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Correlation of estimates

Nov 8, 2010 9:19 AM
(2350 views)

What does it mean, if estimates of a least squares fit are correlated. What values are ok, what values are critical? What can be done, if the correlation is high?

Thanks.

Thanks.

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Re: Correlation of estimates

If your independent variables are correlated, then most likely the estimates of your model parameters will be correlated.

It means that you can't interpret the individual estimates by themselves. The prediction model is still fine, just the estimates are not easily interpretable.

If, for example, beta1 is estimated to be 3 and beta2 is estimated to be 1, then you canNOT say that a one unit change in x1 results in a 3 unit change in Y, because x1 and x2 are correlated, so when x1 changes by 1 unit, x2 is also changing.

What can be done? Remove one (or more) of the highly correlated X's from the model, and adjust your mindset to use the prediction model without trying to interpret the coefficients.

It means that you can't interpret the individual estimates by themselves. The prediction model is still fine, just the estimates are not easily interpretable.

If, for example, beta1 is estimated to be 3 and beta2 is estimated to be 1, then you canNOT say that a one unit change in x1 results in a 3 unit change in Y, because x1 and x2 are correlated, so when x1 changes by 1 unit, x2 is also changing.

What can be done? Remove one (or more) of the highly correlated X's from the model, and adjust your mindset to use the prediction model without trying to interpret the coefficients.

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Re: Correlation of estimates

Thanks a lot.

Can you give me rough numbers, what high correlation means?

Can you give me rough numbers, what high correlation means?

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Re: Correlation of estimates

No, it depends on the situation and the use you are planning to make of the numbers.

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I have now a correlation of one estimate with the estimate of the intercept. Does it matter? How can this be explained? When does this happen? And can it be avoided?

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Re: Correlation of estimates

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