Question #25 / 25 We want to predict the selling price of a house in Newburg Par
ID: 3062167 • Letter: Q
Question
Question #25 / 25 We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of sixteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Also given are the products of the distances from the beach and house prices for each of the sixteen houses. (These products, written in the column labelled "xy," may aid in calculations.) Distance from the Selling price, y beach, x (in thousands of xy (in miles) 12.6 6.6 9.2 12.3 12.2 6.9 12.8 9.8 5.3 3.7 13.3 7.2 17.3 8,8 13.3 4.7 dollars) 211.1 311.6 224.4 279.4 228.6 265.6 202.0 291.0 225.5 318.4 191.0 244.7 219.5 294.9 260.1 271.5 2659.86 2056.56 2064.48 3436.62 2788.92 1832.64 2585.6 2851.8 1195.15 1178.08 2540.3 1761.84 3797.35 2595.12 3459.33 1276.05 350- 250 200 10 Figure 1Explanation / Answer
Line of Regression Y on X i.e Y = bo + b1 X
calculation procedure for regression
mean of X = X / n = 9.75
mean of Y = Y / n = 252.4563
(Xi - Mean)^2 = 219.8
(Yi - Mean)^2 = 23715.7
(Xi-Mean)*(Yi-Mean) = -1303.47501
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
= -1303.47501 / 219.8
= -5.93028
bo = Y / n - b1 * X / n
bo = 252.4563 - -5.93028*9.75 = 310.27651
value of regression equation is, Y = bo + b1 X
Y'=310.27651-5.93028* X
slope = b1 = -5.93028
X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 12.6 211.1 8.1225 1710.3436 -117.86546 6.6 311.6 9.9225 3497.9773 -186.30266 9.2 224.4 0.3025 787.15597 15.43097 12.3 279.4 6.5025 725.96297 68.70644 12.2 228.6 6.0025 569.12305 -58.44794 6.9 265.6 8.1225 172.75685 -37.45955 12.8 202 9.3025 2545.8382 -153.89172 9.8 291 0.0025 1485.6168 1.92719 5.3 225.5 19.8025 726.64211 119.95554 3.7 318.4 36.6025 4348.5716 -398.95939 13.3 191 12.6025 3776.8768 -218.16987 7.2 244.7 6.5025 60.16019 19.77857 17.3 219.5 57.0025 1086.1177 -248.82007 8.8 294.9 0.9025 1801.4677 -40.32151 13.3 260.1 12.6025 58.42615 27.13514 4.7 271.5 25.5025 362.66251 -96.17069