I believe there are limits on how large the input can be for some uses of WolframAlpha, but this is small enough to be accepted.

http://www.wolframalpha.com/input/?i=Fit%5B%7B%7B-4%2C+17.4%7D%2C%7B-3%2C9.3%7D%2C%7B-2%2C+2.4%7D%2C%7B-1%2C-0.08%7D%2C%7B0%2C-0.4%7D%2C%7B1%2C-0.07%7D%2C%7B2%2C2.7%7D%2C%7B3%2C9.3%7D%2C%7B4%2C15.9%7D%7D%2C%7B1%2Cx%2Cx%5E2%7D%2Cx%5D

Can you modify this to work for your data?

This
http://followthedata.wordpress.com/2012/02/25/wolfram-alpha-pro-trial/
says there is a one megabyte upload file size limit.
This
http://www.wolframalpha.com/input/pro/uploadexamples/
shows all the file types it can understand.

So I am assuming it can handle your 1900 data points.
The only question will be how to format the file and how to tell
WolframAlpha Pro you want a fitted line and not some other unwanted calculation.

Strictly as a comparison, if you wanted to post your 1900 comma separated points
and check to see that the posting process didn't appear to mangle any of your data
and state that those were y for x=0,x=1,x=2,...x=1900 then in a couple of seconds I'd
do a linear regression and post the result.