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7 votes

Linear regression: interpret coefficient in terms of percentage change when the outcome variable is a count number

No, you cannot interpret $b_1$ as a percentage. To simplify the argument, say $X_2 = 0$. (Any fixed value for $X_2$ will do.) In this case, the regression equation becomes $Y = a + b_1X_1$. Let's look ...
dipetkov's user avatar
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7 votes
Accepted

Interpretation of logistic regression coefficient

Suppose you have a function in $x$, say $f(x)=x^2$. The derivative is $f'(x)=2x$. This means that if $x$ increases 1 point, the function $x^2$ would increase by $2x$, if we would "believe" ...
BenP's user avatar
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7 votes

Interpretation of logistic regression coefficient

Using equations (4.3) and (4.4): $$\frac{p(X+1)}{1-p(X+1)} = e^{\beta_0+\beta_{1}(X+1)} = e^{\beta_{1}*1} * e^{\beta_0+\beta_{1}X } = e^{\beta_{1}} * \frac{p(X)}{1-p(X)} $$ $$log(\frac{p(X+1)}{1-p(X+...
Lucas Morin's user avatar
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7 votes

Interpretation of logistic regression coefficient

Notice your citation refers to the log-odds, i.e., $$ \log\left(\frac{p(X)}{1-p(X)}\right)=\log(e^{\beta_0+\beta_{1}X})=\beta_0+\beta_{1}X $$ Here, we do have $$ \frac{\partial (\beta_0+\beta_{1}X)}{\...
Christoph Hanck's user avatar
5 votes

Why are my Hazard Ratio coefficients so large or small in Coxph regression?

Please also see my comment. But, assuming your data are correct: Your interpretation is incorrect. Cox PH is not about the likelihood of leaving, it is about the time to leaving. The hazard ratio is ...
Peter Flom's user avatar
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2 votes

Poisson regression given multiple predictors on a repeating ID variable

There are roughly 30K ZIP codes in the US, though not all of these have people in them who are at risk of dying. Let's say you have 20K ZIPs with people at risk your data in your data. You seem to ...
dimitriy's user avatar
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2 votes

Maximum liklihood estimators for simple linear regression with $\sigma^2$ unknown

You assumed $\operatorname{cov}(\varepsilon_i,\varepsilon_j)=0,$ which is weaker than actually assuming independence. If you assume independence, then the likelihood function is $$ L(\beta) = \cdots $$...
Michael Hardy's user avatar
1 vote

Comparing odds ratios on same people but from different models

They are not the same. "Do the 95% CIs overlap?" is much more conservative (that is it requires a much bigger difference) than a Wald test or any of the usual statistical tests. I know there ...
Peter Flom's user avatar
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1 vote

Moderation coefficient in linear mixed models SPSS - interpretation

Here's a quick example of interpreting and visualizing a continuous x continuous interaction: ...
Sointu's user avatar
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1 vote

Maximum liklihood estimators for simple linear regression with $\sigma^2$ unknown

This may actually be fairly straightforward, so I'm going to provide an answer to my own question and people can shout if it's wrong. We can start by setting out the liklihood function and the log-...
hmmmm's user avatar
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2 votes

Interpretation of logistic regression coefficient

My reasoning is the following: $$\frac{\partial e^{\beta_0+\beta_{1}X}}{\partial X}= \beta_1e^{\beta_0+\beta_{1}X},$$ Your reasoning relates to a linear approximation which describes the change for a ...
Sextus Empiricus's user avatar

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