simple_model = LinearRegression()\n",
"simple_model.fit(X_train_s, y_train_s)"
],
"id": "75e6c5289568ef2f",
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression()"
],
"text/html": [
"<style>#sk-container-id-1 {\n",
" /* Definition of color scheme common for light and dark mode */\n",
" --sklearn-color-text: #000;\n",
" --sklearn-color-text-muted: #666;\n",
" --sklearn-color-line: gray;\n",
" /* Definition of color scheme for unfitted estimators */\n",
" --sklearn-color-unfitted-level-0: #fff5e6;\n",
" --sklearn-color-unfitted-level-1: #f6e4d2;\n",
" --sklearn-color-unfitted-level-2: #ffe0b3;\n",
" --sklearn-color-unfitted-level-3: chocolate;\n",
" /* Definition of color scheme for fitted estimators */\n",
" --sklearn-color-fitted-level-0: #f0f8ff;\n",
" --sklearn-color-fitted-level-1: #d4ebff;\n",
" --sklearn-color-fitted-level-2: #b3dbfd;\n",
" --sklearn-color-fitted-level-3: cornflowerblue;\n",
"}\n",
"\n",
"#sk-container-id-1.light {\n",
" /* Specific color for light theme */\n",
" --sklearn-color-text-on-default-background: black;\n",
" --sklearn-color-background: white;\n",
" --sklearn-color-border-box: black;\n",
" --sklearn-color-icon: #696969;\n",
"}\n",
"\n",
"#sk-container-id-1.dark {\n",
" --sklearn-color-text-on-default-background: white;\n",
" --sklearn-color-background: #111;\n",
" --sklearn-color-border-box: white;\n",
" --sklearn-color-icon: #878787;\n",
"}\n",
"\n",
"#sk-container-id-1 {\n",
" color: var(--sklearn-color-text);\n",
"}\n",
"\n",
"#sk-container-id-1 pre {\n",
" padding: 0;\n",
"}\n",
"\n",
"#sk-container-id-1 input.sk-hidden--visually {\n",
" border: 0;\n",
" clip: rect(1px 1px 1px 1px);\n",
" clip: rect(1px, 1px, 1px, 1px);\n",
" height: 1px;\n",
" margin: -1px;\n",
" overflow: hidden;\n",
" padding: 0;\n",
" position: absolute;\n",
" width: 1px;\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-dashed-wrapped {\n",
" border: 1px dashed var(--sklearn-color-line);\n",
" margin: 0 0.4em 0.5em 0.4em;\n",
" box-sizing: border-box;\n",
" padding-bottom: 0.4em;\n",
" background-color: var(--sklearn-color-background);\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-container {\n",
" /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
" but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
" so we also need the `!important` here to be able to override the\n",
" default hidden behavior on the sphinx rendered scikit-learn.org.\n",
" See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
" display: inline-block !important;\n",
" position: relative;\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-text-repr-fallback {\n",
" display: none;\n",
"}\n",
"\n",
"div.sk-parallel-item,\n",
"div.sk-serial,\n",
"div.sk-item {\n",
" /* draw centered vertical line to link estimators */\n",
" background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
" background-size: 2px 100%;\n",
" background-repeat: no-repeat;\n",
" background-position: center center;\n",
"}\n",
"\n",
"/* Parallel-specific style estimator block */\n",
"\n",
"#sk-container-id-1 div.sk-parallel-item::after {\n",
" content: \"\";\n",
" width: 100%;\n",
" border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
" flex-grow: 1;\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-parallel {\n",
" display: flex;\n",
" align-items: stretch;\n",
" justify-content: center;\n",
" background-color: var(--sklearn-color-background);\n",
" position: relative;\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-parallel-item {\n",
" display: flex;\n",
" flex-direction: column;\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
" align-self: flex-end;\n",
" width: 50%;\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
" align-self: flex-start;\n",
" width: 50%;\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
" width: 0;\n",
"}\n",
"\n",
"/* Serial-specific style estimator block */\n",
"\n",
"#sk-container-id-1 div.sk-serial {\n",
" display: flex;\n",
" flex-direction: column;\n",
" align-items: center;\n",
" background-color: var(--sklearn-color-background);\n",
" padding-right: 1em;\n",
" padding-left: 1em;\n",
"}\n",
"\n",
"\n",
"/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
"clickable and can be expanded/collapsed.\n",
"- Pipeline and ColumnTransformer use this feature and define the default style\n",
"- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
"*/\n",
"\n",
"/* Pipeline and ColumnTransformer style (default) */\n",
"\n",
"#sk-container-id-1 div.sk-toggleable {\n",
" /* Default theme specific background. It is overwritten whether we have a\n",
" specific estimator or a Pipeline/ColumnTransformer */\n",
" background-color: var(--sklearn-color-background);\n",
"}\n",
"\n",
"/* Toggleable label */\n",
"#sk-container-id-1 label.sk-toggleable__label {\n",
" cursor: pointer;\n",
" display: flex;\n",
" width: 100%;\n",
" margin-bottom: 0;\n",
" padding: 0.5em;\n",
" box-sizing: border-box;\n",
" text-align: center;\n",
" align-items: center;\n",
" justify-content: center;\n",
" gap: 0.5em;\n",
"}\n",
"\n",
"#sk-container-id-1 label.sk-toggleable__label .caption {\n",
" font-size: 0.6rem;\n",
" font-weight: lighter;\n",
" color: var(--sklearn-color-text-muted);\n",
"}\n",
"\n",
"#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
" /* Arrow on the left of the label */\n",
" content: \"▸\";\n",
" float: left;\n",
" margin-right: 0.25em;\n",
" color: var(--sklearn-color-icon);\n",
"}\n",
"\n",
"#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
" color: var(--sklearn-color-text);\n",
"}\n",
"\n",
"/* Toggleable content - dropdown */\n",
"\n",
"#sk-container-id-1 div.sk-toggleable__content {\n",
" display: none;\n",
" text-align: left;\n",
" /* unfitted */\n",
" background-color: var(--sklearn-color-unfitted-level-0);\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
" /* fitted */\n",
" background-color: var(--sklearn-color-fitted-level-0);\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-toggleable__content pre {\n",
" margin: 0.2em;\n",
" border-radius: 0.25em;\n",
" color: var(--sklearn-color-text);\n",
" /* unfitted */\n",
" background-color: var(--sklearn-color-unfitted-level-0);\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
" /* unfitted */\n",
" background-color: var(--sklearn-color-fitted-level-0);\n",
"}\n",
"\n",
"#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
" /* Expand drop-down */\n",
" display: block;\n",
" width: 100%;\n",
" overflow: visible;\n",
"}\n",
"\n",
"#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
" content: \"▾\";\n",
"}\n",
"\n",
"/* Pipeline/ColumnTransformer-specific style */\n",
"\n",
"#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
" color: var(--sklearn-color-text);\n",
" background-color: var(--sklearn-color-unfitted-level-2);\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
" background-color: var(--sklearn-color-fitted-level-2);\n",
"}\n",
"\n",
"/* Estimator-specific style */\n",
"\n",
"/* Colorize estimator box */\n",
"#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
" /* unfitted */\n",
" background-color: var(--sklearn-color-unfitted-level-2);\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
" /* fitted */\n",
" background-color: var(--sklearn-color-fitted-level-2);\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
"#sk-container-id-1 div.sk-label label {\n",
" /* The background is the default theme color */\n",
" color: var(--sklearn-color-text-on-default-background);\n",
"}\n",
"\n",
"/* On hover, darken the color of the background */\n",
"#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
" color: var(--sklearn-color-text);\n",
" background-color: var(--sklearn-color-unfitted-level-2);\n",
"}\n",
"\n",
"/* Label box, darken color on hover, fitted */\n",
"#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
" color: var(--sklearn-color-text);\n",
" background-color: var(--sklearn-color-fitted-level-2);\n",
"}\n",
"\n",
"/* Estimator label */\n",
"\n",
"#sk-container-id-1 div.sk-label label {\n",
" font-family: monospace;\n",
" font-weight: bold;\n",
" line-height: 1.2em;\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-label-container {\n",
" text-align: center;\n",
"}\n",
"\n",
"/* Estimator-specific */\n",
"#sk-container-id-1 div.sk-estimator {\n",
" font-family: monospace;\n",
" border: 1px dotted var(--sklearn-color-border-box);\n",
" border-radius: 0.25em;\n",
" box-sizing: border-box;\n",
" margin-bottom: 0.5em;\n",
" /* unfitted */\n",
" background-color: var(--sklearn-color-unfitted-level-0);\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-estimator.fitted {\n",
" /* fitted */\n",
" background-color: var(--sklearn-color-fitted-level-0);\n",
"}\n",
"\n",
"/* on hover */\n",
"#sk-container-id-1 div.sk-estimator:hover {\n",
" /* unfitted */\n",
" background-color: var(--sklearn-color-unfitted-level-2);\n",
"}\n",
"\n",
"#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
" /* fitted */\n",
" background-color: var(--sklearn-color-fitted-level-2);\n",
"}\n",
"\n",
"/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
"\n",
"/* Common style for \"i\" and \"?\" */\n",
"\n",
".sk-estimator-doc-link,\n",
"a:link.sk-estimator-doc-link,\n",
"a:visited.sk-estimator-doc-link {\n",
" float: right;\n",
" font-size: smaller;\n",
" line-height: 1em;\n",
" font-family: monospace;\n",
" background-color: var(--sklearn-color-unfitted-level-0);\n",
" border-radius: 1em;\n",
" height: 1em;\n",
" width: 1em;\n",
" text-decoration: none !important;\n",
" margin-left: 0.5em;\n",
" text-align: center;\n",
" /* unfitted */\n",
" border: var(--sklearn-color-unfitted-level-3) 1pt solid;\n",
" color: var(--sklearn-color-unfitted-level-3);\n",
"}\n",
"\n",
".sk-estimator-doc-link.fitted,\n",
"a:link.sk-estimator-doc-link.fitted,\n",
"a:visited.sk-estimator-doc-link.fitted {\n",
" /* fitted */\n",
" background-color: var(--sklearn-color-fitted-level-0);\n",
" border: var(--sklearn-color-fitted-level-3) 1pt solid;\n",
" color: var(--sklearn-color-fitted-level-3);\n",
"}\n",
"\n",
"/* On hover */\n",
"div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
".sk-estimator-doc-link:hover,\n",
"div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
".sk-estimator-doc-link:hover {\n",
" /* unfitted */\n",
" background-color: var(--sklearn-color-unfitted-level-3);\n",
" border: var(--sklearn-color-fitted-level-0) 1pt solid;\n",
" color: var(--sklearn-color-unfitted-level-0);\n",
" text-decoration: none;\n",
"}\n",
"\n",
"div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
".sk-estimator-doc-link.fitted:hover,\n",
"div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
".sk-estimator-doc-link.fitted:hover {\n",
" /* fitted */\n",
" background-color: var(--sklearn-color-fitted-level-3);\n",
" border: var(--sklearn-color-fitted-level-0) 1pt solid;\n",
" color: var(--sklearn-color-fitted-level-0);\n",
" text-decoration: none;\n",
"}\n",
"\n",
"/* Span, style for the box shown on hovering the info icon */\n",
".sk-estimator-doc-link span {\n",
" display: none;\n",
" z-index: 9999;\n",
" position: relative;\n",
" font-weight: normal;\n",
" right: .2ex;\n",
" padding: .5ex;\n",
" margin: .5ex;\n",
" width: min-content;\n",
" min-width: 20ex;\n",
" max-width: 50ex;\n",
" color: var(--sklearn-color-text);\n",
" box-shadow: 2pt 2pt 4pt #999;\n",
" /* unfitted */\n",
" background: var(--sklearn-color-unfitted-level-0);\n",
" border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
"}\n",
"\n",
".sk-estimator-doc-link.fitted span {\n",
" /* fitted */\n",
" background: var(--sklearn-color-fitted-level-0);\n",
" border: var(--sklearn-color-fitted-level-3);\n",
"}\n",
"\n",
".sk-estimator-doc-link:hover span {\n",
" display: block;\n",
"}\n",
"\n",
"/* \"?\"-specific style due to the `<a>` HTML tag */\n",
"\n",
"#sk-container-id-1 a.estimator_doc_link {\n",
" float: right;\n",
" font-size: 1rem;\n",
" line-height: 1em;\n",
" font-family: monospace;\n",
" background-color: var(--sklearn-color-unfitted-level-0);\n",
" border-radius: 1rem;\n",
" height: 1rem;\n",
" width: 1rem;\n",
" text-decoration: none;\n",
" /* unfitted */\n",
" color: var(--sklearn-color-unfitted-level-1);\n",
" border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
"}\n",
"\n",
"#sk-container-id-1 a.estimator_doc_link.fitted {\n",
" /* fitted */\n",
" background-color: var(--sklearn-color-fitted-level-0);\n",
" border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
" color: var(--sklearn-color-fitted-level-1);\n",
"}\n",
"\n",
"/* On hover */\n",
"#sk-container-id-1 a.estimator_doc_link:hover {\n",
" /* unfitted */\n",
" background-color: var(--sklearn-color-unfitted-level-3);\n",
" color: var(--sklearn-color-background);\n",
" text-decoration: none;\n",
"}\n",
"\n",
"#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
" /* fitted */\n",
" background-color: var(--sklearn-color-fitted-level-3);\n",
"}\n",
"\n",
".estimator-table {\n",
" font-family: monospace;\n",
"}\n",
"\n",
".estimator-table summary {\n",
" padding: .5rem;\n",
" cursor: pointer;\n",
"}\n",
"\n",
".estimator-table summary::marker {\n",
" font-size: 0.7rem;\n",
"}\n",
"\n",
".estimator-table details[open] {\n",
" padding-left: 0.1rem;\n",
" padding-right: 0.1rem;\n",
" padding-bottom: 0.3rem;\n",
"}\n",
"\n",
".estimator-table .parameters-table {\n",
" margin-left: auto !important;\n",
" margin-right: auto !important;\n",
" margin-top: 0;\n",
"}\n",
"\n",
".estimator-table .parameters-table tr:nth-child(odd) {\n",
" background-color: #fff;\n",
"}\n",
"\n",
".estimator-table .parameters-table tr:nth-child(even) {\n",
" background-color: #f6f6f6;\n",
"}\n",
"\n",
".estimator-table .parameters-table tr:hover {\n",
" background-color: #e0e0e0;\n",
"}\n",
"\n",
".estimator-table table td {\n",
" border: 1px solid rgba(106, 105, 104, 0.232);\n",
"}\n",
"\n",
"/*\n",
" `table td`is set in notebook with right text-align.\n",
" We need to overwrite it.\n",
"*/\n",
".estimator-table table td.param {\n",
" text-align: left;\n",
" position: relative;\n",
" padding: 0;\n",
"}\n",
"\n",
".user-set td {\n",
" color:rgb(255, 94, 0);\n",
" text-align: left !important;\n",
"}\n",
"\n",
".user-set td.value {\n",
" color:rgb(255, 94, 0);\n",
" background-color: transparent;\n",
"}\n",
"\n",
".default td {\n",
" color: black;\n",
" text-align: left !important;\n",
"}\n",
"\n",
".user-set td i,\n",
".default td i {\n",
" color: black;\n",
"}\n",
"\n",
"/*\n",
" Styles for parameter documentation links\n",
" We need styling for visited so jupyter doesn't overwrite it\n",
"*/\n",
"a.param-doc-link,\n",
"a.param-doc-link:link,\n",
"a.param-doc-link:visited {\n",
" text-decoration: underline dashed;\n",
" text-underline-offset: .3em;\n",
" color: inherit;\n",
" display: block;\n",
" padding: .5em;\n",
"}\n",
"\n",
"/* \"hack\" to make the entire area of the cell containing the link clickable */\n",
"a.param-doc-link::before {\n",
" position: absolute;\n",
" content: \"\";\n",
" inset: 0;\n",
"}\n",
"\n",
".param-doc-description {\n",
" display: none;\n",
" position: absolute;\n",
" z-index: 9999;\n",
" left: 0;\n",
" padding: .5ex;\n",
" margin-left: 1.5em;\n",
" color: var(--sklearn-color-text);\n",
" box-shadow: .3em .3em .4em #999;\n",
" width: max-content;\n",
" text-align: left;\n",
" max-height: 10em;\n",
" overflow-y: auto;\n",
"\n",
" /* unfitted */\n",
" background: var(--sklearn-color-unfitted-level-0);\n",
" border: thin solid var(--sklearn-color-unfitted-level-3);\n",
"}\n",
"\n",
"/* Fitted state for parameter tooltips */\n",
".fitted .param-doc-description {\n",
" /* fitted */\n",
" background: var(--sklearn-color-fitted-level-0);\n",
" border: thin solid var(--sklearn-color-fitted-level-3);\n",
"}\n",
"\n",
".param-doc-link:hover .param-doc-description {\n",
" display: block;\n",
"}\n",
"\n",
".copy-paste-icon {\n",
" background-image: url(data:image/svg+xml;base64,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);\n",
" background-repeat: no-repeat;\n",
" background-size: 14px 14px;\n",
" background-position: 0;\n",
" display: inline-block;\n",
" width: 14px;\n",
" height: 14px;\n",
" cursor: pointer;\n",
"}\n",
"</style><body><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>LinearRegression</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\" data-param-prefix=\"\">\n",
" <div class=\"estimator-table\">\n",
" <details>\n",
" <summary>Parameters</summary>\n",
" <table class=\"parameters-table\">\n",
" <tbody>\n",
" \n",
" <tr class=\"default\">\n",
" <td><i class=\"copy-paste-icon\"\n",
" onclick=\"copyToClipboard('fit_intercept',\n",
" this.parentElement.nextElementSibling)\"\n",
" ></i></td>\n",
" <td class=\"param\">\n",
" <a class=\"param-doc-link\"\n",
" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LinearRegression.html#:~:text=fit_intercept,-bool%2C%20default%3DTrue\">\n",
" fit_intercept\n",
" <span class=\"param-doc-description\">fit_intercept: bool, default=True<br><br>Whether to calculate the intercept for this model. If set<br>to False, no intercept will be used in calculations<br>(i.e. data is expected to be centered).</span>\n",
" </a>\n",
" </td>\n",
" <td class=\"value\">True</td>\n",
" </tr>\n",
" \n",
"\n",
" <tr class=\"default\">\n",
" <td><i class=\"copy-paste-icon\"\n",
" onclick=\"copyToClipboard('copy_X',\n",
" this.parentElement.nextElementSibling)\"\n",
" ></i></td>\n",
" <td class=\"param\">\n",
" <a class=\"param-doc-link\"\n",
" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LinearRegression.html#:~:text=copy_X,-bool%2C%20default%3DTrue\">\n",
" copy_X\n",
" <span class=\"param-doc-description\">copy_X: bool, default=True<br><br>If True, X will be copied; else, it may be overwritten.</span>\n",
" </a>\n",
" </td>\n",
" <td class=\"value\">True</td>\n",
" </tr>\n",
" \n",
"\n",
" <tr class=\"default\">\n",
" <td><i class=\"copy-paste-icon\"\n",
" onclick=\"copyToClipboard('tol',\n",
" this.parentElement.nextElementSibling)\"\n",
" ></i></td>\n",
" <td class=\"param\">\n",
" <a class=\"param-doc-link\"\n",
" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LinearRegression.html#:~:text=tol,-float%2C%20default%3D1e-6\">\n",
" tol\n",
" <span class=\"param-doc-description\">tol: float, default=1e-6<br><br>The precision of the solution (`coef_`) is determined by `tol` which<br>specifies a different convergence criterion for the `lsqr` solver.<br>`tol` is set as `atol` and `btol` of :func:`scipy.sparse.linalg.lsqr` when<br>fitting on sparse training data. This parameter has no effect when fitting<br>on dense data.<br><br>.. versionadded:: 1.7</span>\n",
" </a>\n",
" </td>\n",
" <td class=\"value\">1e-06</td>\n",
" </tr>\n",
" \n",
"\n",
" <tr class=\"default\">\n",
" <td><i class=\"copy-paste-icon\"\n",
" onclick=\"copyToClipboard('n_jobs',\n",
" this.parentElement.nextElementSibling)\"\n",
" ></i></td>\n",
" <td class=\"param\">\n",
" <a class=\"param-doc-link\"\n",
" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LinearRegression.html#:~:text=n_jobs,-int%2C%20default%3DNone\">\n",
" n_jobs\n",
" <span class=\"param-doc-description\">n_jobs: int, default=None<br><br>The number of jobs to use for the computation. This will only provide<br>speedup in case of sufficiently large problems, that is if firstly<br>`n_targets > 1` and secondly `X` is sparse or if `positive` is set<br>to `True`. ``None`` means 1 unless in a<br>:obj:`joblib.parallel_backend` context. ``-1`` means using all<br>processors. See :term:`Glossary <n_jobs>` for more details.</span>\n",
" </a>\n",
" </td>\n",
" <td class=\"value\">None</td>\n",
" </tr>\n",
" \n",
"\n",
" <tr class=\"default\">\n",
" <td><i class=\"copy-paste-icon\"\n",
" onclick=\"copyToClipboard('positive',\n",
" this.parentElement.nextElementSibling)\"\n",
" ></i></td>\n",
" <td class=\"param\">\n",
" <a class=\"param-doc-link\"\n",
" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LinearRegression.html#:~:text=positive,-bool%2C%20default%3DFalse\">\n",
" positive\n",
" <span class=\"param-doc-description\">positive: bool, default=False<br><br>When set to ``True``, forces the coefficients to be positive. This<br>option is only supported for dense arrays.<br><br>For a comparison between a linear regression model with positive constraints<br>on the regression coefficients and a linear regression without such constraints,<br>see :ref:`sphx_glr_auto_examples_linear_model_plot_nnls.py`.<br><br>.. versionadded:: 0.24</span>\n",
" </a>\n",
" </td>\n",
" <td class=\"value\">False</td>\n",
" </tr>\n",
" \n",
" </tbody>\n",
" </table>\n",
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},
"execution_count": 409,
"metadata": {},
"output_type": "execute_result"
}
],
"execution_count": 409
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T15:16:10.648492700Z",
"start_time": "2026-04-25T15:16:10.630533500Z"
}
},
"cell_type": "code",
"source": [
"y_pred_s = simple_model.predict(X_test_s)\n",
"rmse = np.sqrt(mean_squared_error(y_test_s, y_pred_s))"
],
"id": "983db24d45054c97",
"outputs": [],
"execution_count": 410
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-04-25T15:16:25.585898300Z",
"start_time": "2026-04-25T15:16:25.549110800Z"
}
},
"cell_type": "code",
"source": "print(f\"RMSE using ONLY '{feature}': {rmse}\")",
"id": "4cb7c407238e67c1",
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"RMSE using ONLY 'Numeric Installs': 0.4179032096419041\n"
]
}
],
"execution_count": 411
},
{
"metadata": {},
"cell_type": "code",
"outputs": [],
"execution_count": null,
"source": "",
"id": "79c525159dd03465"
}
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