We are given the following equation for the predicted selling price based on square footage:

$\text{Predicted Selling Price} = 32.98 + 0.14 \times (\text{Square Footage})$

We need to find the missing values in the table for an observed selling price of 184.8 and a square footage of 1006. Let's work through the steps:

1. Predicted Selling Price: Using the equation to find the predicted selling price for 1006 square feet:

$\text{Predicted Selling Price} = 32.98 + 0.14 \times 1006 = 32.98 + 140.84 = 173.82 \text{ (thousands of dollars)}$

2. Error: The error is calculated as the difference between the observed selling price and the predicted selling price:

$\text{Error} = \text{Observed Selling Price} - \text{Predicted Selling Price} = 184.8 - 173.82 = 10.98 \text{ (thousands of dollars)}$

3. Squared Error: The squared error is calculated by squaring the error:

$\text{Squared Error} = (\text{Error})^2 = (10.98)^2 = 120.56$

Updated table for the last row:

Observed Selling Price (Thousands of Dollars)	Observed Square Footage	Predicted Selling Price (Thousands of Dollars)	Error	Squared Error
184.8	1006	173.82	10.98	120.56

Summary of findings:

• Predicted Selling Price = 173.82 (thousands of dollars)
• Error = 10.98 (thousands of dollars)
• Squared Error = 120.56

Let me know if you need further clarification or have any other questions! Here are some related questions:

1. How do you calculate the total sum of squared errors for the entire dataset?
2. What does the squared error represent in the context of predicting housing prices?
3. How would the prediction equation change if we added more variables (e.g., number of bedrooms)?
4. What does a large squared error imply about the accuracy of the model's predictions?
5. How would you interpret a negative error in terms of model accuracy?

Tip: If you’re working with a model, always check for consistency in predictions, and try different types of error analysis (like root mean squared error) to assess accuracy more thoroughly.