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Question about polynomial regression
Learner I
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.
201 data，the relationship of x and y is :y=3*x^2-2*x+8
And this what I got from polynomial regression:
Really confused, please help me.
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>
0
Best Answer
-
rjones13
Member Posts: 198 
Unicorn
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="""/>
<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>1
Answers
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.