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Thread: Regression Equation to find Y Intercept?

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    Question Regression Equation to find Y Intercept?

    I am a graduate who is looking over past exam papers for statistics. Basically starting from scratch in my learning since I absorbed very little from when I did it in uni (was compulsory for psychology students to take statistics for two of the four years of the degree).
    I have a question based on Regression, and I'm struggling to get it. See below. I have a feeling it could be super obvious, but here goes.

    "Consider the following regression equation:

    Y = 50 +2A - 10B + 8C

    1-What is the Y intercept?
    2-What Y would you predict for a case where A=3, B=1, and C=0?"


    I'm confused because I know the linear regression equation to be y = ax + b (or whatever variation you may use) with a being the gradient and b being the intercept in this case. So I'm not sure how this new equation fits into that structure - or if it's even meant to?

    Thanks.

  2. #2
    Elite Member stapel's Avatar
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    Quote Originally Posted by Reboika View Post
    "Consider the following regression equation:

    Y = 50 +2A - 10B + 8C

    1-What is the Y intercept?
    How are A, B, and C defined? Are they just constants, so "50 + 2A - 10B + 8C" is just a number, and the equation is like "y = 0x + b = b"?

  3. #3
    Quote Originally Posted by stapel View Post
    How are A, B, and C defined? Are they just constants, so "50 + 2A - 10B + 8C" is just a number, and the equation is like "y = 0x + b = b"?
    Ohhh....that would make sense (I think). So this is more of an algebra question? With the "50 + 2A etc" representing the intercept, so the question is asking me to solve the equation?

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    Elite Member stapel's Avatar
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    Quote Originally Posted by Reboika View Post
    Ohhh....that would make sense (I think). So this is more of an algebra question? With the "50 + 2A etc" representing the intercept,...
    If A, B, and C are defined (somewhere) as being constants then, yes, I think they're asking for the y-intercept of y = 0x + b, so the slope is m = 0 (the line is horizontal) and the y-intercept is at y = b.

    Quote Originally Posted by Reboika View Post
    so the question is asking me to solve the equation?
    Under the stated assumption, I believe the second part of the question is asking you to plug the given values into the specified spots, and simplify in order to find the corresponding value of y.

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    Quote Originally Posted by stapel View Post
    If A, B, and C are defined (somewhere) as being constants then, yes, I think they're asking for the y-intercept of y = 0x + b, so the slope is m = 0 (the line is horizontal) and the y-intercept is at y = b.


    Under the stated assumption, I believe the second part of the question is asking you to plug the given values into the specified spots, and simplify in order to find the corresponding value of y.

    Hmm, it doesn't actually state anywhere - that is literally all the info I was given for that question. Although there was a regression question prior which asked for me to calculate a regression line from some (x,y) data - unrelated though I believe. But your answer made me realise that as that first equation stands, one can't really solve it just like that? So I think it could have been simply asking for a definition..! D'oh. That would then explain the nature of the second question - having given values for the constants afterwards.

  6. #6
    Quote Originally Posted by stapel View Post
    If A, B, and C are defined (somewhere) as being constants then, yes, I think they're asking for the y-intercept of y = 0x + b, so the slope is m = 0 (the line is horizontal) and the y-intercept is at y = b.


    Under the stated assumption, I believe the second part of the question is asking you to plug the given values into the specified spots, and simplify in order to find the corresponding value of y.

    Hmm, it doesn't actually state anywhere - that is literally all the info I was given for that question. Although there was a regression question prior which asked for me to calculate a regression line - unrelated though I think. But your answer made me realise that as that first equation stands, one can't really solve it just like that if I'm correct? So I think it could have been simply asking for a definition..! D'oh. That would then explain the nature of the second question - having given values for the constants afterwards.

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    Quote Originally Posted by Reboika View Post
    I am a graduate who is looking over past exam papers for statistics. Basically starting from scratch in my learning since I absorbed very little from when I did it in uni (was compulsory for psychology students to take statistics for two of the four years of the degree).
    I have a question based on Regression, and I'm struggling to get it. See below. I have a feeling it could be super obvious, but here goes.

    "Consider the following regression equation:

    Y = 50 +2A - 10B + 8C

    1-What is the Y intercept?
    2-What Y would you predict for a case where A=3, B=1, and C=0?"


    I'm confused because I know the linear regression equation to be y = ax + b (or whatever variation you may use) with a being the gradient and b being the intercept in this case. So I'm not sure how this new equation fits into that structure - or if it's even meant to?

    Thanks.

    I think

    this is multi-variable linear regression - going towards ANOVA.

    In that case, A, B & C are variables.

    What is the definition of y-intercept?
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  8. #8
    Surely, a, b, and c are intended to be explanatory variables. So the Y intercept (when a, b, and c are zero) is 50.

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