Question 32 5 pts An analyst is trying to purchase a large tract of land. 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 to the lake. She runs the following multiple regression model for her analysis: Price = [60 | lLotSz'ze + gTrees l gDz'stance + 5 Look at the Summary of Fit portion of the JMP output. Summary of Fit . RSquare 0.242472 RSquare Adj 0.20189 Root Mean Square Ermr 40.24353 Mean of Response 86.71333 Observations (or Sum Wgts) 60 What percentage of variation in PRICE is explained by the model? 20.18% 79.82% 24.24% 75.76% Question 36 5 pts What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between 3; = diamond price (in dollars) and a: = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Coefcient Std Error T P Constant 298.36 158.531 14.50 0.0000 Size 11598.9 230.111 50.41 0.0000 RSquared 0.8925 Resid. Mean Square (MSE) 1248950 Adjusted R-Squared 0.8922 Standard Deviation 1117.56 The model was then used to create 95% condence and prediction intervals for y and for E(Y) when the carat size of the diamond was 1 carat. The results are shown here: 95% condence interval for mean y: ($9091.60, $9509.40) 95% prediction interval for an individual 3;: ($7091.50, $11,510.00) Which of the following interpretations is correct if you want to use the model to estimate mean 3; for all 1-carat diamonds? We are 95% condent that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00. We are 95% condent that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00. ' We are 95% condent that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40. We are 95% confident that the price of a 1-carat diamond will fall between $9091.60 and $9509.40