Measuring the height of a Yellow Meranti is very difficult because these trees grow to heights over 300 feet. In 2016, a group of Yellow Meranti in Sabah’s Danum Valley was announced as the tallest tropical trees in the world. People familiar with these trees understand that the height of a Yellow Meranti is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person (in inches) and the thickness of the bark of the tree (in inches). The file YellowMeranti contains the height, diameter at breast height of a person, and bark thickness for a sample of 40 Yellow Meranti trees. Height Diameter at breast height Bark thickness 134 24 1.2 213 30 3.1 183 22 2.2 90 12 1.3 147 28 2.2 110 33 1.5 190 56 2 89 12 1.2 165 29 2.8 124 13 1.7 92 14 1.5 180 56 2.5 224 47 2.2 191 33 2.8 175 20 3.3 253 46 2.9 246 50 4.7 237 57 4.4 253 43 2.4 210 37 3.9 233 10 1.5 122 22 1.1 194 27 2.8 167 20 2 82 11 1.2 134 25 2 100 30 1.4 173 51 1.8 81 11 1.1 150 26 2.5 113 12 1.5 84 13 1.4 164 51 2.3 203 43 2 174 30 2.5 159 18 3 230 42 2.6 224 45 4.3 215 52 4 230 39 2.2 c.State the multiple linear regression model where the height of Yellow Meranti is treated as the dependent variable while the diameter and bark thickness of the tree are the explanatory variables. d.Based on relevant statistical software, determine the multiple linear regression equation for (c) and show the output of the software. e.By referring to the p-value, determine whether the diameter and bark thickness of Yellow Meranti are significant in explaining its heights. f.Predict the height of the Yellow Meranti when the diameter of the tree at breast height of a person is 20 inches while the bark thickness is 4.4 inches.

Elementary Geometry For College Students, 7e

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ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

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Measuring the height of a Yellow Meranti is very difficult because these trees grow to heights over 300 feet. In 2016, a group of Yellow Meranti in Sabah’s Danum Valley was announced as the tallest tropical trees in the world. People familiar with these trees understand that the height of a Yellow Meranti is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person (in inches) and the thickness of the bark of the tree (in inches). The file YellowMeranti contains the height, diameter at breast height of a person, and bark thickness for a sample of 40 Yellow Meranti trees.

Height	Diameter at breast height	Bark thickness
134	24	1.2
213	30	3.1
183	22	2.2
90	12	1.3
147	28	2.2
110	33	1.5
190	56	2
89	12	1.2
165	29	2.8
124	13	1.7
92	14	1.5
180	56	2.5
224	47	2.2
191	33	2.8
175	20	3.3
253	46	2.9
246	50	4.7
237	57	4.4
253	43	2.4
210	37	3.9
233	10	1.5
122	22	1.1
194	27	2.8
167	20	2
82	11	1.2
134	25	2
100	30	1.4
173	51	1.8
81	11	1.1
150	26	2.5
113	12	1.5
84	13	1.4
164	51	2.3
203	43	2
174	30	2.5
159	18	3
230	42	2.6
224	45	4.3
215	52	4
230	39	2.2

c.State the multiple linear regression model where the height of Yellow Meranti is treated as the dependent variable while the diameter and bark thickness of the tree are the explanatory variables.

d.Based on relevant statistical software, determine the multiple linear regression equation for (c) and show the output of the software.

e.By referring to the p-value, determine whether the diameter and bark thickness of Yellow Meranti are significant in explaining its heights.

f.Predict the height of the Yellow Meranti when the diameter of the tree at breast height of a person is 20 inches while the bark thickness is 4.4 inches.

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