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
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.
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