(Solution) - Use the principle of least squares to write the expression -(2025 Original AI-Free Solution)

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Use the principle of least squares to write the expression you would use to fit a curve of the form Y = aX2 + b. One easy way to solve this is to think of a new measurement Z = X2 and find the linear regression of Y on Z. Plot the linear regression of Y against Z and the curved regression of Y against X2. Compute r2. Which model does better?
Consider the following measurements.
x y
1.0 ........... 1.1
2.0 ........... 3.9
3.0 ........... 8.8
4.0 ........... 16.5