https://file.aiquickdraw.com/mathbot/file/1727395011257xoqb1rt0.jpg

The problem in the image asks you to estimate the residual (error) in the predicted amount of coral growth for a sea surface temperature of 26.7 degrees, using the plotted regression line.

To solve this:

1. **Locate the value on the x-axis**: The sea surface temperature is 26.7°C. Find this point on the x-axis of the scatterplot.
2. **Find the predicted coral growth**: Follow the regression line at \( x = 26.7 \) to find the predicted coral growth value on the y-axis. From the graph, the regression line seems to predict a coral growth rate of approximately 0.83 or slightly higher.
3. **Find the actual value**: Identify the actual observed coral growth for \( x = 26.7 \) by locating the corresponding data point near 26.7°C. The actual value looks slightly above 0.86.
4. **Calculate the residual**: The residual is the difference between the actual value and the predicted value from the regression line. 

So, the residual (error) is:
\[
\text{Residual} = \text{Actual Value} - \text{Predicted Value}
\]
Using rough estimates:
\[
\text{Residual} \approx 0.86 - 0.83 = 0.03
\]

This is an approximate residual error of 0.03 in coral growth for 26.7°C sea surface temperature.

Would you like further clarification or more details on how residuals are calculated?

Here are 5 related questions to think about:
1. What does the residual tell us about the prediction accuracy for coral growth at 26.7°C?
2. How would the residual change if the temperature was 26.5°C?
3. What are the implications of having a large residual in a regression analysis?
4. How does the slope of the regression line affect the prediction?
5. What would be the residual if the predicted and actual values were the same?

**Tip**: Always make sure to check both the predicted and actual values when calculating residuals.

Estimate the residual (error) in the predicted amount of coral growth for a sea surface temperature of 26.7 degrees when using the plotted regression line.

Learn how to estimate the residual error in coral growth predictions based on sea surface temperature using a linear regression model. This problem involves calculating residuals using the formula: Residual = Actual Value - Predicted Value. Suitable for Grades 10-12.

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