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4. (30 pt.] Measuring the height of a California redwood treels very difficult because these trees grow to heights over 300 feet. People familiar with these trees understand that the height of a California redwood tree is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person (In Inches), the thickness of the bark of the tree (In inches), the distance from the closest neighboring tree (in yards), and the number of the other trees neighboring within 10 yards from the tree. Using the data set (redwoods.xdsx), conduct a regression analysis answering the following questions given significance level = 0.10. (a) Express the relation between five Independent variables (X : diameter, X2: thickness, Xy: distance, X: number of neighboring trees) and a dependent variable(Y: height) in a multiple linear regression model. (b) Using the Excel, estimate the regression model coefficients. (c) Compute the expected height of a redwood tree given diameter of 50, thickness of 3.5, distance of 5.0, and the number of neighboring trees of 4. (d) Is there a significant relationship between the height and the four independent variables? Answer based on the Ftest. (e) Is there a significant effect of the thickness on the height? Answer based on the rest in the critical approach. (h. Is there a significant effect of the distance on the height? Answer based on the t test in the p-value approach. (B) Determine the coefficient of determination, and interpret its meaning. (h) Determine the adjusted coefficient of determination, adjusted r2 and interpret its meaning B C D E F 1 2 3 Nm 3 4 5 6 LON 7 8 8 9 D 10 11 12 Diameter at breast Height height 122.0 20 193.5 36 166.5 18 82.0 10 156.0 21 156.0 29 172.5 51 81.0 11 148.0 26 113.0 12 84.0 13 185.0 40 203.3 52 174.0 30 159.0 22 205.0 42 223.5 45 195.0 54 232.5 39 190.5 36 100.0 8 Distance from the Trees within 10 Bark thickness closest yard 1.1 8.5 2.8 8.9 2 2.0 6.1 5 1.2 7.6 1 2.0 0.3 7 1.4 3.3 4 1.8 4.8 2 1.1 3.1 2 2.5 3.6 1 1.5 41 2 1.4 9.7 2.3 3.5 S 2.0 7.2 3 2.5 5.6 4 3.0 7.4 2 2.6 4.4 1 4.3 0.6 5 4.0 6.5 2 2.2 3.1 1 3.5 0.5 1 1.4 5.1 0 ON N 13 14 15 16 17 18 19 20 21 22 0 23 ONNNNNNNNN 24 6 25 26 27 28 29 30 31 32 33