Great! We now want to create a conversion chart. This report should show weekly registration cohorts in rows and the number of conversions (i.e., first purchases) within the first week, the second week, etc. We want the end report to look like this:

Here's the query:

SELECT
  DATE_PART('year', registration_date) AS year,
  DATE_PART('week', registration_date) AS week,
  COUNT(*) AS registered_count,
  COUNT(CASE
    WHEN first_order_id IS NULL
    THEN customer_id
    END) AS no_sale,
  COUNT(CASE
    WHEN first_order_date - registration_date <  INTERVAL '7' day
    THEN customer_id
    END) AS first_week,
  COUNT(CASE
    WHEN first_order_date - registration_date >= INTERVAL '7' day
     AND first_order_date - registration_date <  INTERVAL '14' day
    THEN customer_id
    END) AS second_week,
  COUNT(CASE
    WHEN first_order_date - registration_date >= INTERVAL '14' day
    THEN customer_id
    END) AS after_second_week
FROM customers
GROUP BY DATE_PART('year', registration_date), DATE_PART('week', registration_date)
ORDER BY DATE_PART('year', registration_date), DATE_PART('week', registration_date);

As usual, we used the DATE_PART() function to extract the year and week of registration. Note that we also used the COUNT(CASE WHEN...) technique – this way, we could include multiple metrics in a single report.