ISE529 Module 2 Homework Solution

ISE-529 Predictive Analytics
1. Evaluating regression functions
1A) The file "HW 2 Problem 1 Data.xlsx" contains two datasets - training and test in two different spreadsheet tabs. Read the tables into two dataframes (training_data and test_data) and display the first 10 rows of each dataframe. Hint - look up the Pandas function for reading in Excel files.
In [136… import pandas;

train_df = pandas.read_excel("HW 2 Problem 1 Data.xlsx", sheet_name = "Training Data"); test_df = pandas.read_excel("HW 2 Problem 1 Data.xlsx", sheet_name = "Test Data");
In [137… print("Training Data"); print(train_df.head(10)); print("Test Data"); print(test_df.head(10));
Training Data
X Y
0 61 17661.067682 1 87 15482.455058
2 38 17444.767982
3 6 -4270.225550
4 54 8075.733045 5 29 16820.129406
6 77 23921.367914
7 70 16541.631267
8 21 4425.240897
9 76 30681.044509 Test Data
X Y
0 36 15986.579536 1 64 -2761.487999
2 66 9752.039830
3 88 20038.697197
4 4 -13421.192312 5 80 6644.121448
6 22 -10124.906855
7 85 21502.561217
8 63 12105.189261
9 8 -12161.603294
1b) Using Seaborn, create scatterplots of the two dataframes. For full credit, include a title ("Training Data" and "Test Data") for the two scatterplots.
In [138… import seaborn;
seaborn.scatterplot(data = train_df, x = "X", y = "Y").set(title = "Training Data");

seaborn.scatterplot(data = test_df, x = "X", y = "Y").set(title = "Test Data");
In [139…

1c) Now, we are going to calculate the test and training MSEs for three different candidate regression models:
F1: 300x − 4280
F2: 3.37x2 − 36.8x + 1220
F3: 0.1x3 − 12x2 + 590x − 3600
Create three functions for these three candidate models - f1(), f2(), and f3(). They should take as an input x and return the predicted value of y corresponding to that input:
def f1(x): return 300 * x - 4280;

def f2(x): return 3.37 * pow(x, 2) - 36.8 * x + 1220;

def f3(x): return 0.1 * pow(x, 3) - 12 * pow(x, 2) + 590 * x - 3600;
In [140…
In [141…
In [142…
1d) Now, write a function calc_mse() that takes three parameter inputs:
x - an array (or Pandas series) of predictor X values y - an array (or Pandas series) of response Y values f - a function to be called for each value of the x and y arrays
The function should calculate the MSE for the function f using the x and y data arrays
def calc_mse(x_list, true_y_list, f):
mse = 0; for idx in range(len(x_list)): expect_y = f(x_list[idx]);
mse += pow(true_y_list[idx] - expect_y, 2); mse /= len(x_list); return mse;
In [143…
1e) Call this calc_mse function six times to calculate the training and test MSE for each of the three models:
In [144… print(calc_mse(train_df["X"].tolist(), train_df["Y"].tolist(), f1));
65116445.47500964
In [145… print(calc_mse(train_df["X"].tolist(), train_df["Y"].tolist(), f2));
57922250.15746113
In [146… print(calc_mse(train_df["X"].tolist(), train_df["Y"].tolist(), f3));
54103936.344325066
In [147… print(calc_mse(test_df["X"].tolist(), test_df["Y"].tolist(), f1));
67828868.62264524
In [148… print(calc_mse(test_df["X"].tolist(), test_df["Y"].tolist(), f2));
67805434.17472021
In [149… print(calc_mse(test_df["X"].tolist(), test_df["Y"].tolist(), f3));
71191752.34205785
1f) Which of the three models would you select for use and why?
1g) Insted of writing functions, write a single line of Python code to calculate the test MSE for function F1. Hint: use the Python map and lambda functions.
test_f1_mse = sum( map(
lambda true_y, expect_y: pow(true_y - expect_y, 2), test_df["Y"].tolist(), map(
lambda x: 300 * x - 4280, test_df["X"].tolist()
)
)
) / len(test_df["X"].tolist());

print(test_f1_mse);
In [150…
67828868.62264524
2. KNN and Calculate Misclassification Rates
2a) Read the file "HW 2 Problem 2 Data.csv" into a dataframe called knn_data and display its first 10 rows
In [151… knn_data = pandas.read_csv(filepath_or_buffer = "HW 2 Problem 2 Data.csv"); print(knn_data.head(10));
X1 X2 Category
0 59 43 Yellow 1 60 24 Yellow
2 54 75 Blue
3 27 5 Red
4 96 73 Blue 5 51 43 Yellow
6 21 94 Red
7 100 19 Yellow
8 73 68 Blue
9 62 9 Yellow
2b) Using Seaborn, create a color-coded scatterplot of the data (where each point is colored with its category color). For full credit, be sure to color the points correctly with yellow, blue, and red colors.
import seaborn;

color_dict = dict(
{
"Yellow": "yellow",
"Blue": "blue",
"Red": "red"
}
)
seaborn.scatterplot(data = knn_data, x = "X1", y = "X2", hue = "Category", palette = color_dict);
In [152…

Now, we are going to create and assess predictions for the category of each observation using KNN-1 and KNN-3 algorithms. This means for each observation we are going to determine a prediction for its category color as if we didn't know what it was and then we will be checking to see if the prediction matches its actual category color.
The problem sub-parts below will step you through the process of doing this.
2c) Create a two-dimensional numpy array of size 50x50 that has the distance of each observation to every other observation. Use a Euclidean formula to calculate the distances. Display the first row of the distance table (this row will show the distance of each observation from the first observation)
import numpy; import math;
def euclidean_distance(x1, y1, x2, y2):
return math.sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2));

all_list = []; dist_list = []; for idx1, row1 in knn_data.iterrows():
x1 = row1["X1"]; y1 = row1["X2"]; all_temp_list = [];
In [153…
dist_temp_list = []; for idx2, row2 in knn_data.iterrows():
x2 = row2["X1"]; y2 = row2["X2"];
dist_temp_list.append(euclidean_distance(x1, y1, x2, y2));
all_temp_list.append((euclidean_distance(x1, y1, x2, y2), row2["Category"], idx2)); dist_list.append(dist_temp_list); all_list.append(all_temp_list);

dist_array = numpy.array(dist_list); print(dist_array[0]);
[ 0. 19.02629759 32.38826948 49.67896939 47.63402146 8.
63.60031446 47.50789408 28.65309756 34.13209633 32.01562119 62.76941931 57.93962375 17.02938637 38.07886553 33.42154993 37.44329045 39.44616585 51.623638 28.3019434 42.48529157 58.87274412 38.60051813 28.28427125 31.82766093 43.13930922 21.54065923 44.55333882 23.70653918 38.11823711 31.01612484 59.05929224 38.89730068 35.05709629 29.68164416 13.03840481 20.24845673 42.94182111 49.09175083 39.2173431 51.42956348 53.60037313
62.96824597 52.34500931 31.90611227 25.55386468 49.49747468 37.12142239
47.80167361 53.75872022]
2d) Now create a dataframe with 50 rows (one per observation) and 3 columns labeled 'nn1_cat', 'nn2_cat', and 'nn3_cat'. Populate the dataframe with the category color for the first, second, and third nearest neighbor for each observation. Display the first ten rows of this dataframe
nn1_list = []; nn2_list = []; nn3_list = [];

nn1_cat = []; nn2_cat = []; nn3_cat = [];
for temp_list in all_list:
temp_list.sort();
nn1_cat.append(temp_list[1][1]); nn2_cat.append(temp_list[2][1]); nn3_cat.append(temp_list[3][1]); nn1_list.append(temp_list[1]); nn2_list.append(temp_list[2]); nn3_list.append(temp_list[3]);

knn_cat = pandas.DataFrame( {
"nn1_cat": nn1_cat,
"nn2_cat": nn2_cat, "nn3_cat": nn3_cat
}
)
print(knn_cat.head(10));
In [154…
nn1_cat nn2_cat nn3_cat 0 Yellow Yellow Blue
1 Yellow Yellow Yellow 2 Blue Blue Red
3 Red Yellow Yellow
4 Blue Blue Blue
5 Yellow Blue Yellow 6 Red Red Red
7 Yellow Yellow Yellow
8 Blue Blue Blue
9 Yellow Yellow Yellow
2e) Create a Pandas series nn1_preds that has the prediction for each observation using a KNN1 algorithm. Display the first 10 rows of the series.
In [155… nn1_preds = pandas.Series(data = nn1_cat); print(nn1_preds.head(10));
0 Yellow 1 Yellow
2 Blue
3 Red
4 Blue 5 Yellow
6 Red
7 Yellow
8 Blue
9 Yellow dtype: object
2f) Calculate the misclassification rate for the KNN1 algorithm on this dataset
In [156… knn1_miss_rate = 0;
for idx in range(len(nn1_list)): true_color = all_list[idx][0][1]; predict_color = nn1_cat[idx]; if true_color != predict_color:
knn1_miss_rate += 1;

knn1_miss_rate /= len(nn1_list); print(knn1_miss_rate);
0.12
2g) Create a Pandas series nn3_preds that has the prediction for each observation using a KNN3 algorithm. Display the first 10 rows of the series.
(If the three nearest neighbors all have different color categories, use the first nearest neighbor category as the prediction)
def most_color(color_list):

color_map = [0, 0, 0]; max_count = 0; max_color = "";
for color in color_list: update_count = 0; update_color = ""; if color == "Red":
color_map[0] += 1; update_count = color_map[0]; update_color = "Red"; elif color == "Yellow": color_map[1] += 1; update_count = color_map[1]; update_color = "Yellow"; else:
color_map[2] += 1; update_count = color_map[2]; update_color = "Blue";
if update_count > max_count: max_count = update_count; max_color = update_color;
if max_count > 1:
return max_color;

return color_list[0];
In [157…
nn3_color_list = [];
for idx in range(len(nn1_list)):
color_list = [ nn1_list[idx][1], nn2_list[idx][1], nn3_list[idx][1]
];
nn3_color_list.append(most_color(color_list));

nn3_preds = pandas.Series(data = nn3_color_list); print(nn3_preds.head(10));
In [158…
0 Yellow
1 Yellow 2 Blue
3 Yellow
4 Blue
5 Yellow 6 Red
7 Yellow
8 Blue 9 Yellow dtype: object
2h) Calculate the misclassification rate for the KNN3 algorithm on this dataset
knn3_miss_rate = 0;
for idx in range(len(nn3_list)):
true_color = all_list[idx][0][1]; predict_color = nn3_color_list[idx]; if true_color != predict_color:
knn3_miss_rate += 1;

knn3_miss_rate /= len(nn3_list); print(knn3_miss_rate);
In [159…
0.08