In forestry, the diameter of a tree at breast height (which is fairly easy to me
ID: 3234901 • Letter: I
Question
In forestry, the diameter of a tree at breast height (which is fairly easy to measure) is used to predict the height of the tree (a difficult measurement to obtain). Researchers in British Columbia measured the diameter in centimeters and height (in meters) of a sample of 36 white spruce trees. We use a regression model (y = beta_0 + beta_1 x + epsilon) to analyze this data. Refer to the Minitab output to answer these questions. (a) Identify the least-squares estimates for beta_0 and beta_1 (b) Predict the height of a white spruce tree that has diameter 27 centimeters (c) Interpret the value of beta^0_1 Regression Analysis: HEIGHT versus DIAMETER The regression equation is HEIGHT = 1.23 + 0.385 DIAMETER Predictor Coef BE Coef T F Constant 1.2274 0.7363 1.67 0.165 DIAMETER 0.38546 0.03918 9.84 0.000 S = 1.10161 R-sq = 74.08 R-sq(adj) = 73.28 Analysis of Variance source DF SS RS F FExplanation / Answer
(a)
From the given data,
So, the regression equation becomes: Height = 1.2274 + (0.38546*Diameter)
Thus, 0 = 1.2274 and 1 = 0.38546
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(b)
When diameter = 27 cm
Height = 1.2274 + (27*0.38546) = 11.63482 m
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(c)
Value of 1 is positive, which means that Height and diameter are directly proportional to each-other.
So, Height of the tree will increase as the diameter of tree increases and vice-versa.