Problem statement:

Suppose you are the CEO of a restaurant franchise and are considering different cities for opening a new outlet.

• You would like to expand your business to cities that may give your restaurant higher profits.
• The chain already has restaurants in various cities and you have data for profits and populations from the cities.
• You also have data on cities that are candidates for a new restaurant.
  • For these cities, you have the city population.

Can you use the data to help you identify which cities may potentially give your business higher profits?

Dataset:

You will start by loading the dataset for this task.

• The load_data() function shown below loads the data into variables x_train and y_train
  • x_train is the population of a city
  • y_train is the profit of a restaurant in that city. A negative value for profit indicates a loss.
  • Both X_train and y_train are numpy arrays.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import copy
import math

# Given training data
x_train = np.array([ 6.1101,  5.5277,  8.5186,  7.0032,  5.8598,  8.3829,  7.4764,
        8.5781,  6.4862,  5.0546,  5.7107, 14.164 ,  5.734 ,  8.4084,
        5.6407,  5.3794,  6.3654,  5.1301,  6.4296,  7.0708,  6.1891,
       20.27  ,  5.4901,  6.3261,  5.5649, 18.945 , 12.828 , 10.957 ,
       13.176 , 22.203 ,  5.2524,  6.5894,  9.2482,  5.8918,  8.2111,
        7.9334,  8.0959,  5.6063, 12.836 ,  6.3534,  5.4069,  6.8825,
       11.708 ,  5.7737,  7.8247,  7.0931,  5.0702,  5.8014, 11.7   ,
        5.5416,  7.5402,  5.3077,  7.4239,  7.6031,  6.3328,  6.3589,
        6.2742,  5.6397,  9.3102,  9.4536,  8.8254,  5.1793, 21.279 ,
       14.908 , 18.959 ,  7.2182,  8.2951, 10.236 ,  5.4994, 20.341 ,
       10.136 ,  7.3345,  6.0062,  7.2259,  5.0269,  6.5479,  7.5386,
        5.0365, 10.274 ,  5.1077,  5.7292,  5.1884,  6.3557,  9.7687,
        6.5159,  8.5172,  9.1802,  6.002 ,  5.5204,  5.0594,  5.7077,
        7.6366,  5.8707,  5.3054,  8.2934, 13.394 ,  5.4369])

y_train = np.array([17.592  ,  9.1302 , 13.662  , 11.854  ,  6.8233 , 11.886  ,
        4.3483 , 12.     ,  6.5987 ,  3.8166 ,  3.2522 , 15.505  ,
        3.1551 ,  7.2258 ,  0.71618,  3.5129 ,  5.3048 ,  0.56077,
        3.6518 ,  5.3893 ,  3.1386 , 21.767  ,  4.263  ,  5.1875 ,
        3.0825 , 22.638  , 13.501  ,  7.0467 , 14.692  , 24.147  ,
       -1.22   ,  5.9966 , 12.134  ,  1.8495 ,  6.5426 ,  4.5623 ,
        4.1164 ,  3.3928 , 10.117  ,  5.4974 ,  0.55657,  3.9115 ,
        5.3854 ,  2.4406 ,  6.7318 ,  1.0463 ,  5.1337 ,  1.844  ,
        8.0043 ,  1.0179 ,  6.7504 ,  1.8396 ,  4.2885 ,  4.9981 ,
        1.4233 , -1.4211 ,  2.4756 ,  4.6042 ,  3.9624 ,  5.4141 ,
        5.1694 , -0.74279, 17.929  , 12.054  , 17.054  ,  4.8852 ,
        5.7442 ,  7.7754 ,  1.0173 , 20.992  ,  6.6799 ,  4.0259 ,
        1.2784 ,  3.3411 , -2.6807 ,  0.29678,  3.8845 ,  5.7014 ,
        6.7526 ,  2.0576 ,  0.47953,  0.20421,  0.67861,  7.5435 ,
        5.3436 ,  4.2415 ,  6.7981 ,  0.92695,  0.152  ,  2.8214 ,
        1.8451 ,  4.2959 ,  7.2029 ,  1.9869 ,  0.14454,  9.0551 ,
        0.61705])

# Create DataFrame for better visualization
train_data = pd.DataFrame({'Population (x10,000)': x_train, 'Profit ($10,000)': y_train})

# Display the data
print(train_data.head())

   Population (x10,000)  Profit ($10,000)
0                6.1101           17.5920
1                5.5277            9.1302
2                8.5186           13.6620
3                7.0032           11.8540
4                5.8598            6.8233

View the variables:

print ('The shape of x_train is:', x_train.shape)
print ('The shape of y_train is: ', y_train.shape)
print ('Number of training examples (m):', len(x_train))

The shape of x_train is: (97,)
The shape of y_train is:  (97,)
Number of training examples (m): 97

x_train is a numpy array that contains decimal values that are all greater than zero.

• These values represent the city population times 10,000
• For example, 6.1101 means that the population for that city is 61,101

Similarly, y_train is a numpy array that has decimal values, some negative, some positive.

• These represent your restaurant's average monthly profits in each city, in units of $10,000.
  • For example, 17.592 represents $175,920 in average monthly profits for that city.
  • 2.6807 represents -$26,807 in average monthly loss for that city.