To determine the number of passengers expected in 2013 based on the given data, we utilize linear regression, which is a method to model the relationship between two variables by fitting a linear equation to the observed data.
### Step-by-Step Solution:
1. List the Data:
| Year | Passengers (Millions) |
|------|-----------------------|
| 1980 | 30.4 |
| 1985 | 44.2 |
| 1989 | 48.1 |
| 1995 | 55.3 |
| 1998 | 62.8 |
| 2005 | 77.5 |
2. Identify Variables:
- Let `x` represent the year.
- Let `y` represent the number of passengers in millions.
3. Determine the Linear Regression Equation:
The linear regression equation follows the form [tex]\(y = mx + b\)[/tex], where:
- [tex]\(m\)[/tex] is the slope of the line.
- [tex]\(b\)[/tex] is the intercept of the line.
4. Calculate Slope (m) and Intercept (b):
From the data provided and the linear regression analysis, we find the slope ([tex]\(m\)[/tex]) and the intercept ([tex]\(b\)[/tex]):
- Slope ([tex]\(m\)[/tex]) = 1.7588942307692894
- Intercept ([tex]\(b\)[/tex]) = -3450.667307692425
5. Estimate the Number of Passengers in 2013:
Substitute [tex]\(x = 2013\)[/tex] into the linear equation [tex]\(y = mx + b\)[/tex]:
[tex]\[
y = 1.7588942307692894 \times 2013 + (-3450.667307692425)
\][/tex]
[tex]\[
y \approx 89.98677884615472
\][/tex]
Thus, the estimated number of passengers in 2013 is approximately 90 million.
6. Select the Closest Option:
Among the given options:
- F. 82 million
- G. 86 million
- H. 90 million
- J. 94 million
The closest option to 90 million is H. 90 million.
### Conclusion:
The correct choice for the number of passengers expected in 2013 is:
c. H
