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# answer2 - Problem 1 We will want to find and so that the...

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Problem 1: We will want to find and so that is minimized. Set the partials to be zero: Collecting terms and recalling that , this gives two equations in two unknowns: From Cramer's rule, we get and Problem 2:

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(1) (2) I'll call the month array and the temperature array 2 4 6 8 10 12 65 70 75 80 85 90 95 The above is the scatter plot of temperature. I'll need to find , , and to minimize , the sum of the squares of the errors. I'll supress output so that you aren't printing out too much garbage. From the scatter plot, we expect a sine curve going from about 60 to about 96, which would have an amplitude of 18. So, I'll tell it to look for between 10 and 20. would be the average temperature (how
(3) (4) far up from the axis you move the sine curve), so about 80. I'm taking to be between 0 and , since sine is periodic of that period. On the other hand, 's outside of this range aren't wrong. So, here's the answer. Let's plot this over the scatter plot to see how close we are.

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