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====== Math 445 Lab 9: log-linear relationships ======

For each of the following data sets,  determine a function 
//y(x)// that fits the data, by the following steps

  - Cut & paste the data set to a text file named ''data1.asc'' etc.
  - Load the dataset to Matlab with ''load data1.asc''.
  - Set //x// to the first column of ''data1'', ''y'' to the second.
  - Experiment with ''plot'', ''semilogy'', ''semilogx'', and ''loglog'' to determine the form of log-linear relationship ''x'' and ''y''.
  - Estimate the constants in the log-linear relationship graphically to determine ''y'' as a function of ''x'', e.g. ''y = 3.2 x - 4''.
  - Plot the estimated function and the data together, and fine-tune your function by adjusting the constants until there is a good fit between the function and the data.


Once you have good fit between the data and the function, make a plot that shows

  * the data set's //y// versus //x// as red circles
  * your function //y(x)// as a solid blue line
  * a legend indicating the meaning of each plotting symbol
  * appropriate labels for each axis and a title

The data sets are given as // N x 2// matrices with //x// as the 
first column and //y// as the second. 

==== data set 1====

% data1: y = -0.492*x + 19.33
<code>
-7.3678e+01   5.5580e+01
-3.9780e+01   3.8902e+01
-5.7090e+00   2.2139e+01
 7.2455e+00   1.5765e+01
 2.1237e+01   8.8812e+00
 5.3694e+01  -7.0872e+00
 6.1294e+01  -1.0827e+01
 6.6552e+01  -1.3414e+01
 7.0465e+01  -1.5339e+01
 9.8648e+01  -2.9205e+01
</code>


==== data set 2 ====

% data2: y = 8.480892*log(x)-18.94949

<code>
1.3880e+00  -1.6169e+01
1.6134e+00  -1.4893e+01
3.0034e+00  -9.6227e+00
1.2373e+01   2.3840e+00
1.9897e+01   6.4134e+00
3.7767e+01   1.1848e+01
8.2823e+01   1.8508e+01
6.4551e+02   3.5922e+01
7.3920e+02   3.7072e+01
2.1998e+03   4.6321e+01
</code>


==== data set 3 ====

% data3: y = 678*exp(-0.194*x)

<code>
-1.8137e+01   2.3293e+04
-4.9006e+00   1.7647e+03
 1.5501e+00   5.0186e+02
 1.0603e+01   8.5938e+01
 1.1370e+01   7.4004e+01
 1.2914e+01   5.4770e+01
 3.5890e+01   6.2153e-01
 4.6459e+01   7.9200e-02
 5.6213e+01   1.1830e-02
 5.6826e+01   1.0497e-02
</code>


==== data set 4 ====

% data4: y = 3.286e-03 * x.^0.8402

<code>
1.1028e+00   3.5676e-03
1.7049e+00   5.1446e-03
5.3239e+00   1.3392e-02
6.2795e+00   1.5384e-02
1.2042e+01   2.6588e-02
7.3213e+01   1.2114e-01
1.0667e+02   1.6620e-01
3.2404e+02   4.2274e-01
4.2700e+02   5.3303e-01
6.9222e+02   7.9991e-01
</code>
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