{"id":4148,"date":"2026-03-08T14:21:52","date_gmt":"2026-03-08T14:21:52","guid":{"rendered":"https:\/\/erikap.co.uk\/?page_id=4148"},"modified":"2026-03-08T15:06:01","modified_gmt":"2026-03-08T15:06:01","slug":"invoice-amount-analysis-exploratory-regression","status":"publish","type":"page","link":"https:\/\/erikap.co.uk\/?page_id=4148","title":{"rendered":"Invoice Amount Analysis-Exploratory Regression"},"content":{"rendered":"

[et_pb_section fb_built=”1″ fullwidth=”on” admin_label=”Page Header” _builder_version=”4.27.5″ _module_preset=”3c901e30-8c7f-4173-af71-9e53c9b0862a” background_image=”https:\/\/erikap.co.uk\/wp-content\/uploads\/2026\/01\/pexels-martabranco-30337930-2.jpg” global_colors_info=”{}”][et_pb_fullwidth_header title=”Invoice Amount Analysis” text_orientation=”center” admin_label=”Hero Section” _builder_version=”4.27.5″ _module_preset=”default” title_font=”Montserrat|on|||” title_font_size=”60px” title_line_height=”1.4em” content_font_size=”22px” content_line_height=”1.8em” subhead_font=”||||” background_color=”rgba(255, 255, 255, 0)” use_background_color_gradient=”on” background_color_gradient_stops=”rgba(58,52,226,0.93) 0%|rgba(73,108,220,0.7) 100%” background_color_gradient_start=”rgba(58,52,226,0.93)” background_color_gradient_end=”rgba(73,108,220,0.7)” custom_button_one=”on” button_one_text_size=”16px” button_one_bg_color=”#6eba01″ button_one_border_width=”2px” button_one_border_color=”#6eba01″ button_one_border_radius=”0″ button_one_letter_spacing=”2″ button_one_font=”Montserrat|||on|” button_one_use_icon=”off” custom_button_two=”on” button_two_text_size=”16px” button_two_border_width=”2px” button_two_border_color=”#ffffff” button_two_border_radius=”0″ button_two_letter_spacing=”2″ button_two_font=”Montserrat|||on|” button_two_use_icon=”off” module_alignment=”left” animation_style=”fade” button_one_text_color_hover=”#6eba01″ button_two_text_color_hover=”#6eba01″ button_one_border_color_hover=”#ffffff” button_two_border_color_hover=”#ffffff” button_one_border_radius_hover=”0″ button_two_border_radius_hover=”0″ button_one_letter_spacing_hover=”2″ button_two_letter_spacing_hover=”2″ button_one_bg_color_hover=”#ffffff” button_two_bg_color_hover=”#ffffff” global_colors_info=”{}” button_one_text_size__hover_enabled=”off” button_two_text_size__hover_enabled=”off” button_one_text_color__hover_enabled=”on” button_one_text_color__hover=”#6eba01″ button_two_text_color__hover_enabled=”on” button_two_text_color__hover=”#6eba01″ button_one_border_width__hover_enabled=”off” button_two_border_width__hover_enabled=”off” button_one_border_color__hover_enabled=”on” button_one_border_color__hover=”#ffffff” button_two_border_color__hover_enabled=”on” button_two_border_color__hover=”#ffffff” button_one_border_radius__hover_enabled=”on” button_one_border_radius__hover=”0″ button_two_border_radius__hover_enabled=”on” button_two_border_radius__hover=”0″ button_one_letter_spacing__hover_enabled=”on” button_one_letter_spacing__hover=”2″ button_two_letter_spacing__hover_enabled=”on” button_two_letter_spacing__hover=”2″ button_one_bg_color__hover_enabled=”on” button_one_bg_color__hover=”#ffffff” button_two_bg_color__hover_enabled=”on” button_two_bg_color__hover=”#ffffff”]<\/p>\n

Exploratory Regression (Excel)<\/span><\/p>\n

 <\/p>\n

[\/et_pb_fullwidth_header][\/et_pb_section][et_pb_section fb_built=”1″ admin_label=”Projects” _builder_version=”4.16″ _module_preset=”default” custom_padding=”90px||90px|” global_colors_info=”{}”][et_pb_row _builder_version=”4.16″ _module_preset=”default” background_size=”initial” background_position=”top_left” background_repeat=”repeat” width=”64.7%” custom_padding=”45px|0px|45px|0px” custom_width_px=”710px” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.16″ _module_preset=”default” background_position=”top_left” custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_divider color=”#4e5ed0″ divider_weight=”3px” disabled_on=”off|off|off” _builder_version=”4.16″ _module_preset=”default” background_color_gradient_direction=”90deg” max_width=”100px” module_alignment=”center” height=”5px” custom_margin=”||20px|” custom_padding=”||20px|” animation_style=”slide” animation_direction=”bottom” saved_tabs=”all” locked=”off” global_colors_info=”{}”][\/et_pb_divider][et_pb_text admin_label=”Projects Section Title” _builder_version=”4.27.5″ _module_preset=”default” header_font=”Montserrat||||” header_text_color=”#1f1f1f” header_font_size=”36px” text_orientation=”center” max_width=”710px” module_alignment=”center” animation_style=”fold” animation_direction=”bottom” animation_intensity_fold=”20%” locked=”off” global_colors_info=”{}”]<\/p>\n

Project Context<\/span><\/h1>\n

[\/et_pb_text][et_pb_text _builder_version=”4.27.5″ _module_preset=”default” text_font_size=”16px” hover_enabled=”0″ global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n

This project explores whether simple operational variables in Accounts Payable can help explain or predict invoice amounts. Using a simulated but realistic AP data (14,756 invoices), I built a regression model in Excel\u2019s Analysis ToolPak and visualised the results in Power BI.
This was my first modelling project, created as part of my data analytics learning journey.<\/span><\/p>\n

[\/et_pb_text][et_pb_text admin_label=”Projects Section Title” _builder_version=”4.27.4″ _module_preset=”default” header_font=”Montserrat||||” header_text_color=”#1f1f1f” header_font_size=”36px” text_orientation=”center” max_width=”710px” module_alignment=”center” animation_style=”fold” animation_direction=”bottom” animation_intensity_fold=”20%” global_colors_info=”{}”]<\/p>\n

Dataset<\/span><\/h1>\n

[\/et_pb_text][et_pb_text _builder_version=”4.27.5″ _module_preset=”default” hover_enabled=”0″ global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n

Variables used in the model:<\/p>\n

\n
\n\n\n\n\n\n\n\n\n
Variable<\/th>\nDescription<\/th>\n<\/tr>\n<\/thead>\n
InvoiceAmount<\/td>\nTarget variable<\/td>\n<\/tr>\n
ProcessingDays<\/td>\nNumber of days required to process the invoice<\/td>\n<\/tr>\n
DelayedFlag<\/td>\n0 = on time, 1 = delayed<\/td>\n<\/tr>\n
Category<\/td>\nDepartment category (visualisation only)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\n<\/div>\n<\/div>\n

[\/et_pb_text][et_pb_text _builder_version=”4.27.5″ _module_preset=”default” text_font_size=”16px” locked=”off” global_colors_info=”{}”][\/et_pb_text][et_pb_text admin_label=”Projects Section Title” _builder_version=”4.27.5″ _module_preset=”default” header_font=”Montserrat||||” header_text_color=”#1f1f1f” header_font_size=”36px” text_orientation=”center” max_width=”710px” module_alignment=”center” custom_padding=”0px|||||” animation_style=”fold” animation_direction=”bottom” animation_intensity_fold=”20%” locked=”off” global_colors_info=”{}”]<\/p>\n

Regression Model<\/span><\/h1>\n

[\/et_pb_text][et_pb_text _builder_version=”4.27.5″ _module_preset=”default” text_font_size=”16px” locked=”off” global_colors_info=”{}”]<\/p>\n

I used Excel\u2019s Analysis ToolPak to run a simple linear regression with two predictors:<\/span><\/p>\n

    \n
  • ProcessingDays<\/span><\/strong><\/li>\n
  • DelayedFlag<\/span><\/strong><\/strong><\/li>\n<\/ul>\n

    Regression Output (Excel)<\/span><\/strong><\/p>\n

      \n
    • R\u00b2:<\/span><\/strong> 0.06<\/span><\/li>\n
    • Adjusted R\u00b2:<\/span><\/strong> 0.06<\/span><\/li>\n
    • Standard Error:<\/span><\/strong> 1558.95<\/span><\/li>\n
    • Observations:<\/span><\/strong> 14,756<\/span><\/li>\n<\/ul>\n

      Coefficients<\/span><\/strong><\/p>\n

        \n
      • Intercept:<\/span><\/strong> 530.66<\/span><\/li>\n
      • ProcessingDays:<\/span><\/strong> \u20130.734<\/span><\/li>\n
      • DelayedFlag:<\/span><\/strong> +874.788<\/span><\/li>\n<\/ul>\n

        [\/et_pb_text][et_pb_image src=”https:\/\/erikap.co.uk\/wp-content\/uploads\/2026\/03\/Screenshot-2026-02-20-125107.png” title_text=”Screenshot 2026-02-20 125107″ _builder_version=”4.27.5″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_image][et_pb_code _builder_version=”4.27.5″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_code][et_pb_text _builder_version=”4.27.5″ _module_preset=”default” text_font_size=”16px” locked=”off” global_colors_info=”{}”]<\/p>\n

        Predicted Invoice Amount = <\/span>530.66 <\/span>– 0.734 \u00d7 ProcessingDays <\/span>+ 874.788 \u00d7 DelayedFlag<\/span><\/p>\n

        [\/et_pb_text][et_pb_text _builder_version=”4.27.5″ _module_preset=”default” text_font_size=”16px” hover_enabled=”0″ locked=”off” global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n

        Interpretation<\/span><\/strong><\/p>\n

          \n
        • Start at \u00a3530.66<\/span><\/strong>
          Baseline invoice amount for a non\u2011delayed invoice with minimal processing time.<\/span><\/li>\n
        • ProcessingDays: \u2013\u00a30.73 per day<\/span><\/strong>
          A very small negative effect. Statistically significant due to the large dataset, but not practically meaningful.<\/span><\/li>\n
        • DelayedFlag: +\u00a3875<\/span><\/strong>
          Delayed invoices tend to be around \u00a3875 higher on average.<\/span><\/li>\n<\/ul>\n

          Example Prediction<\/span><\/strong><\/p>\n

          For an invoice with:<\/span><\/p>\n

            \n
          • 12 processing days<\/span><\/li>\n
          • DelayedFlag = 1<\/span><\/li>\n<\/ul>\n

            [ 530.66 – (0.734 * 12) + 874.788 * 1 ]<\/span><\/p>\n

            This is the model\u2019s predicted amount<\/strong>.<\/span><\/p>\n

            [\/et_pb_text][et_pb_text admin_label=”Projects Section Title” _builder_version=”4.27.5″ _module_preset=”default” header_font=”Montserrat||||” header_text_color=”#1f1f1f” header_font_size=”36px” text_orientation=”center” max_width=”710px” module_alignment=”center” custom_padding=”0px|||||” animation_style=”fold” animation_direction=”bottom” animation_intensity_fold=”20%” locked=”off” global_colors_info=”{}”]<\/p>\n

            Model Performance<\/span><\/h1>\n

            [\/et_pb_text][et_pb_text _builder_version=”4.27.5″ _module_preset=”default” text_font_size=”16px” locked=”off” global_colors_info=”{}”]<\/p>\n

            \n
            \n\n\n\n\n\n\n\n
            Metric<\/th>\nValue<\/th>\n<\/tr>\n<\/thead>\n
            R\u00b2<\/td>\n0.06<\/td>\n<\/tr>\n
            Observations<\/td>\n14,756<\/td>\n<\/tr>\n
            Standard Error<\/td>\n1558.95<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

            The model is statistically significant, but the predictive power is low:<\/span><\/p>\n

              \n
            • R\u00b2 = 0.06<\/span><\/strong> \u2192 The model explains only 6% of the variation in invoice amounts.<\/span><\/li>\n
            • Residuals show a wide vertical spread<\/span><\/strong> \u2192 Predictions are often far from actual values.<\/span><\/li>\n
            • Predicted amounts cluster between \u00a3500\u2013\u00a31,400<\/span><\/strong> \u2192 Because the model only uses two simple variables.<\/span><\/li>\n<\/ul>\n

              This is expected for a simple model applied to complex financial data.<\/span><\/p>\n

              [\/et_pb_text][et_pb_text admin_label=”Projects Section Title” _builder_version=”4.27.5″ _module_preset=”default” header_font=”Montserrat||||” header_text_color=”#1f1f1f” header_font_size=”36px” text_orientation=”center” max_width=”710px” module_alignment=”center” custom_padding=”0px|||||” animation_style=”fold” animation_direction=”bottom” animation_intensity_fold=”20%” locked=”off” global_colors_info=”{}”]<\/p>\n

              Visual Analysis<\/span><\/h1>\n

              [\/et_pb_text][et_pb_text _builder_version=”4.27.5″ _module_preset=”default” text_font_size=”16px” locked=”off” global_colors_info=”{}”]<\/p>\n

                \n
              1. Processing Days vs Invoice Amount<\/span><\/strong><\/li>\n<\/ol>\n

                Shows no strong linear relationship \u2014 invoice amounts vary widely regardless of processing time.<\/span><\/p>\n

                  \n
                1. Predicted Amount vs Residual<\/span><\/strong><\/li>\n<\/ol>\n

                  Each dot = one invoice.<\/span><\/p>\n

                    \n
                  • X\u2011axis:<\/span><\/strong> model\u2019s predicted amount<\/span><\/li>\n
                  • Y\u2011axis:<\/span><\/strong> residual (error)<\/span><\/li>\n
                  • Colours:<\/span><\/strong> invoice categories<\/span><\/li>\n<\/ul>\n

                    The residuals are centred\u00a0around zero (good), but spread out vertically (large errors).
                    This confirms the model is unbiased but not highly accurate.<\/p>\n

                    [\/et_pb_text][et_pb_image src=”https:\/\/erikap.co.uk\/wp-content\/uploads\/2026\/03\/Screenshot-2026-02-20-125918.png” title_text=”Screenshot 2026-02-20 125918″ _builder_version=”4.27.5″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_image][et_pb_text admin_label=”Projects Section Title” _builder_version=”4.27.5″ _module_preset=”default” header_font=”Montserrat||||” header_text_color=”#1f1f1f” header_font_size=”36px” text_orientation=”center” max_width=”710px” module_alignment=”center” custom_padding=”0px|||||” animation_style=”fold” animation_direction=”bottom” animation_intensity_fold=”20%” locked=”off” global_colors_info=”{}”]<\/p>\n

                    Key Insights<\/span><\/h1>\n

                    [\/et_pb_text][et_pb_text _builder_version=”4.27.5″ _module_preset=”default” text_font_size=”16px” locked=”off” global_colors_info=”{}”]<\/p>\n

                    Key Insights<\/h1>\n

                    \u2022 Delayed invoices tend to have higher average values<\/strong>
                    \u2022 Processing time has minimal practical impact<\/strong> on invoice value
                    \u2022 Invoice values vary widely across departments
                    \u2022 Additional features (supplier, contract type, purchase order status) could significantly improve predictions<\/p>\n

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                    Exploratory Regression (Excel)  Project ContextThis project explores whether simple operational variables in Accounts Payable can help explain or predict invoice amounts. Using a simulated but realistic AP data (14,756 invoices), I built a regression model in Excel\u2019s Analysis ToolPak and visualised the results in Power BI.This was my first modelling project, created as part of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"class_list":["post-4148","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/erikap.co.uk\/index.php?rest_route=\/wp\/v2\/pages\/4148","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/erikap.co.uk\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/erikap.co.uk\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/erikap.co.uk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/erikap.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4148"}],"version-history":[{"count":3,"href":"https:\/\/erikap.co.uk\/index.php?rest_route=\/wp\/v2\/pages\/4148\/revisions"}],"predecessor-version":[{"id":4169,"href":"https:\/\/erikap.co.uk\/index.php?rest_route=\/wp\/v2\/pages\/4148\/revisions\/4169"}],"wp:attachment":[{"href":"https:\/\/erikap.co.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}