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I need help interpreting the residual plot and model diagnostics. I built a model for number of ticket sales for an event. so the dependent variable is a continuous variable. Below is how the dependent variable looks like.

Histogram

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Boxplot

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I ran linear regression and upon doing validation for regression assumption.

Test of normality

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From test of normality, histogram of dependent variable and boxplot of dependent variable, it does seem like it's skewed to right. So my question is will log transformation of dependent variable help for handling skewness of data?

Test of linearity and heteroskedasticity

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While I do understand that both are violated, but unable to interpret this further and how to proceed further.

VIF of the intercept is 86. One of the reasons can be very few observations in a dummy variable, which is the case for 19 independent variables which identifies buyer demographics and psychological buyer behavior categories. Also, some independent variables have VIF as inf, which means perfect collinearity between variables. Some variables are closely related and i can take these down, no problem.

Can anyone help me get some direction by diagnose the residual plot and point out what I should do next by using this information?

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    $\begingroup$ If ticket sales is a count, then it's only approximately continuous. Either way, your sales distribution seems unusual. There's an appearance of bimodality and of a sharp cutoff at the upper end. Perhaps you should start by telling us more about it. A Poisson regression may make more sense on various grounds. $\endgroup$ – Nick Cox Aug 11 at 7:58
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    $\begingroup$ @Nick I imagine it might have something to do with venue size. e.g. if the sales are all for the same venue then you're going to have a hard cut-off at full capacity but there might be a peak just short of that for a variety of reasons. $\endgroup$ – Glen_b Aug 12 at 0:14
  • $\begingroup$ @Glen_b Good guess (wish I had thought of that), but if so plain regression seems even more ill-suited. I don't want to guess further without more information. $\endgroup$ – Nick Cox Aug 12 at 6:38
  • $\begingroup$ In addition to the comments by Nick and Glen (both excellent, as usual), I'll just point out that your title says "residual" but you give us plots of the DV. The DV does not have to be normally distributed. $\endgroup$ – Peter Flom Aug 12 at 11:08
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    $\begingroup$ @PeterFlom As I understand it, first and second plots show the response (DV in your terms) but third and fourth plots show residuals. It's a little disconcerting that the largest positive residual is about the same size as the largest response, but it supports the idea that plain regression isn't a good idea here. $\endgroup$ – Nick Cox Aug 12 at 12:55

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