**Unformatted text preview: **sion line and comment on the goodness of ﬁt.
3. Interpret the slope of the line of best ﬁt.
4. Use the regression line to predict the annual US energy consumption in the year 2010.
5. Use the regression line to predict when the annual consumption will reach 120 Quads.
Solution.
1. Entering the data into the calculator gives The data certainly appears to be linear in nature.
2. Performing a linear regression produces We can tell both from the correlation coeﬃcient as well as the graph that the regression line
is a good ﬁt to the data.
3. The slope of the regression line is a ≈ 1.287. To interpret this, recall that the slope is the
rate of change of the y -coordinates with respect to the x-coordinates. Since the y -coordinates
represent the energy usage in Quads, and the x-coordinates represent years, a slope of positive
1.287 indicates an increase in annual energy usage at the rate of 1.287 Quads per year.
4. To predict the energy needs in 2010, we substitute x = 2010 into the equation of the line of
best ﬁt to get y = 1.287(2010) − 2473.890 ≈ 112.9...

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