Calculate Price Elasticity

gianluca_scheid

Dear Rapidminer Community

I have a large data set with weekly sales data (price and quantity) of 100+ products over a few months. Is there an efficient way on how to calculate the price elasticity (= %price change/%quantity change) of each individual product?

Thank you in advance

GL

lionelderkrikor

Hi @gianluca_scheid,

I searched on the web the notion of "Elasticity" and I'm understanding that you want to perform a linear regression between 
Price Per Product and Quantity Sold for each of your product , right ?
So I propose this process which uses a Loop to create as many Linear Regression models as products : 

<?xml version="1.0" encoding="UTF-8"?><process version="9.3.001">
  <context>
    <input/>
    <output/>
    <macros/>
  </context>
  <operator activated="true" class="process" compatibility="9.3.001" 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="SYSTEM"/>
    <process expanded="true">
      <operator activated="true" class="read_excel" compatibility="9.3.001" expanded="true" height="68" name="Read Excel" width="90" x="112" y="34">
        <parameter key="excel_file" value="D:\Lionel\Formations_DataScience\Rapidminer\Tests_Rapidminer\LinearRegression_Elasticity\sampledata.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="first_row_as_names" value="true"/>
        <list key="annotations"/>
        <parameter key="date_format" value=""/>
        <parameter key="time_zone" value="SYSTEM"/>
        <parameter key="locale" value="English (United States)"/>
        <parameter key="read_all_values_as_polynominal" value="false"/>
        <list key="data_set_meta_data_information">
          <parameter key="0" value="Product NR.true.integer.attribute"/>
          <parameter key="1" value="Calendar Week.true.integer.attribute"/>
          <parameter key="2" value="Year.true.integer.attribute"/>
          <parameter key="3" value="Price Per Product.true.real.attribute"/>
          <parameter key="4" value="Quantity Sold.true.integer.attribute"/>
          <parameter key="5" value="Turnover.true.real.attribute"/>
          <parameter key="6" value="G.true.polynominal.attribute"/>
          <parameter key="7" value="H.true.polynominal.attribute"/>
          <parameter key="8" value="I.true.polynominal.attribute"/>
        </list>
        <parameter key="read_not_matching_values_as_missings" value="false"/>
        <parameter key="datamanagement" value="double_array"/>
        <parameter key="data_management" value="auto"/>
      </operator>
      <operator activated="true" class="select_attributes" compatibility="9.3.001" expanded="true" height="82" name="Select Attributes" width="90" x="246" y="34">
        <parameter key="attribute_filter_type" value="subset"/>
        <parameter key="attribute" value=""/>
        <parameter key="attributes" value="Product NR|Price Per Product|Quantity Sold"/>
        <parameter key="use_except_expression" value="false"/>
        <parameter key="value_type" value="attribute_value"/>
        <parameter key="use_value_type_exception" value="false"/>
        <parameter key="except_value_type" value="time"/>
        <parameter key="block_type" value="attribute_block"/>
        <parameter key="use_block_type_exception" value="false"/>
        <parameter key="except_block_type" value="value_matrix_row_start"/>
        <parameter key="invert_selection" value="false"/>
        <parameter key="include_special_attributes" value="false"/>
      </operator>
      <operator activated="true" class="set_role" compatibility="9.3.001" expanded="true" height="82" name="Set Role" width="90" x="380" y="34">
        <parameter key="attribute_name" value="Product NR"/>
        <parameter key="target_role" value="id"/>
        <list key="set_additional_roles">
          <parameter key="Quantity Sold" value="label"/>
        </list>
      </operator>
      <operator activated="false" class="numerical_to_polynominal" compatibility="9.3.001" expanded="true" height="82" name="Numerical to Polynominal" width="90" x="514" y="289">
        <parameter key="attribute_filter_type" value="single"/>
        <parameter key="attribute" value="Product NR"/>
        <parameter key="attributes" value=""/>
        <parameter key="use_except_expression" value="false"/>
        <parameter key="value_type" value="numeric"/>
        <parameter key="use_value_type_exception" value="false"/>
        <parameter key="except_value_type" value="real"/>
        <parameter key="block_type" value="value_series"/>
        <parameter key="use_block_type_exception" value="false"/>
        <parameter key="except_block_type" value="value_series_end"/>
        <parameter key="invert_selection" value="false"/>
        <parameter key="include_special_attributes" value="true"/>
      </operator>
      <operator activated="true" class="concurrency:loop" compatibility="9.3.001" expanded="true" height="124" name="Loop" width="90" x="715" y="34">
        <parameter key="number_of_iterations" value="2"/>
        <parameter key="iteration_macro" value="iteration"/>
        <parameter key="reuse_results" value="false"/>
        <parameter key="enable_parallel_execution" value="true"/>
        <process expanded="true">
          <operator activated="true" class="filter_examples" compatibility="9.3.001" expanded="true" height="103" name="Filter Examples" width="90" x="246" y="85">
            <parameter key="parameter_expression" value=""/>
            <parameter key="condition_class" value="custom_filters"/>
            <parameter key="invert_filter" value="false"/>
            <list key="filters_list">
              <parameter key="filters_entry_key" value="Product NR.eq.%{iteration}"/>
            </list>
            <parameter key="filters_logic_and" value="true"/>
            <parameter key="filters_check_metadata" value="true"/>
          </operator>
          <operator activated="true" class="concurrency:cross_validation" compatibility="9.3.001" expanded="true" height="145" name="Cross Validation" width="90" x="581" y="85">
            <parameter key="split_on_batch_attribute" value="false"/>
            <parameter key="leave_one_out" value="false"/>
            <parameter key="number_of_folds" value="10"/>
            <parameter key="sampling_type" value="automatic"/>
            <parameter key="use_local_random_seed" value="false"/>
            <parameter key="local_random_seed" value="1992"/>
            <parameter key="enable_parallel_execution" value="true"/>
            <process expanded="true">
              <operator activated="true" class="linear_regression" compatibility="9.3.001" expanded="true" height="103" name="Linear Regression" width="90" x="179" y="34">
                <parameter key="feature_selection" value="M5 prime"/>
                <parameter key="alpha" value="0.05"/>
                <parameter key="max_iterations" value="10"/>
                <parameter key="forward_alpha" value="0.05"/>
                <parameter key="backward_alpha" value="0.05"/>
                <parameter key="eliminate_colinear_features" value="true"/>
                <parameter key="min_tolerance" value="0.05"/>
                <parameter key="use_bias" value="true"/>
                <parameter key="ridge" value="1.0E-8"/>
              </operator>
              <connect from_port="training set" to_op="Linear Regression" to_port="training set"/>
              <connect from_op="Linear Regression" from_port="model" to_port="model"/>
              <portSpacing port="source_training set" spacing="0"/>
              <portSpacing port="sink_model" spacing="0"/>
              <portSpacing port="sink_through 1" spacing="0"/>
            </process>
            <process expanded="true">
              <operator activated="true" class="apply_model" compatibility="9.3.001" expanded="true" height="82" name="Apply Model" width="90" x="45" y="34">
                <list key="application_parameters"/>
                <parameter key="create_view" value="false"/>
              </operator>
              <operator activated="true" class="performance_regression" compatibility="9.3.001" expanded="true" height="82" name="Performance" width="90" x="179" y="34">
                <parameter key="main_criterion" value="first"/>
                <parameter key="root_mean_squared_error" value="true"/>
                <parameter key="absolute_error" value="false"/>
                <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_port="model" to_op="Apply Model" to_port="model"/>
              <connect from_port="test set" 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="Performance" from_port="performance" to_port="performance 1"/>
              <portSpacing port="source_model" spacing="0"/>
              <portSpacing port="source_test set" spacing="0"/>
              <portSpacing port="source_through 1" spacing="0"/>
              <portSpacing port="sink_test set results" spacing="0"/>
              <portSpacing port="sink_performance 1" spacing="0"/>
              <portSpacing port="sink_performance 2" spacing="0"/>
            </process>
          </operator>
          <connect from_port="input 1" to_op="Filter Examples" to_port="example set input"/>
          <connect from_op="Filter Examples" from_port="example set output" to_op="Cross Validation" to_port="example set"/>
          <connect from_op="Cross Validation" from_port="model" to_port="output 1"/>
          <connect from_op="Cross Validation" from_port="example set" to_port="output 2"/>
          <connect from_op="Cross Validation" from_port="performance 1" to_port="output 3"/>
          <portSpacing port="source_input 1" spacing="0"/>
          <portSpacing port="source_input 2" spacing="0"/>
          <portSpacing port="sink_output 1" spacing="0"/>
          <portSpacing port="sink_output 2" spacing="0"/>
          <portSpacing port="sink_output 3" spacing="0"/>
          <portSpacing port="sink_output 4" spacing="0"/>
        </process>
      </operator>
      <operator activated="false" class="concurrency:loop_values" compatibility="9.3.001" expanded="true" height="68" name="Loop Values" width="90" x="782" y="289">
        <parameter key="attribute" value="Product NR"/>
        <parameter key="iteration_macro" value="loop_value"/>
        <parameter key="reuse_results" value="false"/>
        <parameter key="enable_parallel_execution" value="true"/>
        <process expanded="true">
          <portSpacing port="source_input 1" spacing="0"/>
          <portSpacing port="sink_output 1" spacing="0"/>
        </process>
      </operator>
      <connect from_op="Read Excel" from_port="output" to_op="Select Attributes" to_port="example set input"/>
      <connect from_op="Select Attributes" from_port="example set output" to_op="Set Role" to_port="example set input"/>
      <connect from_op="Set Role" from_port="example set output" to_op="Loop" to_port="input 1"/>
      <connect from_op="Loop" from_port="output 1" to_port="result 1"/>
      <connect from_op="Loop" from_port="output 2" to_port="result 2"/>
      <connect from_op="Loop" from_port="output 3" to_port="result 3"/>
      <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"/>
      <portSpacing port="sink_result 4" spacing="0"/>
    </process>
  </operator>
</process>

Hope this helps,

Regards,

Lionel