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I am a bit confused as to how we find the singular values and therefore condition index number. Some mathematicians say the singular values are the square roots of the eigenvalues of the correlation matrix of the predictors of a model. While others says we use covariance matrix instead. Again some math publications said The singular values are the square roots of the eigenvalues of the square matrix X'X of multiple linear regression model. For convenience I tried doing all three where Correlation Matrix = 1 0.83863 -0.46207 -0.6500
0.83863 1 -0.2796 -0.3557
-0.46207 -0.2796 1 0.06494 -0.6500 -0.3557 0.06494 1

Covariance Matrix = 63.2027 83.5845 -23.49923 -86.503653 83.5845 157.1722 -22.4221 -74.650134
-23.49923 -22.4221 40.92201633 6.9541 -86.503653 -74.650134 6.9541 280.240857

X'X = 49 947.7 2617.27 49647.57 3389.13 947.7 21426.2236 54715.7778 959073.0701 61309.8618
2617.27 54715.7778 147499.4441 2650760.4091 177368.0266 49647.57 959073.0701 2650760.4091 50305703.2789 3434260.5237 3389.13 61309.8618 177368.0266 3434260.5237 248144.0909

Thank you!

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    $\begingroup$ What programming environment are you using? It's true that there's a relationship between the singular values of a matrix and that matrix's eigenvalues (if it has any), but numerically it is best to directly compute the singular values rather than going through the eigenvalues as an intermediary. In R, we use "svd" while in python we use "np.linalg.svd" to do this. You apply svd directly to $\mathbf{X}$; no need to form a covariance/gram matrix. $\endgroup$
    – John Madden
    Commented Jun 28 at 19:50
  • $\begingroup$ We have many discussions of this. See stats.stackexchange.com/…. You might find stats.stackexchange.com/questions/259890, stats.stackexchange.com/questions/479485, or even stats.stackexchange.com/questions/154335 to be especially pertinent to your implied question. Indeed, what is your question? You have only stated you are "confused." We can't give an answer to that! $\endgroup$
    – whuber ♦
    Commented Jun 28 at 22:11
  • $\begingroup$ wait you cant see the whole question? It only displays I am confused? I wrote this "how we find the singular values and therefore condition index number. Some mathematicians say the singular values are the square roots of the eigenvalues of the correlation matrix of the predictors of a model. While others says we use covariance matrix instead. Again some math publications said The singular values are the square roots of the eigenvalues of the square matrix X'X of multiple linear regression model. $\endgroup$
    – NAFISA
    Commented Jun 29 at 1:53
  • $\begingroup$ I didnt understand when you said "you have only stated I am confused". My entrie question is not visible? $\endgroup$
    – NAFISA
    Commented Jun 29 at 1:54
  • $\begingroup$ I still see no question explicitly stated in your comments or your post--only implied questions. You need to be clear about what you wish to ask. $\endgroup$
    – whuber ♦
    Commented Jun 30 at 13:25

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