A pump is tested for power required to deliver water at specified height. The results are given in the table below. Use least-squares regression to fit: 1. A straight line 2. A power equation P= a Hb 3. A saturation-growth-rate equation 4. A parabolic equation Plot the data along with all the curves. Determine r and Sy/x. Is any one of the curves superior? If so, justify. H 1.1 6.2 12.2 18.4 21.9 28.2 33.9 36.1 44.2 47.3 18 26 34 32 41 37 45 49 95 44

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.