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To find the equation of the regression line based on the data from the table, we need to calculate the slope ($ b $) and the intercept ($ a $) of the line in the form:

\[
\hat{\text{Price}} = a + b \cdot \text{Year}
\]

Here are the steps involved in calculating the equation:

1. **Convert the years to a more manageable format**: Since the data spans from 1994 to 1997, we can simplify by letting $ x $ represent the year with a starting point of 1994 (i.e., let $ x = \text{Year} - 1994 $).

2. **Calculate the mean of the years ($ \bar{x} $) and prices ($ \bar{y} $)**.

3. **Calculate the slope $ b $ using the formula**:

\[
b = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}
\]

4. **Calculate the intercept $ a $ using the formula**:

\[
a = \bar{y} - b \cdot \bar{x}
\]

---

### Data extraction from the table:

| Year | Price ($) |
|------|-----------|
| 1994 | 14,072    |
| 1994 | 15,878    |
| 1994 | 15,599    |
| 1994 | 13,303    |
| 1995 | 15,511    |
| 1995 | 18,105    |
| 1995 | 16,134    |
| 1995 | 17,169    |
| 1996 | 21,609    |
| 1996 | 19,489    |
| 1997 | 23,505    |
| 1997 | 22,925    |
| 1997 | 24,492    |
| 1997 | 25,521    |
| 1997 | 22,336    |

Now I will calculate the regression line based on this data.The equation of the regression line, based on the provided data, is:

\[
\hat{\text{Price}} = 14,284 + 3104 \cdot (\text{Year} - 1994)
\]

Rounded to the nearest integer:
\[
\hat{\text{Price}} = 14,284 + 3104 \cdot \text{Year}
\]

Would you like more details on the calculations or have any other questions?

Here are 5 related questions for further exploration:
1. How is the slope $b$ interpreted in the context of this problem?
2. What does the intercept $a$ represent in this regression equation?
3. How well does this regression line fit the data (e.g., calculating the $R^2$ value)?
4. Could you predict the price for the year 1998 using this model?
5. How would the regression equation change if more years were added?

**Tip**: The slope in a regression line indicates how much the dependent variable (Price) is expected to increase for each unit increase in the independent variable (Year).

Find the equation of the regression line using the data provided for years and prices from 1994 to 1997.

Calculate the linear regression line for the price data from 1994 to 1997 using statistical methods. This involves understanding key formulas for slope and intercept based on the least squares method. Suitable for high school students in Grades 10-12.

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