# Assignment 5

Your assignment is to make an SVG graph of the points displayed in the table below, with a least-squares fit line displayed on the same axes. You will then write about the construction of the picture in a LaTeX document. The data record the weights (in grams) of salmon on given days of a study that compared normal salmon growth with that of salmon undergoing stress.

Sample image

Data from the control group of a study of salmon growth
 Day of study -36 0 4 16 26 49 80 208 Salmon weight 4.2 8.5 8.6 9.4 9.8 10.3 11.2 15.5

1. Convert the numbers in such a way as to make an SVG image similar to, or better than the sample image shown on this page. You will need to make your logical space at least 200 by 200 to get the resolution you need - we made this image tiny so you would not be tempted to copy it and turn it in as your own. The line that fits the data best in the least-squares sense is given by $l\left(x\right)=7.97+0.04x,$ where $x$ is the day of the study.
2. Use GIMP or your favorite image conversion program to convert the SVG to a JPEG image.
3. Write a paper in LaTeX that discusses the data and the image. It should have sections with the following topics.
• A section describing briefly what is meant by a "least-squares" fit, and listing these data in a table.
• A section describing the conversions required to change the data into logical coordinates for the SVG plot.
• A section drawing some obvious conclusions about the change in the weight of the salmon over time, and the possible flaws in methodology that we can surmise from the patterns in the data.
4. Your JPEG image will appear somewhere in the paper, with a caption that labels the points and the line (e.g. "the green line is the least-squares fit to the data").

We expect that there will be some equations in this paper, giving technical descriptions of what is meant by a least-squares fit, and giving the conversions you applied in creating your SVG. As noted above, you will put a table similar to that above and the figure you created in the paper as well. There will probably be a need to explain the notation; e.g. in the figure above, I would need to explain what x and y are. There is no required length for this, however I will be surprised if you can do a decent job in less than two pages, and I will become disgruntled if I have to read more than four.

You will mail the completed TeX file, and both the SVG and JPG images to the instructor. This assignment is worth 60 points and is due at 9:00AM on Tuesday, 16 October.

Welcome to Math 300 for summer, 2013.

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