I am reposting this, because I have realised that in my first answer I gave away the source, which may be confidential.

The English is a little strange to the ear of a native speaker. This is from a film made in a country where many people speak English, but generally not as their first language.

So the ellipsis is there because it is laid out as a film script:

"00:14:19 Just to show your institute...
00:14:21 ...you are a management trainee in my company."

(I found this on the Internet. I won't post the url because it reveals the name of the film.)

In a script, an ellipsis at the end of one line and the beginning of the next indicates that they follow on without a break. So there is no pause after "institute", and indeed the timings confirm this.

So "Just to show your institute you are a management trainee in my company" is one continuous sentence, with nothing omitted and no pause. When we see it like this, I think it is clear that it means "Just to show your institute THAT you are a management trainee in my company". Ritu, the boss's daughter, is a student at a management institute. She has done this report, which has turned out so disastrously, in order to show it to her institute -- the institute where she is studying -- so as to demonstrate that she is a trainee in the company. I presume that she is expected to get work experience for her course and to provide evidence of the work she is doing. She has done the report for that purpose. From what her father says she would have difficulty finding a placement other than in the family firm. (But it doesn't matter that she's no good with figures, because of course she will marry the hero and live happily ever after.)


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Note added at 10 hrs (2013-10-27 06:40:35 GMT)
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I am sure that "Just to show your institute" does not mean "Just to impress your institute" here, even if, as Piyush says, that is a direct translation of a Hindi phrase.

Of course, that idea is implicit, in any case: by showing the report to her teachers at the institute, Ritu presumably hopes to impress them. However, "show" can't mean "impress" here. For that to be the meaning, we have to assume that "Just to show your institute" stands in isolation, as a single sentence, and that "you are a management trainee in my company" is a separate sentence. "Show" cannot mean "impress" if "Just to show your institute you are a management trainee in my company" is a single continuous sentence, because if that is the case, then "you are a management trainee in my company" has to be the object of "show": it has to be what Ritu is intending to show the institute. Otherwise it would be syntactically unconnected to "Just to show your institute".

As I have explained, this must be a continuous sentence, because if the two parts were separate sentences, there would be no ellipses in the script; it would read like this:

00:14:19 Just to show your institute.
00:14:21 You are a management trainee in my company.

Since it is not set out like that, it must be a continuous sentence, which means that "show" must mean "demonstrate", and what is demonstrated is the fact that she is a management trainee in the company.