ALVIN B. RUBIN, Circuit Judge:

The owner of an infringed copyright asks this court to increase the amount of damages awarded it by the district court and to find liability on the part of a co-defendant the district court held to have been an innocent infringer. We find that the district court did not err in failing to base the damage award on those profits of the infringer allegedly attributable to the infringement because the infringer did not establish the amount of those profits, if any there were, and the court did not err in finding the co-defendant innocent. Accordingly, we affirm.

I.

The Fair, a chain of retail stores, hired photographer Dean Vane to prepare slides showing its merchandise with the stated purpose of using the slides in printed advertising material to be mailed to its customers. Later, however, The Fair hired Vance-Mathews, Inc., an advertising agency, to produce television commercials, which incorporated some of Vane's slides as well as a substantial amount of material from other sources. Several television stations aired the commercials. Vane brought an action based on copyright infringement against The Fair, asserting that his agreement with The Fair involved merely a license to use the slides to produce mailers and that he retained all other rights to the slides provided by copyright law. Vane also contended that Vance-Mathews, the advertising agency that had produced the commercials, was liable as an infringer. The district court granted Vance-Mathews's motion for a directed verdict on the theory that Vance-Mathews was an innocent infringer and could therefore be liable only to the extent of profits it had gained through the infringement, of which there were none. The court held that The Fair was liable, and it awarded damages in the amount of $60,000, an amount representing the value of the use of the slides in the commercials. 676 F. Supp. 133. The court refused to make a damage award based on profits The Fair had accrued by virtue of the infringement; it found that the evidence was too speculative to support such an award. On appeal, Vane contends that the court erred in denying an award based on The Fair's profits and in granting Vance-Mathews's motion for a directed verdict.

II.

In a copyright infringement action, the infringer is liable for either statutory damages or the copyright owner's actual damages together with any additional profits of the infringer that are attributable to the infringement. Vane elected to seek actual damages and profits. The statute that authorizes this recovery also provides that in establishing the infringer's profits, the copyright owner need prove only the infringer's gross revenues, while the infringer must prove his deductible expenses and must show which elements of profits are attributable to sources other than the copyrighted work.

Vane attempted through discovery to obtain financial records of The Fair that would enable him to satisfy his burden of proving The Fair's gross revenues attributable to the infringement, but the records were not detailed enough to show the amount received from the sales of particular items shown in the slides. Therefore Vane attempted to establish The Fair's gross revenues, and ultimately its profits, by introducing as an expert witness Dr. Herbert Lyon, Professor of Marketing at the University of Houston's College of Business Administration. Dr. Lyon testified that he had conducted a multiple regression analysis designed to show how much each dollar The Fair spent on television advertising would yield in sales. Dr. Lyon examined monthly data, including profit-and-loss statements and summaries of media costs over a five-year period. He calculated that The Fair sold approximately $25.60 in merchandise for every dollar it spent on television advertising. He multiplied $25.60 by the number of dollars The Fair spent on the infringing television commercials to yield a gross revenue figure, then deducted certain costs to The Fair, including the actual cost that The Fair had paid for the merchandise it sold, transportation charges for getting the merchandise to the stores, a 3% allowance for pilferage, and some other direct operating expenses. After adjusting the resulting figure for inflation, Dr. Lyon concluded that The Fair's profits attributable to its infringement of Vane's slides exceeded $694,000. The district court held that Vane had not brought forth sufficient proof of The Fair's profits and refused to award damages based on Dr. Lyon's calculations.

When financial records sufficiently detailed to show an infringer's sales are not available, expert testimony may be used to develop either such proof or, as Vane attempted, proof of its profits rather than its sales. But it is the trial court's role to evaluate this testimony. The trial court in this case concluded, with ample basis, that the testimony introduced was inadequate to establish The Fair's profits attributable to the infringement.

In conducting his analysis, Dr. Lyon took into account a variety of factors designed to refine his calculations. For instance, his model purported to consider seasonal sales trends, specifically the pre-Christmas boom in sales; the downward economic trend in the Houston area in the early 1980's; and the carryover effect by which an advertisement continues to contribute to some sales long after its initial airing. By taking such factors into account, Dr. Lyon testified, he attempted to produce a model that would analyze with the greatest possible precision the relationship between advertising dollars spent and resulting profits.

Cross-examination, however, brought to light a number of potential shortcomings in this analysis. Dr. Lyon's model yielded only a lump-sum figure for profits attributable to the television commercials that contained infringed material as a whole without accounting for the fact that the infringed material constituted only a fraction of any given commercial. Some portion of the profits may have been attributable to the infringement, but much of the profits must be attributed to noninfringing aspects of the commercials. Testimony at trial showed from three perspectives why the use of an undifferentiated figure does not convincingly establish what profits are attributable to the infringement.

First, the cost of slides used in a commercial is only one of many expenses involved. The single figure for "dollars spent on television advertising" must be composed of lesser expenditures for a variety of goods and services: photographs used in the commercial, fees paid to the producer of the commercial, and air time for showing the commercial, to name a few. If, for instance, 50% of the cost to someone airing a commercial went to television stations to pay for air time, another 30% went to the producer, and 20% went to purchase ten slides used in the commercial, which also used five infringed slides, then it would be wholly illogical to treat the entire profits derived from airing the commercial as attributable to the five infringed slides. Yet this is, in essence, what Vane asked the district court to do. Dr. Lyon testified that he had adjusted the sales figures his model yielded to account for air time and production costs, but neither his testimony nor the computer printouts introduced as an exhibit make clear what this adjustment was. Even if Dr. Lyon's analysis accurately showed the relationship between dollars spent on advertising and profits yielded, it did not show the relationship between the dollars that should have been spent on the rights to use Vane's slides and the total television advertising costs. Evidence of this relationship might have provided a basis for showing what portion of the profits the commercials yielded were attributable to the infringement.

Second, the infringed slides appeared during only part of the time the commercials were on the air. Vane testified that the general format of the commercials in question consisted of a "trailer" or introductory film segment setting forth a theme for the commercial, followed by a segment featuring various items of merchandise, concluding with another brief trailer. To the extent that Vane's slides appeared in the commercials, they appeared only in the middle segments, never in the trailers. Moreover, the middle segments that contained infringed slides also contained non-infringed slides. If only eight seconds of a thirty-second commercial contained infringed slides, it would be irrational to believe that all the profits the commercial brought in were due to those slides.

Third, Dr. Lyon's model did not purport to show the relative importance of different elements of the commercials in generating profits for The Fair. On cross-examination, counsel for The Fair asked Dr. Lyon:

If we take your figures that are given here of some $600,000 that you say are attributable to the TV advertising dollar, do you express any opinion as to what percentage of that should be attributable to Mr. Vane's slides as contrasted to the work product of Vance-Matthews in putting the commercials together?

Dr. Lyon responded:

No, sir.... I'm simply looking at the revenue or gross revenues generated by those ads. I did not look at the ads specifically. I don't think — I mean, I thought of that issue, but I don't think it can be answered.

Photographs of particular items featured in commercials doubtless play a role in producing sales, but, we assume, so do such aspects of the commercials as text of the voice-overs, general slogans or phrases promoting the store itself, and overall concept of the commercial's message. Vane himself described the trailers that introduced the commercials as "a very nice attention-getting device, which is the first responsibility of an ad." Dr. Lyon admitted on cross-examination that the carryover benefit of an advertisement promoting a particular sales event, such as a Father's Day sale or an Easter sale, would probably be achieved primarily because the advertisement promoted name recognition of the store that was holding the sale. But Dr. Lyon's model did not show what part of the Fair's profits should be attributed to these factors rather than to the use of the infringed slides.

By pointing to these problems in Dr. Lyon's analysis, we do not suggest that a calculation based on a mathematical formula involving the ratio of fair cost of infringed material to entire cost of commercial, or length of air time of infringed material to length of entire commercial, would be the only means of showing profits. The question will often be highly fact-specific. We merely hold that it was not error for the district court to reject this attempt to show revenues attributable to the infringement as speculative.

III.

The district court orally granted Vance-Mathews's motion for a directed verdict and later rendered judgment in favor of Vance-Mathews "for the reasons announced by the Court at that time." Although the district court did not specifically state the statutory authority for its grant of the motion, we affirm on the basis that Vance-Mathews was an innocent infringer as defined by 17 U.S.C. § 405(b) (1982). That section states, in relevant part:

Any person who innocently infringes a copyright, in reliance upon an authorized copy or phono record from which the copyright notice has been omitted, incurs no liability for actual or statutory damages under Section 504 [ 17 U.S.C. § 504] for any infringing acts before receiving actual notice that registration for the work has been made under Section 408 [ 17 U.S.C. § 408], if such person proves that he or she was misled by the omission of notice.

The Copyright Act defines "copies" as "material objects ... in which a work is fixed" and provides that "[t]he term `copies' includes the material object ... in which the work is first fixed."

Vance-Mathews raised the defense of innocent infringement in its First Amended Original Answer and relied on § 405(b) in its argument in support of its motion for a directed verdict. At trial, the president of Vance-Mathews testified that the agency had no knowledge that the slides were copyrighted, or that anyone claimed that they were copyrighted, or that the slides belonged to anyone other than The Fair. He also stated that if the slides had borne a notice of copyright, the agency would have checked with The Fair to see whether use of the slides in a commercial posed any problems. A senior vice-president of The Fair testified that none of the slides or photographs it received from Vane bore any copyright markings, nor did Vane attempt to have copyright markings affixed after he delivered the materials to The Fair. He further testified that at the time The Fair turned the slides over to Vance-Mathews, none of them bore copyright markings.

Although Vane testified that it was his practice to stamp slides with an indication of his copyright before sending them to clients, he acknowledged that "some could have slipped through, I suppose, considering the volume of slides I tendered." At trial, counsel for The Fair presented Vane with 58 boxes of slides of his work as well as a number of black-and-white photographs that Vane had previously delivered to The Fair. Vane testified that if they were originals rather than copies of his slides and photographs, he would expect them to bear his copyright mark, but after inspecting them, he failed to identify a single slide or photograph that bore notice of copyright.

In this non-jury trial, it was the judge's role to resolve any conflicting inferences arising from witnesses' testimony. Both Vance-Mathews executives testified unequivocally that the slides they received were not marked, and its president further testified that the agency would have inquired about ownership of rights to the slides if they had been so marked. The district court obviously chose to credit the testimony of the Vance-Mathews witnesses, because it entered a finding of fact that Vane failed to affix any copyright mark or notice to the slides he delivered to The Fair. The evidence was, therefore, sufficient to allow the court to grant Vance-Mathews's motion for a directed verdict on the theory that it was an innocent infringer misled by the omission of notice of copyright.

For these reasons, we AFFIRM.