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Suppose we want to best-fit a quadratic function: y=kx2 to three data points as shown below:

Suppose we want to best-fit a quadratic function: y=kx2 to three data points as shown below:

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve both part's correctly
Suppose we want to best-fit a quadratic function: y=kx2 to three data points as shown below: -8 -6 y = kx? -5 --4 -3 data point This means we want to find a value of k, such that the best-fit curve (blue) is 'closest' to the three points given. a) Given that the error, d, between each data point (x, y,) and the best-fit curve is: d;=kx}=y;, Show that the sum of squared errors (SSE) is: SSE=d?+ d?+ d?=(k– 1) ²+ ( 4k – 3) 2+ ( 9k – 8) 2 b) The best-fit curve occurs when the SSE is at a minimum. Solve for the coefficient k of the best-fit curve and show that both the local & global minimum value of the SSE occurs at this value of k
Transcribed Image Text:Suppose we want to best-fit a quadratic function: y=kx2 to three data points as shown below: -8 -6 y = kx? -5 --4 -3 data point This means we want to find a value of k, such that the best-fit curve (blue) is 'closest' to the three points given. a) Given that the error, d, between each data point (x, y,) and the best-fit curve is: d;=kx}=y;, Show that the sum of squared errors (SSE) is: SSE=d?+ d?+ d?=(k– 1) ²+ ( 4k – 3) 2+ ( 9k – 8) 2 b) The best-fit curve occurs when the SSE is at a minimum. Solve for the coefficient k of the best-fit curve and show that both the local & global minimum value of the SSE occurs at this value of k
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