A developer who specializes in summer cottage properties is considering purchasing a large tract of land adjoining a lake. The current owner of the tract has already subdivided the land into separate building lots and has prepared the lots by removing some of the trees. The developer wants to forecast the value of each lot. From previous experience, she knows that the most important factors affecting the price of a lot are size, number of mature trees, and distance from the lake. From a nearby area, she gathers relevant data for 60 recently sold lots. R-square = .2425, R-square (adjusted) = .2019 Sε = 40.24, F = 5.97, p-value = .0013 Intercept: coefficient = 51.39, Standard Error = 23.52, t-stat = 2.19, p-value = .0331 Lot Size: coefficient = .700, Standard Error = .559, t-stat = 1.25, p-value = .2156 Trees: coefficient = .679, Standard Error = .229, t-stat = 2.96, p-value = .0045 Distance: Coefficient = -.378, Standard Error = .195, t-stat = -1.94, p-value = .0577 (Use a 5% significance level) a. Find the regression equation b. What is the standard error of estimate? Interpret it’s value c. What is the coefficient of determination? What does this statistic tell you? d. What is the coefficient of determination, adjusted for degrees of freedom? Why does this value differ from the coefficient of determination? What does this tell you about the model? e. Test the validity of the model. What does the p-value of the test statistic tell you? f. Interpret each of the coefficients g. Test to determine whether each of the independent variables is linearly related to the price of the lot in this model h. Predict with 90% confidence the selling price of a 40,000-square-foot lot that has 50 mature trees and is 25 feet from the lake i. Estimate with 90% confidence the average selling price of 50,000-square-foot lots that have 10 mature trees and are 75 feet from the lake
Price Lot size Trees Distance 105.4 41.2 24 42 91.2 44.8 5 71 183.3 21.3 72 43 93.8 43.9 58 14 207.5 57.7 52 12 130.9 33.4 78 26 162.3 31.4 65 51 18.8 27.4 22 0 80.5 26.2 68 83 38.3 40 57 76 71.3 47.6 53 35 55.5 31.6 36 26 85.7 21.6 23 24 110.5 36.3 48 98 85.1 47.2 61 59 78.3 30.5 41 55 27.2 41.8 1 60 70.9 20.6 20 33 101.4 35.3 38 75 133.3 40.1 68 0 117.7 35.6 24 41 49.7 20.6 16 77 49.6 22.4 32 86 83.2 45.8 77 19 81.3 29.4 40 0 152.5 51.7 60 34 112.2 27.2 0 16 37.1 37 50 49 130.2 38.9 48 63 39.1 32.5 25 45 81.9 34 12 0 24.6 35.8 16 34 101.9 32.9 44 42 117.6 46.4 62 48 148.8 51.9 59 39 60.2 28.9 0 66 43.7 35.2 57 77 113.1 30.4 70 78 38.1 38.3 24 62 89.2 49.2 61 0 3 21.5 46 83 55.8 41.9 10 69 89.7 21.8 79 62 136.1 66.3 56 34 44.7 28.2 73 77 63.2 41.9 64 65 163.4 46.7 69 27 64.1 32.1 12 0 98.7 38.5 59 77 139.9 27.6 0 0 92 47 65 37 66.6 20.7 24 51 16.4 34 12 75 131.9 31.9 76 63 11 28 2 42 27.9 40 52 84 103.5 46.6 26 70 107 23.2 11 83 51.6 46.4 53 44 133.4 32.1 55 98
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