Question

The questions below walk through the use of kNN to predict the value of Y for a new point with (X1, X2)=(4, 4). Distance is calculated in the Euclidean sense.

What is the Euclidean distance between (X1,X2)=(4,4) and the first point in the table ((X1,X2)=(3,5))?

Answer 1

Answer:

The Euclidean distance between the two given points is $\sqrt{2}\text{ units}$.

Step-by-step explanation:

K-NN is used to predict the variable y for a new point with $(X_1,X_2) = (4,4)$

Distance is calculated in the Euclidean sense.

The Euclidean distance between two points is given by the formula:

$\text{Points: }(X_1, X_2), (x_1,x_2)\\\\D = \sqrt{{(x_2-X_2)}^2 + (x_1-X_1)^2}$

The point is $(x_1,x_2) = (3,5)$

The Euclidean distance between the two points is given by:

$D = \sqrt{(5-4)^2 + (3-4)^2} = \sqrt{2}\text{ units}$

Thus, the Euclidean distance between the two given points is $\sqrt{2}\text{ units}$.