Solved: To find the least squares regression line y = ax + b for a set of points (x1

Chapter 8, Problem 86

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Fitting a Line to Data    To find the least squares regression line y = ax + b for a set of points

\(\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right), \ldots,\left(x_{n}, y_{n}\right)\)

you can solve the following system for a and b.

\(\left\{\begin{array}{r}n b+\left(\sum_{i=1}^{n} x_{i}\right) a=\left(\sum_{i=1}^{n} y_{i}\right) \\ \left(\sum_{i=1}^{n} x_{i}\right) b+\left(\sum_{i=1}^{n} x_{i}^{2}\right) a=\left(\sum_{i=1}^{n} x_{i} y_{i}\right) \end{array}\right.\)

In Exercises 85–88, the sums have been evaluated. Solve the given system for a and b to find the least squares regression line for the points. Use a graphing utility to confirm the results.

\(\left\{\begin{array}{r} 5 b+10 a=11.7 \\ 10 b+30 a=25.6 \end{array}\right. \)

Text Transcription:

(x_{1}, y_{1}),(x_{2}, y_{2}), . . . ,(x_{n}, y_{n})

{nb+(sum_{i=1}^{n}x_{i})a=(sum_{i=1}^{n}y_{i}) _(sum_{i=1}^{n}x_{i})b+(sum_{i=1}^{n}x_{i}^{2})a=(sum_{i=1}^{n}x_{i} y_{i})

{5b+10a=11.7 _10b+30a=25.6

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