Question

An article on the cost of housing in California that appeared in the San Luis Obispo Tribune† included the following statement: "In Northern California, people from the San Francisco Bay area pushed into the Central Valley, benefiting from home prices that dropped on average $4000 for every mile traveled east of the Bay area." If this statement is correct, what is the slope of the least-squares regression line, ŷ = a + bx, where y = house price (in dollars) and x = distance east of the Bay (in miles)? Explain. This value is the change in the average home price, in dollars, for each increase of 1 mile in the distance east of the bay. This value is the change in the distance east of the bay, in miles, for each increase of $1 in average home price. This value is the change in the average home price, in dollars, for each decrease of 1 mile in the distance east of the bay. This value is the change in the distance east of the bay, in miles, for each decrease of $1 in average home price.

Answer 1

It is given that home prices that dropped on average $4000 for every mile traveled east of the Bay area.

So, there is a decrease of $4,000 in the home prices for every mile

Thus, change in home prices for every mile = $4000

So, slope = -4000

because slope is the rate of change of y value with respect to x value. Here y is home prices and x is number of miles

It is clear from that the slope that this value is change in home prices in dollars for every mile change in x value

Since people from the San Francisco Bay area pushed into the Central Valley, so for every 1 mile increase, there is a loss of $4000 in home prices

Option A is correct

This value is the change in the average home price, in dollars, for each increase of 1 mile in the distance east of the bay.