Question
In: Statistics and Probability
determine whether the following models are linear in the parameters, or the variables, or both. which...
determine whether the following models are linear in the parameters, or the variables, or both. which of these models are linear regression models? .(a) Yi = b1+ b (1/xi) +ui , (b) Yi = bi + b2InXi + Ui. (c) InYi= Inb1 + b2InXi + ui (d) InYi =b1 + b2(1/Xi) + ui (e) InYi = bi + b2Xi + ui
Solutions
Expert Solution
By Theorem:
The Regression Equation is
(i) The Regression Equation is linear in Parameters: b1. b2, ..., bn
(ii) The Regression Equation is linear in variables: X1, X2,...,Xn
(a)
The Regression Equation:
(i) The Regression Equation is linear in Parameters, since the Parameters b1 and b are linear.
(ii) The Regression Equation is not linear in
Variables, since 
is occurring.
(b)
The Regression Equation:
(i) The Regression Equation is linear in Parameters, since the Parameters bi and b2 are linear.
(ii) The Regression Equation is not linear in Variables, since ln (Xi) is occurring.
(c)
The Regression Equation:
(i) The Regression Equation is not linear in Parameters, since ln b1 is occurring.
(ii) The Regression Equation is not linear in Variables, since ln (Xi) and ln (Yi) is occurring.
(d)
The Regression Equation:
(i) The Regression Equation is linear in Parameters, since b1 and b2 are linear.
(ii) The Regression Equation is not linear in
Variables, since
is occurring.
(e)
The Regression Equation:
(i) The Regression Equation is linear in Parameters, since bi and b2 are linear.
(ii) The Regression Equation is not linear in Variables, since ln (Yi) is occurring.
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