Question 1190381
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The data table seems a bit garbled. 
This is what I'm assuming it looks like<table border = "1" cellpadding = "5"><tr><td>0</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td>10</td></tr><tr><td>(1,7)</td><td>(1,7)</td><td>(2,3)</td><td>(2,9)</td><td>(3,0)</td><td>(3,5)</td><td>(4,0)</td><td>(11,0)</td><td>(9,5)</td><td>(9,7)</td><td>(9,9)</td></tr></table>You could find the linear regression equation by hand, but it's a tedious process that may take a while. 
I strongly recommend using a graphing calculator or computer software. There are many free options online if you don't have a graphing calculator.


Whichever method you use, the linear regression equation is approximately this:
y = -0.0929x + 5.1832


The correlation coefficient (r value) is a similar story to finding the regression equation. It's better to use a calculator.
You should find that r = -0.1004 approximately
Since this is much closer to r = 0 than it is to r = 1, this makes the negative linear correlation fairly weak. 
It's not a good idea to use a linear model here.


Because you mentioned the data is periodic, a sine or cosine model would likely provide a better fit.
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