To predict the selling price of a house based on square footage using a simple linear regression model, the formula is typically:

$\hat{y} = \beta_0 + \beta_1x$

Where:

• $\hat{y}$ is the predicted selling price.
• $\beta_0$ is the intercept (the predicted selling price when the square footage is 0).
• $\beta_1$ is the slope (the increase in the predicted selling price for every additional square foot).
• $x$ is the square footage of the house.

To calculate the expected selling price:

1. Substitute the given values of $\beta_0$, $\beta_1$, and $x$ into the formula.
2. Perform the calculation.

If you provide the values for $\beta_0$, $\beta_1$, and the specific square footage ($x$), I can calculate the expected price for you.

Would you like to provide these details, or should I make a generic example? Let me know!

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Questions to deepen understanding:

1. What do the intercept and slope represent in real-world terms for this regression model?
2. How can one determine if a linear regression model is appropriate for predicting house prices?
3. How do outliers in square footage or selling price impact the accuracy of this regression model?
4. What assumptions must be satisfied for the predictions of this model to be valid?
5. Can this regression model account for other factors influencing house prices, and why might this be a limitation?

Tip:

Always visualize your data with a scatter plot and the regression line to check if the relationship is truly linear before interpreting or predicting.