a. Rewrite the data in Example 1 with new x-coordinates in mean deviation form. Let X be the associated design matrix. Why are the columns of X orthogonal?b. Write the normal equations for the data in part (a), and solve them to find the least-squares line, y = β₀ + β₁ x* where x* = x – 5.5.

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EXAMPLE 1 Find the equation y = Bo + Bix of the least-squares line that best fits the data points (2, 1), (5,2), (7,3), and (8,3).