Suggest a Transformation in the Variables That Will Linearize the Deterministic

question 43

Essay

Suggest a transformation in the variables that will linearize the deterministic part of the population regression functions below. Write the resulting regression function in a form that can be estimated by using OLS.
(a)Y_i = β₀
$X _ { 1 i } ^ { \beta _ { 1 } }$ $x _ { 2 i } ^ { \beta _ { 2 } }$ (b)Y_i = $\frac { X _ { i } } { \beta _ { 0 } + \beta _ { 1 } X _ { i } }$ (c)Y_i = $\frac { e ^ { \beta _ { 0 } + \beta _ { 1 } X _ { 1 } } } { 1 + e ^ { \beta _ { 0 } + \beta _ { 1 } X _ { 1 } } }$ (d)Y_i = β₀
$X _ { 1 i } ^ { \beta _ { 1 } }$ ${ e } ^ { \beta _ { 2 } \beta _ { 2 } X _ { 2 i } }$

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Definitions:

Multicollinearity

A statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, making it difficult to interpret the effect of independent variables on the dependent variable.

Independent Variables

Independent variables are variables in a study or experiment that are manipulated or changed to observe their effect on dependent variables.

Multicollinearity

A situation in statistical modeling where two or more predictors are highly correlated, making it difficult to discern their individual effects on the dependent variable.

Regression Coefficients

Values that represent the relationship between a dependent variable and one or more independent variables in regression analysis.