A developer who specializes in summer cottage properties is considering purchasing …

     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