If a set of paired data gives the indication that the regression equation is of the form μY|x = α · βx, it is cus-tomary to estimate α and β by fitting the line log ˆy = log ˆα + x · log βˆ to the points {(xi, log yi);i = 1, 2, ... , n} by the methodof least squares. Use this technique to fit an exponentialcurve of the form ˆy = αˆ · βˆx to the following data on thegrowth of cactus grafts under controlled environmentalconditions: Weeks after Heightgrafting (inches)x y1 2.02 2.44 5.15 7.36 9.48 18.3

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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If a set of paired data gives the indication that the

regression equation is of the form μY|x = α · βx, it is cus-
tomary to estimate α and β by fitting the line

log ˆy = log ˆα + x · log βˆ

to the points {(xi, log yi);i = 1, 2, ... , n} by the method
of least squares. Use this technique to fit an exponential
curve of the form ˆy = αˆ · βˆx to the following data on the
growth of cactus grafts under controlled environmental
conditions:

Weeks after Height
grafting (inches)
x y
1 2.0
2 2.4
4 5.1
5 7.3
6 9.4
8 18.3

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