Minimizing Sums of Squares The linear regression line is
Chapter 2, Problem 2.1.1.89(choose chapter or problem)
Minimizing Sums of Squares The linear regression line is often called the least-square lines because it minimizes the sum of the squares of the residuals, the differences between actual y values and predicted y values:
\(\text { residual }=y_{i}-\left(a x_{i}+b\right)\)
where \(\left(x_{i}, y_{i}\right)\) are the given data pairs and y = ax + b is the regression equation, as shown in the figure.
Use these definitions to explain why the regression line obtained from reversing the ordered pairs in Table 2.2 is not the inverse of the function obtained in Example 3.
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