Consider the estimated regression equation for the simple linear regression: ŷ = 30,000 + 250x, where y is the estimated sale price of a home, and x is the size of the house in square feet. What does the slope indicate?

A. A decrease in the sale price of a house for every additional 250 square feet of space.

B. A $250 increase in the sale price of a house for every additional square foot of space.

C. An increase in the sale price of a house for every additional 250 square feet of space.

D. A $250 decrease in the sale price of a house for every additional square foot of space.

Intercept (30,000): This represents the estimated sale price of a home when [tex]x = 0[/tex], which is not practically meaningful in this scenario because you cannot have a house with 0 square feet. However, it provides a starting point for understanding the relationship between house size and price.
Slope (250): This is crucial for understanding what the equation tells us. The slope represents the change in the estimated sale price of a house for each additional square foot of space. Specifically, a slope of 250 indicates that for every additional square foot of size [tex]x[/tex], the sale price [tex]\hat{y}[/tex] is expected to increase by $250.

So, the slope indicates that option b. a $250 increase in the sale price of a house for every additional square foot of space is correct.

The slope is a key component in regression analysis as it quantifies the strength and direction of the relationship between the two variables involved. Here, a positive slope of 250 suggests a direct and positive relationship between the size of a house and its sale price: as the size increases, the price tends to increase too.