Question about polynomial regression

FredLee
FredLee New Altair Community Member
edited November 5 in Community Q&A
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>

Tagged:

Best Answer

  • RolandJones
    RolandJones
    Altair Employee
    Answer ✓
    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>

Answers

  • RolandJones
    RolandJones
    Altair Employee
    Answer ✓
    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>
  • FredLee
    FredLee New Altair Community Member
    Thank you very much, Roland.
    I've tested what you gave to me.
    The result is very good.
    And I know that if you want to get a good result you need to modify the parameters.
    It really helps a lot.

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