Question 975289: With the aim of predicting the selling price of a house in Newburg Park, Florida, from the distance between the house and the beach, we might examine a regression equation relating the two variables. In the table below, the distance from the beach (x, in miles) and selling price (y, in thousands of dollars) for each of a sample of sixteen homes sold in Newburg Park in the past year are given. The least-squares regression equation relating the two variables is yhat=296.54-4.73x. The line having this equation is plotted in Figure 1.
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Figure 1
Distance from the beach, x (in miles):
6.8
7.4
14.2
3.8
6.5
11.7
12.1
10.9
9.6
10.6
14.6
8.4
17.8
4.6
13.1
5.5
Selling price, y 9 (in thousands of dollars):
240.0
217.6
188.0
259.0
303.0
222.9
281.7
284.4
233.8
197.6
265.9
296.2
226.0
313.1
200.9
268.4
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Based on the above information, answer the following:
(1) For these data, house prices that are greater than the mean of the house prices tend to be paired with distances from the beach that are [greater than or less than?] the mean of the distances from the beach.
(2) According to the regression equation, for an increase of one mile in distance from the beach, there is a corresponding decrease of how many thousand dollars in house price?
(3) What was the observed house price (in thousands of dollars) when the distance (in miles) from the beach was 17.8 miles?
(4) From the regression equation, what is the predicted house price (in thousands of dollars) when the distance (in miles) from the beach is 17.8 miles?
Answer by Fombitz(32388)   (Show Source):
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