Consider the polynomial fit problem where you want to find the best polynomial approximation of order to a set of data points.

a)Implementthepolynomialfitsolverfor2-dimensionalinputdataasalinearregressionlearner.

Make sure your implementation can handle polynomial fits of different order (at least to 4th order).

b)Apply your regression learner to the following data set and plot the resulting function for order 1,2, 3, and 4.

Plot the resulting polynomial surface together with the data points .(GRAPH)

D={

((6.4432,9.6309)50.9155),

((3.7861,5.4681)29.9852),

((8.1158,5.2114)42.9626),

((5.3283,2.3159)24.7445),

((3.5073,4.8890)27.3704),

((9.3900,6.2406)51.1350),

((8.7594,6.7914)50.5774),

((5.5016,3.9552)30.5206),

((6.2248,3.6744)31.7380),

((5.8704,9.8798)49.6374),

((2.0774,0.3774)10.0634),

((3.0125,8.8517)38.0517),

((4.7092,9.1329)43.5320),

((2.3049,7.9618)33.2198),

((8.4431,0.9871)31.1220),

((1.9476,2.6187)16.2934),

((2.2592,3.3536)19.3899),

((1.7071,6.7973)28.4807),((2.2766,1.3655)13.6945),

((4.3570,7.2123)36.9220),((3.1110,1.0676)14.9160),

((9.2338,6.5376)51.2371),((4.3021,4.9417)29.8112),

((1.8482,7.7905)32.0336),((9.0488,7.1504)52.5188),

(9.7975,9.0372)61.6658),((4.3887,8.9092)42.2733),

((1.1112,3.3416)16.5052),((2.5806,6.9875)31.3369),

((4.0872,1.9781)19.9475),((5.9490,0.3054)20.4239),

((2.6221,7.4407)32.6062),((6.0284,5.0002)35.1676),

((7.1122,4.7992)38.2211),((2.2175,9.0472)36.4109),

((3.1878,8.5944)37.9213),((4.2417,8.0549)38.8327),

((5.0786,5.7672)34.4707)}

c)Evaluate your polynomial regression functions by computing the error on the following data points(generatedfromtheoriginalfunction.

Comparetheerrorresults andtrytodetermine forwhat polynomials overfitting might be a problem. Which order polynomial would you consider the best prediction function and why.

T={((0.8552,1.8292)11.5848),((2.6248,2.3993)17.6138),

((8.0101,8.8651)54.1331),((0.2922,0.2867)5.7326),((9.2885,4.8990)46.3750),

((7.3033,1.6793)29.4356),((4.8861,9.7868)46.4227),((5.7853,7.1269)40.7433),((2.3728,5.0047)24.6220),((4.5885,4.7109)29.7602)}