Question

Question 1

1. Data collected (including the normalized values) by a riding mower manufacturer on its existing customers are listed below.

   Customer ID	Income	Lot_Size	Normalized Income	Normalized Lot_Size	Ownership
   1	61.5	20.8	-0.351	0.762	Owner
   2	82.8	22.4	0.726	1.421	Owner
   3	52.8	20.8	-0.790	0.762	Nonowner
   4	84	17.6	0.786	-0.556	Nonowner
   5	63	14.8	-0.275	-1.709	Nonowner

   The riding mower manufacturer wants to classify a new customer (data given below) as either an owner or a nonowner using k-Nearest Neighbors method.

   Income	Lot_Size	Normalized Income	Normalized Lot_Size
   81	20	0.635	0.532

   Round your answers to 3 digits after the decimal point.

   The Euclidean distance between the new customer and Customer 1 is?

   The Euclidean distance between the new customer and Customer 2 is?

   The Euclidean distance between the new customer and Customer 3 is?

   The Euclidean distance between the new customer and Customer 4 is?

   The Euclidean distance between the new customer and Customer 5 is?

   The new customer should be classified as?(owner or nonowner?) if k is set to 3.

Answer 1

Let's consider X as the features and y as out target variable. Thus all the columns 'Customer ID', 'Income', 'Lot Size', 'Normalized Income' and 'Normalized Lot size' are our feature columns, Xi and column 'Ownership' is y

Euclidean Distance for a given data x is calculated using the formula

where Xi are the column values of each row in the data set and xi are the column values for each row of the new data.

Given, xi = {81, 20, 0.635, 0.432} corresponding to Income, Lot_size, Normalized income, Normalized Lot_size respectively of the new customer.

We calculate the Euclidean distance of the new data point xi as shown below:

Cust. ID	Income	Lot_size	Normalized Income	Normalized Lot_size	Distance
1	61.5	20.8	-0.351	0.762
2	82.8	22.4	0.726	1.421
3	52.8	20.8	-0.790	0.762
4	84	17.6	0.786	-0.556
5	63	14.8	-0.275	-1.709

Arranging each customer ID by their Euclidean distances in ascending order we get:

Customer ID	Euclidean Distance
2	3.160
4	3.969
5	18.879
1	19.544
3	28.249

Since k = 3 we have to consider 3 nearest neighbors to classify the new data point as owner or nonowner.

As you can see the Customer IDs 2, 5 and 4 are the nearest 3 neighbors to the new data-point. (New data is the red circle)

Since among the 3 circles (2, 5 and 4) there are 2 circles that are purple (5 and 4) respectively, the new data will be considered a purple circle or a non-owner.

Thus for the given condition of k = 3 , we classify the new data / new customer with income 81 , Lot_size: 20, Normalized income: 0.635 and Normalized Lot_size = 0.432 as a nonowner.