How to use Excel Solver for piecewise linear fit?

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I am trying to use Excel Solver to get fits for a piecewise linear function (here, a three line fit). The Solver explanation here is helpful for a single linear case, but I am not sure how to set the model up "smartly" so that it re-calculates the hinge-points (i.e., x-values of line intersections will change with the input data). I've never used Solver before.

x   y
1   0.1552
2   0.1877
3   0.2016
4   0.2094
5   0.2142
6   0.2176
7   0.2201
8   0.2220
9   0.2235
10  0.2247
11  0.2256
12  0.2265
13  0.2272
14  0.2278
15  0.2283
16  0.2288
17  0.2292
18  0.2296
19  0.2299
20  0.2302

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