Question

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 (, 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 y=297.33-5.01x The line having this equation is plotted in Figure 1. Distance from the Selling price, y beach, x(in thousands of (in miles) 11.6 12.7 15.5 6.9 17.8 12.8 dollars) 208.8 283.5 267.1 210.0 219.9 186.9 317.4 263.1 225.3 303.5 189.8 259.6 283.5 233.2 237.6 290.7 350 300 250 12.1 200 13.2 5.4 150 9.7 7.6 7.3 Send data to Excel 10 20 Figure 1 Based on the above information, answer the following: 1. Fill in the blank: For these data, distances from the beach that are greater than the mean of the distances from the beach tend to be paired with house prices that aret Choose one the mean of the house prices 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. From the regression equation, what is the predicted house price (in thousands of dollars) when the distance (in miles) from the beach is 6.1 miles? (Round your answer to at least one decimal place.) 4. What was the observed house price (in thousands of dollars) when the distance (in miles) from the beach was 6.1 miles?

Answer 1

1. Since the slope of given regression line is negative, greater values of x associated with lesser value of y.

The answer is Less than

2. Predicted decrease = Slope = 5.01

3. Predicted house price = 297.33 - 5.01*6.1 = 266.8

4. Observed house price = 303.5