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    type of regression model




    Which type of regression model is it
    y=a+bx+e

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    Re: type of regression model

    In principle, it could be many things; it depends on the distribution assumed for the error term.

    In practice, it is probably a linear regression (often mistakenly refered to as OLS; it is a mistake because Ordinary Least Squares is te algorithm used for finding the estimates, not the model itself).

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    Re: type of regression model

    Can we say it normal equation

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    Re: type of regression model

    Quote Originally Posted by maartenbuis View Post
    In principle, it could be many things; it depends on the distribution assumed for the error term.

    In practice, it is probably a linear regression (often mistakenly refered to as OLS; it is a mistake because Ordinary Least Squares is te algorithm used for finding the estimates, not the model itself).
    thanks Maarten

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    Re: type of regression model

    Quote Originally Posted by sara b View Post
    Can we say it normal equation
    I would not call it a normal equation. It is the simplest equation that can describes the relationship between two variables.

    An equation can become steadily more complex by adding more IVs, then interactions between IVs, then quadratic terms, then cubic terms, and finally nonlinear terms.

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    Re: type of regression model

    I have never heard the expression "normal" used for an equation. That describes a distribution of the residuals not an equation. Aside from the examples miner already gave equations can also have splines (although I guess those are non-linear).
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: type of regression model

    Quote Originally Posted by noetsi View Post
    I have never heard the expression "normal" used for an equation. That describes a distribution of the residuals not an equation. Aside from the examples miner already gave equations can also have splines (although I guess those are non-linear).
    thanks everyone for correcting my concepts

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    Re: type of regression model

    Quote Originally Posted by sara b View Post
    Can we say it normal equation
    The following is usually referred to as the normal equation:

    X'Xb-X'y=0

    which is derived in the following way

    \frac{d}{db}e'e=\frac{d}{db}(y-Xb)'(y-Xb)=\frac{d}{db}(y'y+b'X'Xb-2b'X'y)=2X'Xb-2X'y=0 \Leftrightarrow X'Xb=X'y \Leftrightarrow b=(X'X)^{-1}X'y.

    A fancy thing with the normal equation is that you can show that X'e=0.

    X'Xb-X'y=-X'(y-Xb)=-X'e=0.

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    Re: type of regression model

    Quote Originally Posted by maartenbuis View Post
    In principle, it could be many things; it depends on the distribution assumed for the error term.
    Despite the distribution of the error terms we can say that the model is linear in its parameters, which is usually referred to when we're saying that a model is linear. The model

    y_i=\alpha+\beta_1x_{1,i}+\beta_2x_{1,i}^2+\epsilon

    is also linear (in its parameters, that is). But the relationship between y and x is nonlinear.
    Last edited by Englund; 01-16-2014 at 09:45 PM.

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    Re: type of regression model

    Exactly. This is always linear regression, irrespective of the values of X and distributional properties. The word "linear" stands for the dependence of y on b... Since there is only one predictor, many textbooks call this model "simple linear regression".

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    Re: type of regression model


    Quote Originally Posted by Englund View Post
    The following is usually referred to as the normal equation:

    X'Xb-X'y=0

    which is derived in the following way

    \frac{d}{db}e'e=\frac{d}{db}(y-Xb)'(y-Xb)=\frac{d}{db}(y'y+b'X'Xb-2b'X'y)=2X'Xb-2X'y=0 \Leftrightarrow X'Xb=X'y \Leftrightarrow b=(X'X)^{-1}X'y.

    A fancy thing with the normal equation is that you can show that X'e=0.

    X'Xb-X'y=-X'(y-Xb)=-X'e=0.
    Can you elaborate this further? I have an assignment on this where i need to prove that X'XB=X'y and B=(X'X)^-1*X'y for the given matrix as attached herewith.
    Attached Images  

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