I read from Hair et al., (2017)'s book that R square of 0.2 is acceptable in consumer behaviour research, however, they did not provide reasons for that. I think this is because human behaviour is less predictable than pure science. The reviewer requires me to provide more references for this, anyone has suggestions?
Very valid concerns, Kara,
Reinforcing Timo Mandler 's comments, above you should consider whether you are using your regression model for prediction or for explanation. In social research, then it's almost always explanation: variation in these IVs explains this much variation in this DV. The unexplained variation is a combination of random variation in the data and the effects of other influences that have not been measured and included in the model.
Econometricians are usually interested in prediction, so they want high R2, and they usually don't much care why. Psychologists usually are interested in explanation, but they recognise that people are fickle and that their measurements are really very crude, so there is a great deal of random variation in the data, in both predictor variables and dependant variable. For example, if you are using Likert scales or, worse, single item rating scales (1-5, 1-7, 0-10) then you should expect that more than half of the variation in each variable is just random.
Prove it to yourself in a spreadsheet: Generate columns with three random numbers with equal means and distributions. Then create two variables that are the sum of two random numbers:
Var1=rand_1+rand_2,
Var2=rand_1+rand_3
so now you have two variables and you know that half of the variation in one is shared with the other (because rand_1 is half of each variable). Now calculate the squared correlation for the two variables. You'll see that r2 rarely goes above 0.3. Fiddle with your formulae so you can change the amount of shared variance present between the variables. For example,
Var1=rand_1+(0.1*rand_2),
Var2=rand_1+(0.1*rand_3)
gives you two variables with about 91% shared variance.
Frankly, this sort of thing should be understood by your reviewers. Welcome to the club.
Generally we do research to reach to the reality or truth about specific issue concerns the researcher. From statistical point of view, High value of R square helps you in explaining the issue being investigated, and getting more explanation about the involved factors. The marginal error will be much less as long as you have greater level of R square. It is also a good indicator for any future predication.
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