# Variables with different scales

I have a dependent interval variable with a scale that looks like this:

Percent of employees who work at home:

1-5%          31-35%        61-65%        91-95%
6-10%         36-40%        66-70%        96-100%
11-15%        41-45%        71-75%
16-20%        46-50%        76-80%
21-25%        51-55%        81-85%
26-30%        56-60%        86-90%


My independent variable is another interval variable but the response scale uses different intervals:

Percent of employees who live outside of the city:

None          41-50%
1-5%          51-60%
6-10%         61-70%
11-20%        71-80%
21-30%        81-90%
31-40%        91-100%


Can I conduct a regression analysis using variables with scales that have different intervals? Would I have to recode the variable responses so that they have the same interval levels in order to have valid regression results?

• "Would I have to recode the variable responses so that they have the same interval levels in order to have valid regression results?" Does this mean that you have the raw percentages to work with? In that case, it makes far more sense to use the raw data than binned data – Richard Border Mar 25 '18 at 17:14
• Thank you for your response. I don't have the raw percentages. I just have the response to percent range category – user3424836 Mar 25 '18 at 17:47
• Given that you have many levels of each variable (>=10), it's very likely that a simple linear model will work. Try coding your first variable as 1:20 and your second as 1:10, fit a linear model, and then check examine some diagnostic plots, e.g. as QQ-plot of the residuals. I'd only worry about complicating your model if that approach is demonstrably problematic! – Richard Border Mar 25 '18 at 18:14
• This is very helpful - thank you for your time and help. – user3424836 Mar 25 '18 at 18:16

You can transform both the Y and X variables into categorical variables. Each would have a number of different levels (1, 2, etc.). Then you could use a Logit Regression. Make sure that the type you use can handle a categorical variable that is more than just binomial. Many software interpret Logit Regression as just a yes/no (0,1) dependent variable. That would not work in your case.

Otherwise, Discriminant Analysis would work. It is very much exactly like a Logit Regression but earmarked for more than just two categories.

Also, an ANOVA model may work just fine.

I think the above would be an effective solution to your problem (dealing with X and Y that have different % range categories).

• Thank you very much for your response. So a multinomial logit regression would work once I transform the scales into similar interval levels? I am wondering is there a specific reason why it's not possible to run regression using variables with different interval ranges? – user3424836 Mar 25 '18 at 17:51
• It is not impossible to do so. It is probably not optimal. You may try it following Richard Border's suggestion. And, observing how readily interpretable each model structure is (comparing linear regression vs. logit regression and ANOVA as respectively structured). Given that you deem my answer helpful, I am puzzled of why I get a -1. – Sympa Mar 27 '18 at 15:40
• Thank you so much - this is helpful. I don't know why it says -1 either, I did not click on that. I tried clicking on 1 but it went to zero? – user3424836 Mar 28 '18 at 16:11
• Thank you for the constructive feedback. I gather another user (not you) deemed my answer unhelpful for some reason. So, my answer score was moved downward to -1. Then, you came in and gave me a + 1. So, it returned my rating to zero. Many users are rather officious in their ratings of colleagues. And, unless one does provide a paragraph of R codes in their answer, one is vulnerable to down-votes regardless if R coding is truly relevant to answering the question. That is just silly group dynamic stuff. The main things are that I helped you out, and that you recognized that I did. – Sympa Mar 29 '18 at 15:48