https://file.aiquickdraw.com/mathbot/file/1727103026101gmn1w9ny.jpg

Give the equation for the least squares regression line, and interpret it in context. answer this in 9th grade reading level 

The equation of the least squares regression line shown in the image is:

\[ y = -0.393x + 994.19 \]

### Interpretation:
This equation tells us how the data is changing over time. The slope is \(-0.393\), which means that for every year that passes, the value of the data decreases by about 0.393 units. The y-intercept is 994.19, which is the estimated value of the data when \(x = 0\) (which would be in the far past, outside the range of the data we see here).

The \(R^2\) value is 0.7934, which means that about 79.34% of the variation in the data can be explained by the linear trend in this model. This indicates a fairly strong relationship between the time and the values shown in the plot.

Would you like more details or have any questions?

Here are 5 related questions to think about:
1. What does the y-intercept of 994.19 represent in this context?
2. Why does a negative slope indicate a decrease over time?
3. What does an \(R^2\) value of 0.7934 suggest about the data?
4. How would the graph change if the slope were positive?
5. What happens if the slope becomes steeper, say -1 instead of -0.393?

**Tip:** The closer the \(R^2\) value is to 1, the better the line fits the data!

Give the equation for the least squares regression line, and interpret it in context. Answer this in 9th grade reading level.

This problem introduces the least squares regression line with the equation y = -0.393x + 994.19. Learn how the slope of -0.393 indicates a decrease over time and how the R² value of 0.7934 suggests a strong correlation. Suitable for Grade 9 students learning linear regression and data interpretation.

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