In the image you uploaded, it appears that the question is asking you to fill in the blank with the appropriate term related to regression analysis.

The statement reads: "The ________ measures the proportion of total variation in the response variable that is explained by the least squares regression line."

The correct term to fill in the blank is "coefficient of determination" (often represented as $R^2$).

Explanation:

• Coefficient of determination ($R^2$) is used to describe how well the regression model explains the variability in the response variable. It ranges from 0 to 1, where a value closer to 1 means a better fit of the regression line to the data.

If you'd like more details or have any further questions, feel free to ask!

Here are some related questions to explore the topic further:

1. What is the significance of $R^2$ in regression analysis?
2. How do you calculate the coefficient of determination in a simple linear regression?
3. What does a low $R^2$ value indicate in a regression model?
4. How is the residual sum of squares related to the coefficient of determination?
5. What are some other common statistical metrics used in regression analysis?

Tip: When interpreting $R^2$, remember that a higher value does not always mean the model is better—it depends on the context and the nature of the data!