*This preview shows
page 1. Sign up
to
view the full content.*

**Unformatted text preview: **ow close the data is to being on
the same line. The closer |r| is to 1, the better the linear ﬁt. Since r ≈ 0.327, this tells us that the
line of best ﬁt doesn’t ﬁt all that well - in other words, our data points aren’t close to being linear.
The value r2 is called the coeﬃcient of determination and is also a measure of the goodness of
ﬁt.3 Plotting the data with its regression line results in the picture below. Our ﬁrst example looks at energy consumption in the US over the past 50 years.4
Year Energy Usage,
in Quads5
1950
34.6
1960
45.1
1970
67.8
1980
78.3
1990
84.6
2000
98.9
Example 2.5.1. Using the energy consumption data given above,
1. Plot the data using a graphing calculator.
3 We refer the interested reader to a course in Statistics to explore the signiﬁcance of r and r2 .
See this Department of Energy activity
5
The unit 1 Quad is 1 Quadrillion = 1015 BTUs, which is enough heat to raise Lake Erie roughly 1◦ F 4 172 Linear and Quadratic Functions 2. Find the least squares regres...

View
Full
Document