To find the missing values for the observed selling price of 223.5 and square footage of 1625, we need to follow the steps below:

Step 1: Calculate the Predicted Selling Price

We use the equation for the predicted selling price:

$\text{Predicted Selling Price} = 18.03 + 0.13 \times (\text{Square Footage})$

Substitute the given square footage of 1625:

$\text{Predicted Selling Price} = 18.03 + 0.13 \times 1625$

$\text{Predicted Selling Price} = 18.03 + 211.25 = 229.28 \text{ (Thousands of Dollars)}$

Step 2: Calculate the Error

The error is the difference between the observed selling price and the predicted selling price. The observed selling price is given as 223.5.

$\text{Error} = \text{Observed Selling Price} - \text{Predicted Selling Price}$

$\text{Error} = 223.5 - 229.28 = -5.78 \text{ (Thousands of Dollars)}$

Step 3: Calculate the Squared Error

The squared error is the square of the error:

$\text{Squared Error} = \text{Error}^2$

$\text{Squared Error} = (-5.78)^2 = 33.45 \text{ (Thousands of Dollars squared)}$

Final Results

• Predicted Selling Price: 229.28
• Error: -5.78
• Squared Error: 33.45

Would you like further clarification on any of the steps or additional help with another problem? Here's a list of related questions that could help build a deeper understanding of this topic:

1. How do you interpret the error and squared error in the context of model accuracy?
2. What is the meaning of the equation used to predict the selling price of a house?
3. How can we use the sum of squared errors to evaluate the overall fit of the model?
4. What is the relationship between the square footage of a house and its predicted selling price according to this model?
5. How can you calculate the coefficient of determination (R-squared) from the sum of squared errors?

Tip: The sum of squared errors (SSE) is an important metric in regression analysis. It helps to measure the total deviation of the predicted values from the observed values. A lower SSE indicates that the model fits the data better.