Thank you for uploading the image again! Based on the question, here's the interpretation:

Part (a) - What is the meaning of $R^2$ in this context?

In the context of the regression model, $R^2$ measures the proportion of the variation in the dependent variable (CO$_2$ levels) that is explained by the independent variable (likely time, in this case). The higher the $R^2$ value, the better the model explains the variation in CO$_2$ levels.

Correct Answer:

The correct choice is:

A. A linear trend over time can account for [ ]% of the variance in CO$_2$.

Filling in the Blank:

To complete this, you need the actual $R^2$ value from the regression output (likely provided when clicking the link in the question). The $R^2$ value is typically a percentage that you input in the blank.

For example, if the regression output shows $R^2 = 0.89$, then you would write:

"A linear trend over time can account for 89% of the variance in CO$_2$."

Additional Guidance:

Would you like help finding or interpreting the $R^2$ value if you share it or have access to the linked regression data?

Related Questions for Deeper Understanding:

1. Why is $R^2$ important in evaluating a regression model?
2. What does it mean if $R^2$ is very low (e.g., less than 20%)?
3. How can residuals help determine the validity of the regression model?
4. What is the difference between $R^2$ and adjusted $R^2$?
5. What does an $R^2$ value of 100% indicate?

Tip:

When interpreting regression models, ensure you understand both the $R^2$ value and the residual plots for a more complete analysis! Residual plots can reveal issues like non-linearity or outliers.