Question

Section 3.3 10. There is a relationship between the height and the volume of wood in a tree a) Use regression to find a power equation to model the data. Round the numbers in your equation to 2 decimal places. b) Use your equation to find the height a tree should be to have a volume of 300 ft, rounded to the nearest tenth. c) Use your equation to find the height a tree should be to have a volume of 1600 ft', rounded to the nearest tenth. Height (ft) 12 20 26 34 40 50 Volume (ft) 82 180 267 395 501 691 898 1235 60 75 Tree Height -vs- Volume 1400 1200 1000 800 Volume (ft) 600 400 200 D 10 20 30 40 50 50 70 80 Height (ft)

Answer 1

Power regression ylni 1) mean : In x 2) trend line : y= AxB, n ? ylnyi Iny = Sry B A= exp(lny - Blnx) n Suz) 3) correlation coefficient : r= Szy SIS -2 -2 Sqz = E(In xi – In x)2 = [ In x; – n · Inx Syy = E(In yi – Iny)2 = { Iny; - n-Iny Szy = E(In I; – In x)(In Yi – Iny) = ln z; In Yi – n. In x Iny

function value mean of x 34.28571826 mean of y 395.4182619 correlation coefficient r 0.99987516 A 2.1392466 B 1.47663103

y = 2.139 X^1.4766

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