Math Problem Statement
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.
Solution
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:
where:
- is the predicted "antal" (number),
- represents the number of years after 2002.
The given data is:
\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.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Algebra
Statistics
Formulas
f(x) = a * x + b
Slope formula a = (Σxy - n*x̄*ȳ) / (Σx² - n*x̄²)
Intercept formula b = ȳ - a * x̄
Theorems
Least Squares Regression
Suitable Grade Level
Grades 10-12
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