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Thread: Two variable OLS Regression - using normal equations

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    Two variable OLS Regression - using normal equations




    Hi,
    I am experiencing difficulties in understanding the following question;

    We wish to obtain the OLS regression line Y = b0 + b1X by solving the pair of normal equations given as

    b0 = B - Ab1 ....... (1)
    Cb0 +Db1 = E...... (2)

    Write down the numeric values of A, B, C, D and E
    I have been assigned two variables (X and Y), and have been given a data-set which consists of 50 data entries for both variables X and Y, ranging from 15-60. I have also calculated ƩX, ƩX^2, ƩXY and ƩY. Essentially, the difficulties that I am having are finding the numeric values of A, B, C, D and E. I don't understand how to calculate one specific value for each letter. I tried using b0 + (xvalue)b1 = (yvalue) and rearranged to fit the above formula, so that B = yvalue and A= xvalue. However, as I have 50 data entries, wouldn't that produce 50 different equations? Therefore, how can A and B be single numeric values? And as far as calculating the values of C, D, and E, I have no idea how to even start working those out.

    So just to clarify, in order to find a numeric value for A and B, I tried to equate the following (derived from the dataset)
    b0 + (89.9132376)b1 = 32.1870705
    b0 + (108.033851)b1 = 45.7627858
    b0 + (111.243776)b1 = 44.2921641
    … (for all values of X and Y)

    I then tried to rearrange these equations to match the normal equation listed above (1) and so I obtained;
    b0 = 32.1870705 - (89.9132376)b1
    b0 = 45.7627858 - (108.033851)b1
    b0 = 44.2921641 - (111.243776)b1
    … (for all values of X and Y)

    But then in this instance B could be 32.1870705 or 45.7627858 or (and so on).... and likewise with A. And so, I cannot find a single numerical value which goes in place of A and B, and the same goes for C, D, and E.

    I have looked across multiple sites, textbooks, and forums, but to no avail. I cannot find any examples which relate to this question. I apologise if this question is more so common sense than it is hard-core theory, but I just really don't understand how to approach this.
    Any help would be much appreciated, thanks.
    Last edited by UniApply; 03-01-2016 at 03:48 PM. Reason: For simplification

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