To find the missing values for the observed selling price of 294.9 and square footage of 1871, we need to calculate the predicted selling price, the error, and the squared error.

We are given the equation for the predicted selling price:

$\text{Predicted Selling Price} = 29.74 + 0.14 \times (\text{Square Footage})$

Step 1: Calculate the predicted selling price

Using the square footage of 1871, we can plug this value into the equation:

$\text{Predicted Selling Price} = 29.74 + 0.14 \times 1871$ $\text{Predicted Selling Price} = 29.74 + 261.94 = 291.68 \text{ (Thousands of Dollars)}$

Step 2: Calculate the error

The error is the difference between the observed selling price and the predicted selling price:

$\text{Error} = \text{Observed Selling Price} - \text{Predicted Selling Price}$ $\text{Error} = 294.9 - 291.68 = 3.22 \text{ (Thousands of Dollars)}$

Step 3: Calculate the squared error

The squared error is simply the square of the error:

$\text{Squared Error} = (\text{Error})^2$ $\text{Squared Error} = (3.22)^2 = 10.3684$

Summary of Missing Values:

• Predicted Selling Price: 291.68 (Thousands of Dollars)
• Error: 3.22 (Thousands of Dollars)
• Squared Error: 10.37 (Thousands of Dollars)

Would you like further details or have any questions on the process? Here are some related questions for your learning:

1. How would you calculate the sum of squared errors for all the data points?
2. What does the squared error tell us about the accuracy of the prediction?
3. How would you interpret the coefficients in the linear equation for predicting home prices?
4. What other factors could influence home prices aside from square footage?
5. How can the residual sum of squares (RSS) help in evaluating the performance of a model?

Tip: When working with regression models, always check for outliers, as they can have a disproportionate impact on the model’s performance.