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I have a survey analysis data which has responses regarding Consumer Satisfaction (on a scale of 1 to 5)and I am trying to fit a linear regression model to it. As per my understanding, the basic assumption for linear regression is that the independent variables must not show significant correlation. In my case however, since the responses are filled by people (homo-sapiens), the responses are showing correlations within a category and across categories (Food, Facility etc). Is this a cause for concern? Can I still go ahead and apply linear regression or should I combine the correlated responses? Also if I were to combine responses, how should I go about it? I have had to make changes to the responses (independent and dependent variables) based on a scorecard:

Excellent 100 Very good 90 Good 75 Fair 25 Poor 0

I have two approaches in mind:

  1. I can run a linear regression based on the scorecard
  2. I keep the responses to my dependent variable as "Excellent, Very good, Good, Fair, Poor", change the responses to the independent variables according to the scorecard and apply an Ordinal Logistic Regression

Can you guys help me pick the most proper approach.

Thanks!

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  • $\begingroup$ What are you trying to predict? $\endgroup$
    – Steve S
    Aug 1, 2014 at 12:07
  • $\begingroup$ Overall Consumer Satisfaction. Responses vary from Poor to Excellent. I have 4 predictor categories: Food, Menu, Facility, Team. Each category has some questions. When I calculate the correlation, these questions show strong response with the category and also across categories. $\endgroup$
    – Raunak87
    Aug 1, 2014 at 12:41
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    $\begingroup$ You should not do linear regression. $\endgroup$
    – TLJ
    Aug 1, 2014 at 18:13
  • $\begingroup$ Advices about not using linear regression on categorical responses are right, but that independent variables aren't correlated is not an assumption of linear regression - although it poses some challenges. In the other hands, residuals must be uncorrelated, but this is a different issue. $\endgroup$
    – Pere
    Feb 18, 2017 at 15:32

5 Answers 5

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If I understood correction, you want to do a simultaneous regression on several independent variables (multivariable regression). You can still do it if the independent variables correlate strongly among each other, just remember the interpretation of the results will be very difficult. The problem of correlation between the independent variable is called collinearity or multicollinearity, in your case. The bottom line, as explained in the link, is that it does not reduce the predictive power of the model, but interpretation of the variables and their usage, especially if you want to manipulate them independently, is virtually impossible because of the correlation among them.

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  • $\begingroup$ Hi Pedro, I have made some edits to my question. Can you provide some help here. Thanks! $\endgroup$
    – Raunak87
    Aug 5, 2014 at 9:43
  • $\begingroup$ I do not have an opinion on whether you should use a continuous variable and linear regression or a discrete variables and a probit regression. I am not experienced with probit regression and it looks like some people with more of a background can inform you. Still, I am a bit puzzled by your words: "the responses are showing correlations within a category and across categories (Food, Facility etc)". Could you please describe this more in detail? $\endgroup$ Aug 5, 2014 at 15:10
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Linear regression is not appropriate for this problem.

You should consider setting criteria for satisfied customers (say those who marked 4 or 5, e.g. a "Top 2 box") and then create a binary variable (say "satisfied", where 1 = respondent marked 4 or 5, 0 = else). Use this binary "satisfied" variable as the dependent variable in a logistic regression.

Executives (who would usually be the ones utilizing the result) tend to favor this model, as you can tell them odds ratios for effects making a customer satisfied. That is a lot easier to interpret than a regression to individual score (which, being self-responses, aren't really comparable at that high of resolution anyways).

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1) When Predictor and Response Variables are Categorical in nature, you must apply logistic regression or some Naive Bayes technique. With Linear Regression, your output is non-interpretable - Co-Efficients, Residuals, Intercept, Standard Error >> Nothing will be useful.

2) For the highly correlated variables, you have a few choices: Approach (a) Do a Principal Component Analysis and group some of the predictors into a category (For E.g.: All Questions Related to After Sales Service could become one category). Use the Factor Loadings from the PCA multiplied by the actual survey rating to create a factor score for each respondent on each category of questions.

Approach (b) Apply transformations to one of the predictors like log or quadratic transformation or third degree polynomials. But Beware! Applying complex transformations can result in over-fitting and the T-Value of variable is usually too high.

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First of all, I would not run a linear regression since your dependent variable ranges from 1 to 5 so you are not dealing with an interval variable but an ordinal one. An ordered probit regression would be the best approach to it (I am aware that in some disciplines such as psychology OLS is still used for 5 point scales). You could run some tests for multicollinearity (such as variance inflation factor) and assess to what extent it is a good idea to keep the variables in the model - in the end, it depends on what's the goal of your research. If the variables are highly correlated and you still think they should be included in the model, you could apply some data reduction techniques such as factor analysis.

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Strictly to your dilemma: In your case, even if "Food" and "Facility" may, at a glance, vary together, that doesn't mean automatically that they are "correlated" in the proper sense to dismiss one and it's legitimate to investigate which one is a better predictor for, i.e., a nice place to spend the vacation, regressing on both. It can be a 5 stars place with nice rooms, but lousy food. However, you should dismiss from start variables which describe the same thing in different ways or levels of detail (i.e. food - breakfast - dinner). Judge and be creative on that. I agree that it's not the best practice to regress on categorical data, but you can do it if you have a clear picture on what you are doing. Logistic regression will work only if your outcome is a dichotomic variable. In your, case I suggest to consider classification instead of linear regression. Cheers!

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