Sure! Let's carefully walk through the steps required to solve this problem using linear regression:
1. Organize the Data:
- We have two sets of data points: years and the corresponding number of marriage licenses issued.
- Years: [tex]\([2001, 2005, 2008, 2010, 2011, 2014]\)[/tex]
- Marriage licenses: [tex]\([142,000, 132,000, 120,000, 110,000, 106,000, 93,800]\)[/tex]
2. Determine the Linear Regression Equation:
- The linear regression equation is of the form [tex]\( y = mx + b \)[/tex], where [tex]\( y \)[/tex] is the number of marriage licenses, [tex]\( x \)[/tex] is the year, [tex]\( m \)[/tex] is the slope of the line, and [tex]\( b \)[/tex] is the y-intercept.
3. Calculate the Parameters of the Model:
- Slope ([tex]\( m \)[/tex]): [tex]\(\approx -3804.99\)[/tex]
- Intercept ([tex]\( b \)[/tex]): [tex]\(\approx 7758358.50\)[/tex]
4. Predict the Number of Marriage Licenses Issued in 2003:
- The year [tex]\( x = 2003 \)[/tex].
- Use the linear regression equation [tex]\( y = mx + b \)[/tex]:
[tex]\[
y = (-3804.99) \times 2003 + 7758358.50
\][/tex]
- Performing the calculation gives us:
[tex]\[
y \approx 136959.13
\][/tex]
5. Round the Result to the Nearest Hundred:
- [tex]\( 136959.13 \)[/tex] rounded to the nearest hundred is [tex]\( 137,000 \)[/tex].
Therefore, the number of marriage licenses issued in 2003, according to the model and rounded to the nearest hundred, is:
[tex]\[ \boxed{137,000} \][/tex]
Hence, the correct answer is: A. 137,000
