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:

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).