In the accompanying table, we list the estimated number g of genes and the estimated number z of cell typesfor various organisms. a. Fit a function of the form log ( z ) = c 0 + c 1 log ( g ) to the data points ( log ( g i ) , log ( z i ) ) , using leastsquares. b. Use your answer in part (a) to fit a power function z = k g n to the data points ( g i , z i ) . c. Using the theory of self-regulatory systems, scientists developed a model that predicts that z is asquare-root function of g (i.e., a = k g , for someconstant k). Is your answer in part (b) reasonablyclose to this form?
In the accompanying table, we list the estimated number g of genes and the estimated number z of cell typesfor various organisms. a. Fit a function of the form log ( z ) = c 0 + c 1 log ( g ) to the data points ( log ( g i ) , log ( z i ) ) , using leastsquares. b. Use your answer in part (a) to fit a power function z = k g n to the data points ( g i , z i ) . c. Using the theory of self-regulatory systems, scientists developed a model that predicts that z is asquare-root function of g (i.e., a = k g , for someconstant k). Is your answer in part (b) reasonablyclose to this form?
Solution Summary: The author explains the linear function of the form to the data points using least squares. The linear system has the unique least-squares solution.
In the accompanying table, we list the estimated number g of genes and the estimated number z of cell typesfor various organisms.
a. Fit a function of the form
log
(
z
)
=
c
0
+
c
1
log
(
g
)
to the data points
(
log
(
g
i
)
,
log
(
z
i
)
)
, using leastsquares. b. Use your answer in part (a) to fit a power function
z
=
k
g
n
to the data points
(
g
i
,
z
i
)
. c. Using the theory of self-regulatory systems, scientists developed a model that predicts that z is asquare-root function of g (i.e.,
a
=
k
g
, for someconstant k). Is your answer in part (b) reasonablyclose to this form?
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