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I did regression analysis.

It's about incoming calls and amount of orders.

I got a result like this.

summary(ireg)

Call:

lm(formula = 1/sqrt(ie) ~ ia + id)

Residuals:

   Min         1Q     Median         3Q        Max 

-0.0075193 -0.0019483 0.0002774 0.0018405 0.0093027

Coefficients:

          Estimate Std. Error t value Pr(>|t|)    

(Intercept) 3.364e-02 4.348e-04 77.374 < 2e-16 ***

ia -6.968e-05 1.308e-05 -5.326 1.40e-07 ***

id -7.322e-06 1.379e-06 -5.311 1.51e-07 ***


Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.002648 on 629 degrees of freedom

Multiple R-squared: 0.08148, Adjusted R-squared: 0.07856

F-statistic: 27.9 on 2 and 629 DF, p-value: 2.462e-12

The model was ok. But verifying the assumption about regression analysis, I got a problem about independence assumption.

When I did D-W test, I got this result

durbinWatsonTest(ireg)

lag Autocorrelation D-W Statistic p-value

1 0.5997129 0.7925516 0

Alternative hypothesis: rho != 0

Yes, it doesn't satisfy the assumption.

But the graph from the plot looks ok.

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Was my interpreting wrong? what should I do?

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    $\begingroup$ You can't judge whether a model is 'good' based on output alone. What kind of data is this? Why are you using an inverse-square-root transformation? Also, using hypothesis testing to check multiple assumptions is bound to result in false positives. Is there reason to assume auto-correlation between these observations; Are they not independent? Lastly, your model explains 8.1% of the variance in your response variable. Is this considered good in your field? $\endgroup$ – Frans Rodenburg Aug 3 '18 at 9:37
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    $\begingroup$ indent all your output 4 spaces (select a block of output, click the code tool at the top of the edit window) $\endgroup$ – Glen_b Aug 3 '18 at 9:50
  • $\begingroup$ @FransRodenburg As I explained at the top of this question, these data is about incoming calls and amount of orders. y is inbound calls and x is amount of orders. The reason I used inverse-square-root transformation is I found that this model is heteroscedasticity. So I transformed y. They are independent. Cause the method getting this values are not related. So I can say it's independent. I am also guess that there is auto-corelation, but I don't think they have. Of course we can't say 8.1% of explains are good model. But I just want to get the model which doesn't have any problem. $\endgroup$ – Doyeong Park Aug 6 '18 at 9:07
  • $\begingroup$ Why not the other way around? Are you interested in how orders cause calls or visa versa? Since these are both counts, I don't think you should transform you response. Instead, you can model these counts with a Poisson or negative binomial GLM. $\endgroup$ – Frans Rodenburg Aug 6 '18 at 9:31

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