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A regression is calculated on a data set of coordinate pairs (, ). The resulting regression

model is = + ln , where A > 0 and B > 1. The same model can be expressed
as = + log5 . What is the value of in terms of ?

User RToyo
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1 Answer

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The value of in terms C of B is C = g(x)/log₅(x) - [f(x) - Bln(x)]/Blog₅(x)

What is the value of in terms C of A?

From the question, we have the following parameters that can be used in our computation:

f(x) = AB + Bln(x)

g(x) = A + Clog₅(x)

From the first equation, we have

AB = f(x) - Bln(x)

So, we have

A = [f(x) - Bln(x)]/B

Recall that

g(x) = A + Clog₅(x)

So, we have

g(x) = [f(x) - Bln(x)]/B + Clog₅(x)

This gives

Clog₅(x) = g(x) - [f(x) - Bln(x)]/B

Divide through by log₅(x)

C = g(x)/log₅(x) - [f(x) - Bln(x)]/Blog₅(x)

Hence, the value of in terms C of B is C = g(x)/log₅(x) - [f(x) - Bln(x)]/Blog₅(x)

Question

A regression is calculated on a data set of coordinate pairs (x, y). The resulting regression model is f(x) = AB + Bln(x) , where A > 0 and B > 1.

The same model can be expressed as g(x) = A + Clog₅(x) . What is the value of in terms C of B?

User Pierre Prinetti
by
8.2k points

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