Once we determine that a set of data is linear using the correlation coefficient, we can use the regression line to make predictions. As we learned previously, a regression line is a line that is closest to the data in the scatter plot, which means that only one such line is a best fit for the data.

### Example 6: 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 the table below.^{[1]} Determine whether the trend is linear, and if so, find a model for the data. Use the model to predict the consumption in 2008.

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 |

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

### Solution

We can introduce new input variable, *t*, representing years since 1994.

The least squares regression equation is:

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 [latex]\left(t=14\right)[/latex],

The model predicts 144.244 billion gallons of gasoline consumption in 2008.

### Try It 2

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