Question about polynomial regression

FredLee

Hi there:
I'm a newcomer here. I really need some help about polynomial regression.
This is the data I've given to polynomial regression.

x	y
-100	30208
-99	29609
-98	29016
-97	28429
-96	27848
-95	27273
-94	26704
-93	26141
-92	25584
-91	25033
-90	24488
-89	23949
-88	23416
-87	22889
-86	22368
-85	21853
-84	21344
-83	20841
-82	20344
-81	19853
-80	19368
-79	18889
-78	18416
-77	17949
-76	17488
-75	17033
-74	16584
-73	16141
-72	15704
-71	15273
-70	14848
-69	14429
-68	14016
-67	13609
-66	13208
-65	12813
-64	12424
-63	12041
-62	11664
-61	11293
-60	10928
-59	10569
-58	10216
-57	9869
-56	9528
-55	9193
-54	8864
-53	8541
-52	8224
-51	7913
-50	7608
-49	7309
-48	7016
-47	6729
-46	6448
-45	6173
-44	5904
-43	5641
-42	5384
-41	5133
-40	4888
-39	4649
-38	4416
-37	4189
-36	3968
-35	3753
-34	3544
-33	3341
-32	3144
-31	2953
-30	2768
-29	2589
-28	2416
-27	2249
-26	2088
-25	1933
-24	1784
-23	1641
-22	1504
-21	1373
-20	1248
-19	1129
-18	1016
-17	909
-16	808
-15	713
-14	624
-13	541
-12	464
-11	393
-10	328
-9	269
-8	216
-7	169
-6	128
-5	93
-4	64
-3	41
-2	24
-1	13
0	8
1	9
2	16
3	29
4	48
5	73
6	104
7	141
8	184
9	233
10	288
11	349
12	416
13	489
14	568
15	653
16	744
17	841
18	944
19	1053
20	1168
21	1289
22	1416
23	1549
24	1688
25	1833
26	1984
27	2141
28	2304
29	2473
30	2648
31	2829
32	3016
33	3209
34	3408
35	3613
36	3824
37	4041
38	4264
39	4493
40	4728
41	4969
42	5216
43	5469
44	5728
45	5993
46	6264
47	6541
48	6824
49	7113
50	7408
51	7709
52	8016
53	8329
54	8648
55	8973
56	9304
57	9641
58	9984
59	10333
60	10688
61	11049
62	11416
63	11789
64	12168
65	12553
66	12944
67	13341
68	13744
69	14153
70	14568
71	14989
72	15416
73	15849
74	16288
75	16733
76	17184
77	17641
78	18104
79	18573
80	19048
81	19529
82	20016
83	20509
84	21008
85	21513
86	22024
87	22541
88	23064
89	23593
90	24128
91	24669
92	25216
93	25769
94	26328
95	26893
96	27464
97	28041
98	28624
99	29213
100	29808

201 data，the relationship of x and y is :y=3*x^2-2*x+8

And this what I got from polynomial regression:

  2.998 * x ^ 2.000
+ 22.316

Really confused, please help me.

<?xml version="1.0" encoding="UTF-8"?><process version="10.3.001">

  <operator activated="true" class="read_excel" compatibility="10.3.001" expanded="true" height="68" name="Read Excel" width="90" x="45" y="442">

    <parameter key="excel_file" value="C:\Users\Administrator\Desktop\test1.xlsx"/>

    <parameter key="sheet_selection" value="sheet number"/>

    <parameter key="sheet_number" value="1"/>

    <parameter key="imported_cell_range" value="A1"/>

    <parameter key="encoding" value="SYSTEM"/>

    <parameter key="use_header_row" value="true"/>

    <parameter key="header_row" value="1"/>

    <parameter key="first_row_as_names" value="true"/>

    <list key="annotations"/>

    <parameter key="date_format" value=""/>

    <parameter key="time_zone" value="SYSTEM"/>

    <parameter key="locale" value="英文 (美国)"/>

    <parameter key="read_all_values_as_polynominal" value="false"/>

    <list key="data_set_meta_data_information">

      <parameter key="0" value="x.true.integer.attribute"/>

      <parameter key="1" value="y.true.integer.attribute"/>

    </list>

    <parameter key="read_not_matching_values_as_missings" value="false"/>

  </operator>

</process>

<?xml version="1.0" encoding="UTF-8"?><process version="10.3.001">

  <operator activated="true" class="blending:select_attributes" compatibility="10.3.001" expanded="true" height="82" name="Select Attributes" width="90" x="179" y="442">

    <parameter key="type" value="include attributes"/>

    <parameter key="attribute_filter_type" value="a subset"/>

    <parameter key="select_attribute" value=""/>

    <parameter key="select_subset" value="x␞y"/>

    <parameter key="also_apply_to_special_attributes_(id,_label..)" value="true"/>

  </operator>

</process>

<?xml version="1.0" encoding="UTF-8"?><process version="10.3.001">

  <operator activated="true" class="blending:set_role" compatibility="10.3.001" expanded="true" height="82" name="Set Role" width="90" x="313" y="442">

    <list key="set_roles">

      <parameter key="y" value="label"/>

    </list>

  </operator>

</process>

<?xml version="1.0" encoding="UTF-8"?><process version="10.3.001">

  <operator activated="true" class="split_data" compatibility="10.1.003" expanded="true" height="82" name="Split Data" origin="GENERATED_TUTORIAL" width="90" x="715" y="85">

    <enumeration key="partitions">

      <parameter key="ratio" value="0.7"/>

      <parameter key="ratio" value="0.3"/>

    </enumeration>

    <parameter key="sampling_type" value="automatic"/>

    <parameter key="use_local_random_seed" value="false"/>

    <parameter key="local_random_seed" value="1992"/>

  </operator>

</process>

<?xml version="1.0" encoding="UTF-8"?><process version="10.3.001">

  <operator activated="true" class="polynomial_regression" compatibility="10.3.001" expanded="true" height="82" name="Polynomial Regression" width="90" x="849" y="85">

    <parameter key="max_iterations" value="5000"/>

    <parameter key="replication_factor" value="1"/>

    <parameter key="max_degree" value="5"/>

    <parameter key="min_coefficient" value="-100.0"/>

    <parameter key="max_coefficient" value="100.0"/>

    <parameter key="use_local_random_seed" value="false"/>

    <parameter key="local_random_seed" value="1992"/>

  </operator>

</process>

RolandJones

Hi @FredLee,

The key parameter is the replication factor, which then allows it to have x appear twice in the equation. Please see the following process to give a pretty decent result for only 201 points.

Best,

Roland

<?xml version="1.0" encoding="UTF-8"?><process version="10.3.001">

  <context>

    <input/>

    <output/>

    <macros/>

  </context>

  <operator activated="true" class="process" compatibility="10.3.001" expanded="true" name="Process">

    <parameter key="logverbosity" value="init"/>

    <parameter key="random_seed" value="2001"/>

    <parameter key="send_mail" value="never"/>

    <parameter key="notification_email" value=""/>

    <parameter key="process_duration_for_mail" value="30"/>

    <parameter key="encoding" value="UTF-8"/>

    <process expanded="true">

      <operator activated="true" class="open_file" compatibility="10.3.001" expanded="true" height="68" name="Open File" width="90" x="45" y="34">

        <parameter key="resource_type" value="repository blob entry"/>

        <parameter key="repository_entry" value="//Community-Content/poly.txt"/>

      </operator>

      <operator activated="true" class="read_csv" compatibility="10.3.001" expanded="true" height="68" name="Read CSV" width="90" x="179" y="34">

        <parameter key="column_separators" value="\s+"/>

        <parameter key="trim_lines" value="false"/>

        <parameter key="multiline_text" value="false"/>

        <parameter key="use_quotes" value="true"/>

        <parameter key="quotes_character" value="&quot;"/>

        <parameter key="escape_character" value="\"/>

        <parameter key="skip_comments" value="false"/>

        <parameter key="comment_characters" value="#"/>

        <parameter key="starting_row" value="1"/>

        <parameter key="parse_numbers" value="true"/>

        <parameter key="decimal_character" value="."/>

        <parameter key="grouped_digits" value="false"/>

        <parameter key="grouping_character" value=","/>

        <parameter key="infinity_representation" value=""/>

        <parameter key="date_format" value=""/>

        <parameter key="use_header_row" value="true"/>

        <parameter key="header_row" value="1"/>

        <parameter key="first_row_as_names" value="true"/>

        <list key="annotations"/>

        <parameter key="time_zone" value="SYSTEM"/>

        <parameter key="locale" value="English (United States)"/>

        <parameter key="encoding" value="UTF-8"/>

        <parameter key="read_all_values_as_polynominal" value="false"/>

        <list key="data_set_meta_data_information"/>

        <parameter key="read_not_matching_values_as_missings" value="true"/>

      </operator>

      <operator activated="true" class="blending:set_role" compatibility="10.3.001" expanded="true" height="82" name="Set Role" width="90" x="313" y="34">

        <list key="set_roles">

          <parameter key="y" value="label"/>

        </list>

      </operator>

      <operator activated="true" class="polynomial_regression" compatibility="10.3.001" expanded="true" height="82" name="Polynomial Regression" width="90" x="447" y="34">

        <parameter key="max_iterations" value="50000"/>

        <parameter key="replication_factor" value="2"/>

        <parameter key="max_degree" value="2"/>

        <parameter key="min_coefficient" value="-8.0"/>

        <parameter key="max_coefficient" value="8.0"/>

        <parameter key="use_local_random_seed" value="false"/>

        <parameter key="local_random_seed" value="1992"/>

      </operator>

      <operator activated="true" class="apply_model" compatibility="10.3.001" expanded="true" height="82" name="Apply Model" width="90" x="581" y="34">

        <list key="application_parameters"/>

      </operator>

      <operator activated="true" class="performance_regression" compatibility="10.3.001" expanded="true" height="82" name="Performance" width="90" x="514" y="187">

        <parameter key="main_criterion" value="first"/>

        <parameter key="root_mean_squared_error" value="true"/>

        <parameter key="absolute_error" value="true"/>

        <parameter key="relative_error" value="false"/>

        <parameter key="relative_error_lenient" value="false"/>

        <parameter key="relative_error_strict" value="false"/>

        <parameter key="normalized_absolute_error" value="false"/>

        <parameter key="root_relative_squared_error" value="false"/>

        <parameter key="squared_error" value="false"/>

        <parameter key="correlation" value="false"/>

        <parameter key="squared_correlation" value="false"/>

        <parameter key="prediction_average" value="false"/>

        <parameter key="spearman_rho" value="false"/>

        <parameter key="kendall_tau" value="false"/>

        <parameter key="skip_undefined_labels" value="true"/>

        <parameter key="use_example_weights" value="true"/>

      </operator>

      <connect from_op="Open File" from_port="file" to_op="Read CSV" to_port="file"/>

      <connect from_op="Read CSV" from_port="output" to_op="Set Role" to_port="example set input"/>

      <connect from_op="Set Role" from_port="example set output" to_op="Polynomial Regression" to_port="training set"/>

      <connect from_op="Polynomial Regression" from_port="model" to_op="Apply Model" to_port="model"/>

      <connect from_op="Polynomial Regression" from_port="exampleSet" to_op="Apply Model" to_port="unlabelled data"/>

      <connect from_op="Apply Model" from_port="labelled data" to_op="Performance" to_port="labelled data"/>

      <connect from_op="Apply Model" from_port="model" to_port="result 1"/>

      <connect from_op="Performance" from_port="performance" to_port="result 2"/>

      <portSpacing port="source_input 1" spacing="0"/>

      <portSpacing port="sink_result 1" spacing="0"/>

      <portSpacing port="sink_result 2" spacing="0"/>

      <portSpacing port="sink_result 3" spacing="0"/>

    </process>

  </operator>

</process>