
<PAGE>   1


                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                             ----------------------

                                 SCHEDULE 13E-3
                        Rule 13e-3 Transaction Statement

                        (Pursuant to Section 13(e) of the
                 Securities Exchange Act of 1934 and Rule 13e-3
                          (ss. 240.13e-3) thereunder)

                                BRAD RAGAN, INC.
--------------------------------------------------------------------------------
                              (Name of the Issuer)

                                BRAD RAGAN, INC.
                       THE GOODYEAR TIRE & RUBBER COMPANY
--------------------------------------------------------------------------------
                      (Name of Person(s) Filing Statement)

                     Common Stock, par value $1.00 per share
--------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    750626103
--------------------------------------------------------------------------------
                      (CUSIP Number of Class of Securities)


            Michael R. Thomann                       George E. Strickler
  President and Chief Executive Officer                 Vice President
             Brad Ragan, Inc.                 The Goodyear Tire & Rubber Company
      4404-G Stuart Andrew Boulevard               1144 East Market Street
     Charlotte, North Carolina 28217                  Akron, Ohio 44316
--------------------------------------------------------------------------------
           (Name, Address and Telephone Number of Person Authorized to
            Receive Notices and Communications on Behalf of Person(s)
                                Filing Statement)

      The Commission is requested to send copies of all communications to:


<TABLE>
<CAPTION>
         Garza Baldwin, III                         Robin L. Hinson                              Clarence W. Walker
Womble Carlyle Sandridge & Rice, PLLC       Robinson, Bradshaw & Hinson, P.A.        Kennedy Covington Lobdell & Hickman, L.L.P.
    3300 One First Union Center            101 North Tryon Street, Suite 1900             100 North Tryon Street, Suite 4200
     301 South College Street                     Charlotte, NC 28246                   Charlotte, North Carolina 28202-4006
Charlotte, North Carolina 28202-6025
<S>                                        <C>                                       <C>
</TABLE>

     This statement is filed in connection with (check the appropriate box):

         a.  [X]  The filing of solicitation materials or an information
                  statement subject to Regulation 14A, Regulation 14C, or Rule
                  13e-3(c) under the Securities Exchange Act of 1934.

         b.  [ ]  The filing of a registration statement under the
                  Securities Act of 1933.

         c.  [ ]  A tender offer.

         d.  [ ]  None of the above.


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         Check the following box if the soliciting materials or information
         statement referred to in checking box (a) are preliminary copies: [X]


                            Calculation of Filing Fee

-------------------------------------------------------------------------------


Transaction                             Amount of
valuation*  $20,745,419                 filing fee  $4,149.08

-------------------------------------------------------------------------------


*       Pursuant to Rule 0-11(c)(1), the transaction valuation is based on the
        amount of cash to be received by the issuer's public shareholders in
        connection with the proposed share exchange.

[ ]     Check box if any part of the fee is offset as provided by Rule
        0-11(a)(2) and identify the filing with which the offsetting fee was
        previously paid. Identify the previous filing by registration statement
        number or the Form or Schedule and the date of its filing.

        Amount Previously Paid:

        Filing Party:

        Form or Registration No.:

        Date Filed:



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                              CROSS REFERENCE SHEET

     The information contained in the Preliminary Proxy Statement of Brad Ragan,
Inc. (the "Preliminary Proxy Statement") is incorporated by reference in answer
to the items of this Rule 13e-3 Transaction Statement on Schedule 13E-3 (the
"Transaction Statement"). This cross reference sheet shows the location of such
information required to be included in the response to the items of the
Transaction Statement. The Preliminary Proxy Statement is being filed
concurrently herewith as Exhibit 17(d) to this Transaction Statement.

<TABLE>
<CAPTION>
                                       Location in
Item     Caption in Schedule 13E-3     Preliminary Proxy Statement
----     -------------------------     ---------------------------
<S>     <C>                            <C>
 1.      Issuer and Class of
         Security Subject to the
         Transaction

                  1(a)                 Cover Page; "Summary--Parties to the Exchange
                                       Agreement"

                  1(b)                 Cover Page; "Summary--Votes Required"; "General
                                       Information--Voting Procedures"

                  1(c) and (d)         "Summary--Market Prices; Dividends"; "The
                                       Exchange--Terms of the Exchange--Conduct of the
                                       Business of the Company"

                  1(e) and (f)         *

 2.      Identity and Background

                  This Transaction Statement is being filed by Brad Ragan, Inc.,
         the issuer of the class of equity securities which is the subject of
         the Rule 13e-3 transaction (the "Company"), and The Goodyear Tire &
         Rubber Company, an Ohio corporation ("Goodyear"). The address of
         Goodyear's principal executive offices is 1144 East Market Street,
         Akron, Ohio 44316. Goodyear currently owns approximately 74.5% of the
         outstanding shares of common stock, par value $1.00 per share, of the
         Company (the "Common Stock"). The transaction (the "Exchange") will be
         a share exchange between the Company and Goodyear pursuant to which all
         outstanding shares of Common Stock, other than shares already held by
         Goodyear, will be acquired by Goodyear, and each such share (other than
         shares held by dissenting shareholders) will be converted into the
         right to receive $37.25 in cash from Goodyear.

</TABLE>


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<TABLE>
<S>     <C>                            <C>

                  2(a)-(d)             "Corporate Governance-Nominees for Directors";
                                       "Corporate Governance--Executive Officers";
                                       "Information Concerning Directors and Executive
                                       Officers of Goodyear"

                  2(e)                 Neither the Company nor Goodyear nor any of 
                                       their respective executive officers,        
                                       directors or controlling persons have been  
                                       convicted during the past five years in a   
                                       criminal proceeding (excluding traffic      
                                       violations or similar misdemeanors).        
                                       
                                    

                  2(f)                 Neither the Company nor Goodyear nor any of their
                                       executive officers, directors or controlling persons
                                       have been a party during the last five years to a civil
                                       proceeding of a judicial or administrative body of
                                       competent jurisdiction and as a result of such
                                       proceeding were or are subject to a judgment,
                                       decree or final order enjoining further violations of,
                                       or prohibiting activities subject to, federal or state
                                       securities laws or finding any violation of such
                                       laws.

                  2(g)                 "Corporate Governance--Nominees for Directors";
                                       "Corporate Governance--Executive Officers";
                                       "Information Concerning Directors and Executive
                                       Officers of Goodyear"

 3.      Past Contacts, Transactions
         or Negotiations

                  3(a)                 "Compensation Committee Interlocks and Insider
                                       Participation"; "Special Factors--Background of,
                                       and Reasons for, the Exchange"

                  3(b)                 *

 4.      Terms of the Transaction

                  4(a)                 Cover Page; "Summary--The Exchange"; "The
                                       Exchange--Terms of the Exchange"

                  4(b)                 Goodyear will not exchange its shares of Common
                                       Stock pursuant to the Exchange Agreement.

</TABLE>

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<TABLE>
<S>     <C>                            <C>
 5.      Plans or Proposals of the
         Issuer or Affiliate

                  5(a)                 *

                  5(b) and 5(c)        "Special Factors--Purpose of Exchange; Plans for
                                       the Company"

                  5(d)                 *

                  5(e)-(g)             "Special Factors--Purpose of Exchange; Plans for
                                       the Company"

 6.      Source and Amounts of Funds
         or Other Consideration

                  6(a) and (b)         "Summary--Termination; Fees and Expenses";
                                       "Special Factors--Estimated Fees and Expenses";
                                       "The Exchange--Terms of the Exchange--
                                       Termination; Fees and Expenses"; "The Exchange--
                                       Source and Amount of Funds"

                  6(c) and (d)         *

 7.      Purpose(s), Alternatives,
         Reasons and Effects

                  7(a)-(c)             "Special Factors--Background of, and Reasons for,
                                       the Exchange"; "Special Factors--Purpose of
                                       Exchange; Plans for the Company"

                  7(d)                 "Summary--Parties to the Exchange; The
                                       Exchange"; "Special Factors--Purpose of the
                                       Exchange; Plans for the Company"; "Special
                                       Factors--Certain Tax Consequences of the
                                       Exchange"

 8.      Fairness of the Transaction

                  8(a)                 "Summary--Recommendation of the Board;
                                       Fairness of the Exchange"; "Special Factors--
                                       Fairness of the Exchange"
</TABLE>



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<TABLE>
<S>     <C>                            <C>

                  8(b)                 "Summary--Recommendation of the Board;
                                       Fairness of the Exchange"; "Summary--Opinion of
                                       the Financial Advisor"; "Special Factors--
                                       Background of, and Reasons for, the Exchange";
                                       "Special Factors--Opinion of Financial Advisor"

                  8(c)                 "Summary--Votes Required"; General Information--
                                       Voting Procedures"; "Special Factors--Background
                                       of, and Reasons for, the Exchange"

                  8(d)                 "Special Factors--Fairness of the Exchange"

                  8(e)                 "Summary--Recommendation of the Board;
                                       Fairness of the Exchange"; "Special Factors--
                                       Background of, and Reasons for, the Exchange";
                                       "Special Factors--Fairness of the Exchange"

                  8(f)                 *

 9.      Reports, Opinions, Appraisals
         and Certain Negotiations

                  9(a) and (b)         "Summary--Opinion of Financial Advisor";
                                       "Special Factors--Background of, and Reasons for,
                                       the Exchange"; "Special Factors--Opinion of
                                       Financial Advisor"

                  9(c)                 "Special Factors--Opinion of Financial Advisor"

10.      Interest in Securities
         of the Issuer

                  10(a)                "Summary--Votes Required"; "Summary--Interests
                                       of Certain Persons in the Exchange"; "Special
                                       Factors--Interests of Certain Persons in the
                                       Exchange"; "Security Ownership of Management
                                       and Certain Beneficial Owners"

                  10(b)                "Corporate Governance--Executive Officers of the
                                       Company"; "Information Concerning Directors and
                                       Executive Officers of Goodyear"
</TABLE>




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<TABLE>
<S>     <C>                            <C>

11.      Contracts, Arrangements or
         Understandings with respect
         to the Issuer's Securities    "Summary--Votes Required"; "Summary--Interests
                                       of Certain Persons in the Exchange"; "General
                                       Information--Voting Procedures"; "Special Factors--
                                       Interests of Certain Persons in the Exchange";
                                       "Special Factors--Background of, and Reasons for,
                                       the Exchange"; "The Exchange--Proposal to Amend
                                       the Articles"; "Security Ownership of Management
                                       and Certain Beneficial Owners"


12.      Present Intention and
         Recommendation of Certain
         Persons with Regard to
         the Transaction

                  12(a)                "Summary--Votes Required"; "General
                                       Information--Voting Procedures"

                  12(b)                Goodyear has not made any recommendation in
                                       support of or opposed to the Exchange.

13.      Other Provisions of
         the Transaction

                  13(a)                "Summary--Dissenters' Rights"; "The Exchange--
                                       Dissenters' Rights"

                  13(b)                *

                  13(c)                *

14.      Financial Information

                  14(a)                The information set forth in the Company's
                                       Annual Report on Form 10-K for the year   
                                       ended December 31, 1997 is incorporated   
                                       herein by reference                       
                                       
                                    

                  14(b)                *

</TABLE>

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<TABLE>
<S>     <C>                            <C>

15.      Persons and Assets
         Employed, Retained or
         Utilized

                  15(a)                "General Information--Proxy Solicitation"

                  15(b)                *

16.      Additional Information        Included throughout the Preliminary Proxy
                                       Statement
</TABLE>

<TABLE>
<CAPTION>
17.      Material to be Filed
         as Exhibits

         Exhibit                                                      Method
           No.          Description                                   of Filing
           ---          -----------                                   ---------
<S>                     <C>                                           <C>    

         17(b)(1)       Opinion of Interstate/Johnson                 Filed herewith
                        Lane Corporation dated February 13, 1998

         17(b)(2)       Opinion of Interstate/Johnson Lane            Filed herewith
                        Corporation dated May 4, 1998

         17(b)(3)       Opinion of Interstate/Johnson Lane            To be included as  Annex II to the
                        Corporation dated _________ __, 1998          Preliminary Proxy Statement,
                                                                      filed as Exhibit 17(d) hereto

         17(c)          Agreement and Plan of Exchange                See Annex I to the Preliminary
                                                                      Proxy Agreement, filed as Exhibit
                                                                      17(d) hereto

         17(d)          Preliminary Proxy Statement                   Filed herewith

         17(e)          Article 13 of the North Carolina Business
                        Corporation Act                               See Annex IV to the Preliminary
                                                                      Proxy Statement, filed as Exhibit
                                                                      17(d) hereto
</TABLE>

----------------------
* Item not applicable or answer is negative.


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                                   SIGNATURES


         After due inquiry and to the best of our knowledge and belief, the
undersigned certify that the information set forth in this Transaction Statement
is true, complete and correct.


                                       BRAD RAGAN, INC.



Date:                                  By:    /s/ Michael R. Thomann
                                              -------------------------------
                                       Name:  Michael R. Thomann
                                              -------------------------------
May 12, 1998                           Title: President and Chief Executive
                                              Officer
                                              -------------------------------




                                       THE GOODYEAR TIRE & RUBBER COMPANY


Date:                                  By:    /s/ G. E. Strickler
                                              -------------------------------
                                       Name:  G. E. Strickler
                                              -------------------------------
May 12, 1998                           Title: Vice President
                                              -------------------------------



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