Polynomial Regression with PHP

Polynomial Regression with PHP-ML

An extension where the relationship between variables is non-linear. Polynomial regression transforms input variables to higher powers (e.g., $x2,x3x^2, x^3x2,x3$) but remains a linear model concerning the parameters, making it suitable for more complex patterns. In polynomial regression, we aim to model a non-linear relationship by transforming the input variable $x$ to include higher powers. The model equation for a polynomial regression of degree is: $y = \beta_0 + \beta_1 x + \beta_2 x^2 + \beta_3 x^3 + \dots + \beta_d x^d + \epsilon$

In this example we compare RM: average number of rooms per dwelling vs PRICE.

Dataset

Test Data


                        
CRIM,ZN,INDUS,CHAS,NOX,RM,AGE,DIS,RAD,TAX,PTRATIO,B,LSTAT,PRICE
0.00632,18.0,2.31,0,0.538,6.575,65.2,4.09,1,296,15.3,396.9,4.98,25.0
0.02731,0.0,7.07,0,0.469,6.421,78.9,4.9671,2,242,17.8,396.9,9.14,22.6
0.02729,0.0,7.07,0,0.469,7.185,61.1,4.9671,2,242,17.8,392.83,4.03,33.4
0.03237,0.0,2.18,0,0.458,6.998,45.8,6.0622,3,222,18.7,394.63,2.94,33.4
0.06905,0.0,2.18,0,0.458,7.147,54.2,6.0622,3,222,18.7,396.90,5.33,36.2
0.02985,0.0,2.18,0,0.458,6.430,58.7,6.0622,3,222,18.7,394.12,5.21,28.7
0.08829,12.5,7.87,0,0.524,6.012,66.6,5.5605,5,311,15.2,395.60,12.43,20.6
0.14455,12.5,7.87,0,0.524,6.172,96.1,5.9505,5,311,15.2,396.90,19.15,22.9
0.21124,12.5,7.87,0,0.524,5.631,100.0,6.0821,5,311,15.2,386.63,29.93,16.9
0.17004,12.5,7.87,0,0.524,6.004,85.9,6.5921,5,311,15.2,386.71,17.10,18.9
0.22489,12.5,7.87,0,0.524,6.377,94.3,6.3467,5,311,15.2,392.52,20.45,21.6
0.11747,12.5,7.87,0,0.524,6.009,82.9,6.2267,5,311,15.2,396.90,13.27,18.9
0.09378,12.5,7.87,0,0.524,5.889,39.0,5.4509,5,311,15.2,390.50,15.71,21.7
0.62976,0.0,8.14,0,0.538,5.949,61.8,4.7075,4,307,21.0,396.90,8.26,20.4
0.63796,0.0,8.14,0,0.538,6.096,84.5,4.4619,4,307,21.0,380.02,10.26,21.2
0.62739,0.0,8.14,0,0.538,5.834,56.5,4.4986,4,307,21.0,395.62,8.47,19.9
0.41238,0.0,8.14,0,0.538,5.989,61.8,4.7075,4,307,21.0,396.90,10.62,22.2
0.36894,22.0,5.86,0,0.431,8.259,8.4,8.9067,7,330,19.1,396.90,3.54,37.7
0.37578,22.0,5.86,0,0.431,8.183,7.5,8.9067,7,330,19.1,396.90,3.54,37.3
0.21719,22.0,5.86,0,0.431,7.853,33.2,8.9067,7,330,19.1,396.90,3.54,40.1
0.19133,22.0,5.86,0,0.431,7.255,92.2,8.9067,7,330,19.1,393.63,6.48,37.2
0.33983,22.0,5.86,0,0.431,6.383,67.7,7.8265,7,330,19.1,396.90,9.69,25.7
0.19657,22.0,5.86,0,0.431,6.816,40.5,8.3248,7,330,19.1,392.90,5.37,31.6
0.16439,22.0,5.86,0,0.431,7.420,71.9,8.3248,7,330,19.1,396.90,4.21,38.7
0.19073,22.0,5.86,0,0.431,7.685,17.7,8.3248,7,330,19.1,396.90,3.01,38.1

Chart:

Regression:

Result: Memory: 0.122 Mb Time running: 0.01 sec.


                Dataset Statistics:
-----------------
Number of samples: 25
Average rooms: 6.66
Room range: 5.6 - 8.3

Training model...

Predicting house prices...

Price Predictions:
-----------------
A house with 5.5 rooms is predicted to cost $18,361.73
A house with 6.0 rooms is predicted to cost $20,378.35
A house with 8.0 rooms is predicted to cost $39,283.73
A house with 6.9 rooms is predicted to cost $32,376.76
A house with 5.6 rooms is predicted to cost $18,369.81
A house with 8.3 rooms is predicted to cost $37,143.58