https://file.aiquickdraw.com/mathbot/file/1727251864253dyub3fnw.jpg

To solve this problem, we need to perform linear regression on the given data and determine the equation of the line of best fit in the form:

\[
f(x) = a \cdot x + b
\]

where:
- \( f(x) \) is the predicted "antal" (number),
- \( x \) represents the number of years after 2002.

### The given data is:
\[
\begin{array}{|c|c|}
\hline
\text{Årtal (x)} & \text{Antal (f(x))} \\
\hline
2002 (x=0) & 98 \\
2003 (x=1) & 109 \\
2004 (x=2) & 104 \\
2005 (x=3) & 120 \\
2006 (x=4) & 119 \\
2007 (x=5) & 111 \\
\hline
\end{array}
\]

We will use this data to find the slope \( a \) and intercept \( b \) of the line.

Let me calculate that for you.The result of the linear regression gives the following equation for \( f(x) \):

\[
f(x) = 3.17 \cdot x + 102.24
\]

This means:
- The slope \( a = 3.17 \), which indicates that the "antal" increases by approximately 3.17 units for each year after 2002.
- The intercept \( b = 102.24 \), which is the estimated "antal" for the year 2002.

Would you like more details or have any further questions?

Here are 5 related questions for deeper exploration:
1. How can we interpret the significance of the slope in this context?
2. How well does this linear model fit the data (e.g., calculating the \( R^2 \))?
3. What would the "antal" be in 2008 according to this model?
4. How does linear regression handle outliers in data?
5. What happens if we use a quadratic model instead of a linear one?

**Tip:** Linear regression is ideal for data that shows a straight-line trend, but for more complex patterns, other models may be needed.

Bestem ved regression på data en lineær model af formen f(x) = a * x + b, hvor f(x) beskriver antal og x angiver antal år efter 2002. Data: 2002-98, 2003-109, 2004-104, 2005-120, 2006-119, 2007-111.

Learn how to determine a linear regression model for a dataset ranging from 2002 to 2007. The problem focuses on finding the line of best fit, using algebraic concepts and statistical techniques to determine the slope and intercept. Suitable for students in Grades 10-12.

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