SQL XML Explicit problems with creating xml tree (parent-child)

I'm facing some problems with xml explicit in sql server where it doesn't output xml according to the relationship I specified in sql query. The query is done on pubs database and though xml path is easier to use my trainer needs it done on xml explicit.

    SELECT  1               AS Tag,
        NULL            AS Parent,
        NULL            AS [TitleTypes!1],
        NULL            AS [TitleType!2!Type],
        NULL            AS [TitleType!2!AveragePrice],
        NULL            AS [Title!3!title_id],
        NULL            AS [Title!3!price]

UNION ALL
SELECT  2,
        1,
        NULL            ,
        type            AS [TitleType!2!Type],
        AVG(price)      AS [TitleType!2!AveragePrice],
        NULL            AS [Title!3!title_id],
        NULL            AS [Title!3!price]
from titles 
GROUP BY type   
UNION ALL
SELECT  3,
        2,
        NULL            ,
        type            AS [TitleType!2!Type],
        NULL            AS [TitleType!2!AveragePrice],
        title_id        AS [Title!3!title_id],
        price           AS [Title!3!price]

from titles     

FOR XML EXPLICIT;

The output it produces:

    <TitleTypes>
  <TitleType Type="business    " AveragePrice="13.7300" />
  <TitleType Type="mod_cook    " AveragePrice="11.4900" />
  <TitleType Type="popular_comp" AveragePrice="21.4750" />
  <TitleType Type="psychology  " AveragePrice="13.5040" />
  <TitleType Type="trad_cook   " AveragePrice="15.9633" />
  <TitleType Type="UNDECIDED   ">
    <Title title_id="BU1032" price="19.9900" />
    <Title title_id="BU1111" price="11.9500" />
    <Title title_id="BU2075" price="2.9900" />
    <Title title_id="BU7832" price="19.9900" />
    <Title title_id="MC2222" price="19.9900" />
    <Title title_id="MC3021" price="2.9900" />
    <Title title_id="MC3026" />
    <Title title_id="PC1035" price="22.9500" />
    <Title title_id="PC8888" price="20.0000" />
    <Title title_id="PC9999" />
    <Title title_id="PS1372" price="21.5900" />
    <Title title_id="PS2091" price="10.9500" />
    <Title title_id="PS2106" price="7.0000" />
    <Title title_id="PS3333" price="19.9900" />
    <Title title_id="PS7777" price="7.9900" />
    <Title title_id="TC3218" price="20.9500" />
    <Title title_id="TC4203" price="11.9500" />
    <Title title_id="TC7777" price="14.9900" />
  </TitleType>
</TitleTypes>

The output I want:

   <TitleTypes>
    <TitleType Type="business" AveragePrice="11.22">
        <Title title_id="BU1111" Price="11.34"/>
        <Title title_id="TC7777" Price="14.2"/>
    </TitleType>
    <TitleType Type="popular_comp" AveragePrice="13.99">
        <Title title_id="BU1111" Price="15.9"/>
        <Title title_id="TC7777" Price="16.22"/>
    </TitleType>
</TitleTypes>

Usually, you don't need explicit mode at all. You can generate almost every xml you want with for xml path:

select
    t1.type as [@Type],
    avg(t1.price) as [@AveragePrice],
    (
        select
            t2.title_id as [@title_id],
            t2.price as [@price]
        from titles as t2
        where t2.type = t1.type
        for xml path('Title'), type
    )
from titles as t1
group by t1.type
for xml path('TitleType'), root('TitleTypes')

But since your xml is attribute-centric, it's even easier for you to use for xml raw:

select
    t1.type as [Type],
    avg(t1.price) as AveragePrice,
    (
        select
            t2.title_id
            t2.price
        from titles as t2
        where t2.type = t1.type
        for xml raw('Title'), type
    )
from titles as t1
group by t1.type
for xml raw('TitleType')

sql fiddle demo