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find the appropriate regression equation using y1~mx1+b

To find the regression equation in the form $ y = mx + b $ using the data you provided, we can use linear regression techniques. This involves calculating the slope $ m $ and intercept $ b $ for the line that best fits the data points.

### Data:
- Year (x): 0, 1, 2, 3, 4, 6, 10
- Value (y): 18,500, 15,900, 13,750, 11,600, 10,120, 9,200, 8,000

Let's calculate the linear regression and find the equation $ y = mx + b $. I'll start by performing these calculations now.The linear regression equation based on the given data is:

\[
y = -1001.36x + 16157.90
\]

Where:
- $ m = -1001.36 $ (slope)
- $ b = 16157.90 $ (intercept)

This equation describes the relationship between the year and the value in dollars.

Would you like a detailed explanation of how this equation was derived, or any further analysis? 

Here are 5 related questions you might want to explore:
1. How accurate is this linear model in predicting future values?
2. Can we calculate the residuals to evaluate the fit of the model?
3. How would the equation change if another data point were added?
4. What is the significance of the negative slope in this context?
5. Could a different type of regression (e.g., quadratic) provide a better fit?

**Tip:** The slope $m$ indicates the rate of change, showing how much the value decreases per year in this model.

Find the appropriate regression equation using y1~mx1+b.

Learn how to find the linear regression equation for the data of year and value ($). Using the least squares method, the equation y = -1001.36x + 16157.90 shows the relationship between time and value. Suitable for students in Grades 10-12 studying algebra and linear regression techniques.

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