14. The data in Table P-14 were collected as part of a study of real estate property evaluation. The numbers are observations on (in thousands of dollars) on the city assessor’s books and (selling price in thousands of dollars) for parcels of land that sold in a particular calendar year in a certain geographical area.

TABLE P-12 Obs. Y X Obs. Y X Obs. Y X (1) 1.0 10 (48) 2.2 180 (95) 2.0 330 (2) 0.9 10 (49) 2.4 180 (96) 2.4 340 (3) 0.8 10 (50) 1.6 180 (97) 2.2 340 (4) 1.3 20 (51) 1.8 190 (98) 2.0 340 (5) 0.9 20 (52) 4.1 190 (99) 2.5 350 (6) 0.6 30 (53) 2.0 190 (100) 2.8 350 (7) 1.1 30 (54) 1.5 200 (101) 2.3 350 (8) 1.0 30 (55) 2.1 200 (102) 2.7 350 (9) 1.4 40 (56) 2.5 200 (103) 2.8 360 (10) 1.4 40 (57) 1.7 220 (104) 3.1 360 (11) 1.2 40 (58) 2.0 220 (105) 2.5 370 (12) 1.7 50 (59) 2.3 220 (106) 2.9 370 (13) 0.9 50 (60) 1.8 220 (107) 2.6 370 (14) 1.2 50 (61) 1.3 230 (108) 3.0 380 (15) 1.3 50 (62) 1.6 230 (109) 3.2 380 (16) 0.7 60 (63) 2.8 230 (110) 2.9 390 (17) 1.0 60 (64) 2.2 230 (111) 2.6 390 (18) 1.3 70 (65) 2.6 230 (112) 2.5 390 (19) 1.5 70 (66) 1.4 240 (113) 2.7 400 (20) 2.0 70 (67) 1.6 240 (114) 3.1 400 (21) 0.8 80 (68) 1.7 240 (115) 2.4 400 (22) 0.6 80 (69) 1.5 250 (116) 3.0 400 (23) 1.8 80 (70) 2.2 250 (117) 3.4 420 (24) 1.0 90 (71) 2.5 250 (118) 3.5 420 (25) 2.0 100 (72) 2.4 260 (119) 3.1 420 (26) 0.5 100 (73) 2.0 260 (120) 2.9 420 (27) 1.5 100 (74) 2.7 260 (121) 2.8 430 (28) 1.3 110 (75) 2.0 270 (122) 3.3 430 (29) 1.7 110 (76) 2.2 270 (123) 2.5 440 (30) 1.2 110 (77) 2.4 270 (124) 2.8 440 (31) 0.8 110 (78) 1.8 280 (125) 2.4 450 (32) 1.0 120 (79) 2.8 290 (126) 2.6 450 (33) 1.8 120 (80) 2.2 290 (127) 3.0 450 (34) 2.1 120 (81) 2.4 290 (128) 3.4 460 (35) 1.5 130 (82) 2.1 290 (129) 3.0 460 (36) 1.9 130 (83) 1.9 290 (130) 3.3 470 (37) 1.7 140 (84) 2.4 300 (131) 3.4 470 (38) 1.2 150 (85) 2.5 300 (132) 3.1 470 (39) 1.4 150 (86) 2.9 300 (133) 3.6 480 (40) 2.1 150 (87) 2.0 300 (134) 3.0 480 (41) 0.9 160 (88) 1.9 310 (135) 2.9 480 (42) 1.1 160 (89) 2.5 310 (136) 3.2 480 (43) 1.7 160 (90) 2.6 310 (137) 2.6 490 (44) 2.0 160 (91) 3.2 320 (138) 3.8 490 (45) 1.6 170 (92) 2.8 320 (139) 3.3 490 (46) 1.9 170 (93) 2.4 320 (140) 2.9 500 (47) 1.7 170 (94) 2.5 320 TABLE P-13 Batch Number of Defectives Y Batch Size X 1 4 25 2 8 50 3 6 75 4 16 100 5 22 125 6 27 150 7 36 175 8 49 200 9 53 225 10 70 250 11 82 275 12 95 300 13 109 325 TABLE P-14 Parcel Assessed Market Parcel Assessed Market 1 68.2 87.4 16 74.0 88.4 2 74.6 88.0 17 72.8 93.6 3 64.6 87.2 18 80.4 92.8 4 80.2 94.0 19 74.2 90.6 5 76.0 94.2 20 80.0 91.6 6 78.0 93.6 21 81.6 92.8 7 76.0 88.4 22 75.6 89.0 8 77.0 92.2 23 79.4 91.8 9 75.2 90.4 24 82.2 98.4 10 72.4 90.4 25 67.0 89.8 11 80.0 93.6 26 72.0 97.2 12 76.4 91.4 27 73.6 95.2 13 70.2 89.6 28 71.4 88.8 14 75.8 91.8 29 81.0 97.4 15 79.2 94.8 30 80.6 95.4

a. Plot the market value against the assessed value as a scatter diagram.

b. Assuming a simple linear regression model, determine the least squares line relating market value to assessed value.

c. Determine and interpret its value.

d. Is the regression significant? Explain.

e. Predict the market value of a property with an assessed value of 90.5. Is there any danger in making this prediction?

f. Examine the residuals. Can you identify any observations that have a large influence on the location of the least squares line?