The table in the image relates to "Housing Prices and Square Footage," comparing the Observed Selling Price, Observed Square Footage, Predicted Selling Price, Error, and Squared Error for various data points. The task is to find missing values for an Observed Selling Price of 201 and a Square Footage of 1293.

Steps:

1. Error Calculation: $\text{Error} = \text{Observed Selling Price} - \text{Predicted Selling Price}$ Substituting for Observed Selling Price of 201: $\text{Error} = 201 - \text{Predicted Selling Price}$

2. Squared Error Calculation: $\text{Squared Error} = \text{Error}^2$

To solve:

1. Identify the predicted selling price by finding the correct error value using the squared error.
2. Once the predicted selling price is known, compute the error.

I'll calculate these values based on the relationship between the error and squared error in the table. Give me a moment to work on it.For the observed selling price of 201 and a squared error of 208.2249, the following results are derived:

• The error is calculated to be approximately 14.43.
• This gives two possible predicted selling prices:
  • Predicted Selling Price = 201 + 14.43 = 215.43
  • Predicted Selling Price = 201 - 14.43 = 186.57

Since the error in the table is listed as -14.43, the correct Predicted Selling Price is 215.43 (thousands of dollars).

Summary:

• Predicted Selling Price: 215.43 (thousands of dollars)
• Error: -14.43

Would you like further details or any other calculations? Here are five related questions for further exploration:

1. How would the predicted price change if the observed square footage were different?
2. Can you explain the relationship between square footage and predicted price in this context?
3. What would happen to the error if the predicted price were overestimated?
4. How does the squared error help in determining the accuracy of predictions?
5. What other statistical methods could be used to analyze the accuracy of predicted selling prices?

Tip: When comparing actual and predicted values, always double-check if the error's sign aligns with expectations for overestimation or underestimation.