Unformatted text preview: . Using advanced mathematical machinery,2 it is possible to
ﬁnd the line which results in the lowest value of E . This line is called the least squares regression
line, or sometimes the ‘line of best ﬁt’. The formula for the line of best ﬁt requires notation we
won’t present until Chapter 9.1, so we will revisit it then. The graphing calculator can come to our
assistance here, since it has a built in feature to compute the regression line. We enter the data
and perform the Linear Regression feature and we get
2 and authors with more expertise in this area,
Like Calculus and Linear Algebra 2.5 Regression 171 The calculator tells us that the line of best ﬁt is y = ax + b where the slope is a ≈ 0.214 and the
y -coordinate of the y -intercept is b ≈ 1.428. (We will stick to using three decimal places for our
approximations.) Using this line, we compute the total squared error for our data to be E ≈ 1.786.
The value r is the correlation coeﬃcient and is a measure of h...
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