Based on the coefficient of determination you calculated in Question 3, what percentage in the variability in the dependent variable is explained by year? 0.2429

The coefficient of determination (\(R^2\)) represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). In your case, \(R^2\) is given as 0.2429.

To find the percentage of the variability in the dependent variable that is explained by the year:

\[
\text{Percentage of variability explained} = R^2 \times 100
\]

Substituting the given value:

\[
\text{Percentage of variability explained} = 0.2429 \times 100 = 24.29\%
\]

So, 24.29% of the variability in the dependent variable is explained by the year.

Would you like more details or have any other questions?

Here are some related questions you might find helpful:
1. What does a higher \(R^2\) value indicate in a regression analysis?
2. What factors might contribute to the remaining 75.71% of unexplained variability?
3. How do you interpret an \(R^2\) value close to 1?
4. What are the limitations of using \(R^2\) to assess the fit of a model?
5. How can you improve the \(R^2\) value in a regression model?
6. What is the difference between \(R^2\) and adjusted \(R^2\)?
7. How does the number of independent variables affect the \(R^2\) value?
8. Why might a model with a low \(R^2\) still be useful?

**Tip:** Always consider the context of your data when interpreting \(R^2\); a lower \(R^2\) does not necessarily mean your model is ineffective, especially in fields where high variability is common.

Explore how to interpret the percentage of variability in the dependent variable explained by the year in regression analysis. Learn the formula to calculate this percentage using the coefficient of determination (R^2).

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