K-Nearest Neightbors Regression

Age	Loan	HousePriceIndex
25	40000	135
35	60000	256
45	80000	231
20	20000	267
35	120000	139
52	18000	150
23	95000	127
40	62000	216
60	100000	139
48	220000	250
33	150000	264

New customer Age: 48 has Loan: 142000 House Price Index?

Data raw

Age,Loan,HousePriceIndex
25,40000,135
35,60000,256
45,80000,231
20,20000,267
35,120000,139
52,18000,150
23,95000,127
40,62000,216
60,100000,139
48,220000,250
33,150000,264

Distance function

Euclidean	Manhattan
$$d(x,y)=\sqrt{\sum\limits_{i=1}^m(x_i-y_i)^2}$$	$$d(x,y)=\sum\limits_{i=1}^m\left\|x_i-y_i\right\|$$

Calculate KNN manually

Age	Loan	HousePriceIndex	Distance	Rank
25	40000	135	102000	9
35	60000	256	82000	8
45	80000	231	62000	5
20	20000	267	122000	10
35	120000	139	22000	2
52	18000	150	124000	11
23	95000	127	47000	4
40	62000	216	80000	7
60	100000	139	42000	3
48	220000	250	78000	6
33	150000	264	8000	1

Standardization

Standard Scaler	Min Max Scaler	Min Max Mean Scaler	Max Abs Scaler
$$Xs=\frac{X-mean}{s.d}$$	$$Xs=\frac{X-min}{max - min}$$	$$Xs=\frac{X-mean}{max - min}$$	$$Xs=\frac{X-mean}{\|max\|}$$