Example 6 from Algebra and Trigonometry, 4.3 Fitting Linear Models to Data

Using a Regression Line to Make Predictions

Gasoline consumption in the United States has been steadily increasing. Consumption data from 1994 to 2004 is shown in Table 3.8 Determine whether the trend is linear, and if so, find a model for the data. Use the model to predict the consumption in 2008.

http://www.bts.gov/publications/national_transportation_statistics/2005/html/table_04_10.html

Year	'94	'95	'96	'97	'98	'99	'00	'01	'02	'03	'04
Consumption (billions of gallons)	113	116	118	119	123	125	126	128	131	133	136

Table 3

The scatter plot of the data, including the least squares regression line, is shown in Figure 8.

Scatter plot, showing the line of best fit. It is titled 'Gas Consumption VS Year'. The x-axis is 'Year After 1994', and the y-axis is 'Gas Consumption (billions of gallons)'. The points are strongly positively correlated and the line of best fit goes through most of the points completely.

Figure 8

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
We can introduce a new input variable, $t,$ representing years since 1994.
The least squares regression equation is:

$C (t) = 113.318 + 2.209 t$

Using technology, the correlation coefficient was calculated to be 0.9965, suggesting a very strong increasing linear trend.

Using this to predict consumption in 2008 $(t = 14),$

$\begin{array}{l} C (14) = 113.318 + 2.209 (14) \\ = 144.244 \end{array}$
The model predicts 144.244 billion gallons of gasoline consumption in 2008.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Use the model we created using technology in Example 6 to predict the gas consumption in 2011. Is this an interpolation or an extrapolation?

How did it go?

Solution

Your turn

Solution

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