High School

Refer to the simple linear regression model above. Suppose that the simple linear regression model for the house price example has \(\beta_0 = 190,000\) and \(\beta_1 = 40\).

What would one expect a house with 2000 square feet to sell for?

_________

Answer :

Final answer:

Using the given simple linear regression model, a house with 2000 square feet is expected to sell for $270,000.

Explanation:

The question asks how much a house with 2000 square feet would sell for, given the simple linear regression model with parameters eta_{0} = 190,000 (the intercept) and eta_{1} = 40 (the slope). To find the expected selling price for a 2000 square feet house, we simply need to plug the square footage into the regression equation, which is y = eta_{0} + eta_{1}x, where y is the expected house price and x is the square footage of the house. Following the model:

y = 190,000 + (40 imes 2000)

y = 190,000 + 80,000

y = 270,000

Therefore, one would expect a house with 2000 square feet to sell for $270,000.