# Regression on Negatively Skewed Data

I am trying to explore the relationship between a customer satisfaction rating and a response time (in days). I have been using linear, logistic and quantile regression, to no avail. I believe the issues lies with the distribution of the data. 85% of respondents give a 9 or 10 rating (regardless of response time) and 70% of the data lies in the 9/10 rating and the 0-4 day response time.

Since the data is so negatively skewed, I'm looking for some advice on whether or not to normalize the data and if regression is the right method to define the relationship between the variables (and if not, what would be a better method).

I've attached a summary of the data distributions percents. The range for the rating is 1-10 inclusive and the response rate is continuous, but we limit to 10 days because of low volume for 10+ days. Any assistance is appreciated. • Can you describe what is the "no avail" when you attempted to use logistic and quantile regressions? What failed in those two techniques? From what it looks, using logistics to predict if anyone would even rate lower than 9 seems reasonable. So, I'd like to know more why it didn't work. – Penguin_Knight Oct 1 '13 at 19:04
• I would suggest some ordinal logistic regression, for example logistic regression with cumulative link. – O_Devinyak Oct 1 '13 at 19:05
• The skewness I take as a secondary issue; the major issue is just the lack of relation between rating and response time. For example, the mean rating from these summaries is lowest for time 3 days at 9.265 and highest for 10 days at 9.379! I'd plot summary statistics for each time rather than try to force this into any kind of regression model, because the total fit is likely to be disappointing. – Nick Cox Oct 1 '13 at 19:05
• @Penguin_Knight "To no avail" meaning not getting any models with any kind of significance (R^2 <1). – Eudora Oct 1 '13 at 20:55
• @NickCox, If that is the case, is there any better way to prove that there is no relationship between the two? – Eudora Oct 1 '13 at 20:56

## 1 Answer

This isn't a complete answer, just an attempt to explore the lack of relationship graphically.

Various plots are naturally possible for these data. Here I give a two-way bar chart or graphical table in which the height of each bar is proportional to the percent in each cell: and another in which conditional distributions are given for each time: 