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Thread: Condition to put regression analysis zero?

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    Condition to put regression analysis zero?




    Under what situation intercept can be force to zero in regression analysis?

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    Re: Condition to put regression analysis zero?

    The Capital Asset Pricing Model in portfolio theory would be a situation.

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    Re: Condition to put regression analysis zero?

    Quote Originally Posted by Dragan View Post
    The Capital Asset Pricing Model in portfolio theory would be a situation.
    The CAPM doesn't specify a zero-intercept, though. The intercept is the risk free rate, which is typically non-zero.

    I think it would be okay to set it to zero in cases where the theory or logic dictates that when x is 0 y is 0. Although, I have heard it may be better not to force the intercept to 0 in most cases, but allow for the estimation. If it should be zero, the estimates will be very close to if you forced the intercept to 0. Maybe someone else can clarify what I have heard.

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    Re: Condition to put regression analysis zero?

    Quote Originally Posted by ondansetron View Post
    The CAPM doesn't specify a zero-intercept, though. The intercept is the risk free rate, which is typically non-zero.

    I think it would be okay to set it to zero in cases where the theory or logic dictates that when x is 0 y is 0. Although, I have heard it may be better not to force the intercept to 0 in most cases, but allow for the estimation. If it should be zero, the estimates will be very close to if you forced the intercept to 0. Maybe someone else can clarify what I have heard.
    Well, it depends on "who you ask." See Damodar Gujarati's text (Basic Econometrics) where he uses the CAPM as an example (zero intercept).

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    Re: Condition to put regression analysis zero?

    Quote Originally Posted by Dragan View Post
    Well, it depends on "who you ask." See Damodar Gujarati's text (Basic Econometrics) where he uses the CAPM as an example (zero intercept).
    Fair enough-- I was going off of coursework and papers we had to read in an MS finance program. Interestingly, I don't recall Gujarati, but I'll have to take a look at his work!

    What are your thoughts on estimating the intercept irrespective of whether you suspect it should be zero or not? As I mentioned, I heard this is a bit more conservative than choosing to force the intercept to zero.

    Edit: I glossed over this, but I am actually familiar with what you're saying-- the CAPM is presented as
    E(ri) = rf + B(Rm-rf) Rm is return on the market, rf is risk free rate

    The case you're describing is when you subtract rf from both sides to look at the excess return on security i over the market return. E(ri)- rf = B(Rm-rf) should have an intercept of zero if CAPM holds. Something to that effect-- it's been a couple years, but that's the gist. Thanks for making me check back on it!
    https://people.duke.edu/~charvey/cla...an/riskman.htm
    Look at part 2 "Implementing the CAPM"...
    Last edited by ondansetron; 05-13-2017 at 01:34 PM.

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    Re: Condition to put regression analysis zero?

    Gujarati is expressing the CAPM as:

    (ER_i - r_f) = Beta_i*(ER_m - r_f) where

    ER_i: is the expected rate on security i

    ER_m: is the expected rate of return on the market portfolio as (say a S&P composite stock index)

    r_f: is the risk free rate of return e.g. 90 day treasury bills

    Beta_i: is the Beta coefficient, a measure of systematic risk, risk that cannot be eliminated through diversification. And, also a measure of the extent to which the i-th security's rate of moves with the market. For example for Beta_i >1 implies a volatile or aggressive security, whereas a Beta_i<1 a defensive security. (Note: do not confuse Beta_i with the slope coefficient of a two variable regression model.)

    For empirical purposes:

    R_i - r_f = Beta_i*(R_m - r_f) + error

    or

    R_i - r_f = alpha_i +Beta_i*(R_m - r_f) + error

    where alpha_i is expected to be zero if CAPM holds.

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    Re: Condition to put regression analysis zero?

    Quote Originally Posted by Dragan View Post
    Gujarati is expressing the CAPM as:

    (ER_i - r_f) = Beta_i*(ER_m - r_f) where

    ER_i: is the expected rate on security i

    ER_m: is the expected rate of return on the market portfolio as (say a S&P composite stock index)

    r_f: is the risk free rate of return e.g. 90 day treasury bills

    Beta_i: is the Beta coefficient, a measure of systematic risk, risk that cannot be eliminated through diversification. And, also a measure of the extent to which the i-th security's rate of moves with the market. For example for Beta_i >1 implies a volatile or aggressive security, whereas a Beta_i<1 a defensive security. (Note: do not confuse Beta_i with the slope coefficient of a two variable regression model.)

    For empirical purposes:

    R_i - r_f = Beta_i*(R_m - r_f) + error

    or

    R_i - r_f = alpha_i +Beta_i*(R_m - r_f) + error

    where alpha_i is expected to be zero if CAPM holds.
    Just as I recall. Not sure why the rearrangement slipped my mind, but it was typically looked at for excess returns. Interesting to see another econ/finance person here!

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    Re: Condition to put regression analysis zero?

    Hi thanks for the input.
    Here I am dealing with regression from marketing perspective.
    I am measuring customer satisfaction=y
    Independent variable are no. of attempt you made to reach customer care before query is resolved & time taken to resolve query

    Equation with intercept is Y= 1.73+ 0.52(no. of attempt) +0.04(time taken)
    Equation without intercept is Y = 0.82(no.of attempt) + 0.16(time taken).

    Kindly suggest intercept can be forced to zero in thiss case?

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    Re: Condition to put regression analysis zero?

    Hi,
    there would be several points to consider:

    1. Physical plausibility : 0 time to resolve the issue is quite impossible, so who cares what the customer satisfaction would be in that case?
    Also, it seems that the longer it takes the happier the customer??

    Do you have a model of the system that actually predicts 0 y for 0 x? E.g. if I want to model the percentage defective parts as a function of applied force it seems reasonable that the parts would show no defect if there was no applied force. If I would expect from theory some residual y even if my x were 0 I would definitely not set the coefficient to zero.


    2. Modelling - if you set a0 to 0 you will overestimate the model fit (r-squared). This is a reason not to set the coefficient to zero even if this would make theoretically sense.

    In your case I think it would be better to keep the coefficient.

    You might want to scale the x variables Xscaled=X-Mean(X). That would make the coefficient much easier to interpret as the average satisfaction at average values of attempts and time.

    regards

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    Re: Condition to put regression analysis zero?

    1)Yes from above equation we can see, that consumer satisfaction is least or no where related to time taken to resolved the query. We are checking on that.
    2) Also, I do agree removing intercept increase (r-squared for the regression equation)
    3) Result is obtained on scaled data already..

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    Re: Condition to put regression analysis zero?

    Quote Originally Posted by Meenakshi Tiwari View Post
    3) Result is obtained on scaled data already..
    Hi,
    if it is already scaled as above then you definitely have to keep the constant.

    regards

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    Re: Condition to put regression analysis zero?


    Ok. Thanks!

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