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I am trying to conduct a research on brand preferences and I am trying to analyze regression equation i.e. which factors affects the consumer preferences (dependent factor) and other determined factors (independent variable). So my question is how to design a questionnaire to calculate the linear regression among these factors

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    $\begingroup$ This sounds like conjoint analysis to me. $\endgroup$
    – SmallChess
    May 5, 2017 at 13:10

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As (standard) linear regression requires a quantitative dependent variable and quantitative explanatory variables, linear regression is not the tool you search.

Your dependent variable has a nominal scale and the explanatory variables have (as it is typical for questionaires) ordinal or nominal scale, you want to look for log-linear models.

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It's probably not a good idea to "design a survey in a way that allows me to run a linear regression model on the results." You want to design your questionnaire to capture the constructs you are interested in the best way possible. As you are doing that, you can think about what statistical tool might be most appropriate for analyzing the question you created. It might end up being linear regression or it might not. And you might not know the answer until after you actually see the data.

To be more specific:

If you are interested in what factors drive brand preference, controlling for other factors, then your questionnaire needs to include questions that do a "good job" of measuring each of those things. What "good job" means depends on the specifics of what "construct" you are trying to measure: if you think that being an introvert is a predictor of preference then you need one or more questions that you can be confident actually measure whether a person is an introvert (and just asking "are you an introvert?" is probably NOT a good solution). You should make all these decisions independently of what kind of statistical model you will eventually run. When in doubt steal questions from pre-existing surveys on similar topics that have already been validated as actually measuring the things they say they are.

Once you have developed a good set of questions, then you can ask the question of what sort of statistical model would best be suited to analyzing it. A linear regression is appropriate when your dependent variable is continuous, not censored and has a distribution that isn't massively skewed one way or the other, etc. But if you decide that the best way to analyze brand preference is to ask people "which brand do you like best: A, B, C or D?" then that variables can NOT be analyzed with a linear regression model, because it is a nominal categorical variable. You would need to use some other method (like a multinomial logit model) to analyze it. It also might be that you don't end up wanting to use a regression analysis at all.

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  • $\begingroup$ I disagree with this. Every analytical method has limitations and constraints, and the data collection process (whether observational such as a survey, or an experiment) ought to be designed with those in mind. If not, there is a risk that the data collected is uninterpretable and cannot be analysed well. This is an extremely common problem! Hence Fisher's old line: To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. He can perhaps say what the experiment died of. $\endgroup$
    – mkt
    Aug 25, 2023 at 8:03
  • $\begingroup$ I agree that one shouldn't be fixated on a linear regression if that is unlikely to be suitable for the data - but one ought to have the better model(s) in mind when designing the survey. $\endgroup$
    – mkt
    Aug 25, 2023 at 8:31
  • $\begingroup$ I totally agree that data collection should be designed with analytic and statistical issues "in mind." You need to make sure you have enough power and you want to design questions with a mind towards how you might analyze them once the data come in. So yes, a statistician should be involved in research design. But you can't know for sure what method will be appropriate unless you see the data (e.g. how skewed it is). My point was merely that the primary goal of designing a question shouldn't be trying to ensure that you can run an OLS on it, which seemed to be the implication of the OP. $\endgroup$ Aug 25, 2023 at 12:13
  • $\begingroup$ I think we agree then. But some of the statements in your answer go well beyond this: "...get good data first, then decide how to analyze it." & "Once you have [collected the data], you then want to choose the best statistical tool for the job." both imply a role for statistics that begins after data collection, which I think oversimplifies your actual opinion. $\endgroup$
    – mkt
    Aug 25, 2023 at 12:18
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    $\begingroup$ Ok. I cut the last statement and edited the first to try and make that clearer. $\endgroup$ Aug 25, 2023 at 13:30
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I think you would probably want to plot the distribution of your response variable prior to making any decisions on modeling.

Often times it helps to see how your data is distributed, prior to assuming a particular model choice.

That being said if you're using R, you can use packages like DHARMa to assess whether your model choice is appropriate: https://cran.r-project.org/web/packages/DHARMa/vignettes/DHARMa.html

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