Dear Community,
I was wondering whether it is possible or not to validate hypothesis testing based on OLS regression with 2 indep variables only? Or will such thing decrease the credibility of OLS regression results?
If we push it to the extreme, is it possible to validate hypothesis testing with uni-variate regression analysis?
Hello Yuko,
I'm not sure I understand exactly what you're asking.
You certainly can:
1. Use OLS regression to develop a model having two IVs and one DV (which is a univariate model: one DV).
2. Use OLS regression, with additional data, to determine how well a previously developed model having two IVs works to account for variance in the DV in the added/new data batch.
3. Use OLS regression to evaluate the relationship between scores on a single IV with those of a single DV (simple bivariate regression).
4. Use OLS regression to address questions of whether a categorical IV can help explain differences in scores on a single metric DV.
If none of these gets at the intention of your query, perhaps you could elaborate a bit so as to increase the likelihood of getting a more constructive response.
Good luck with your work.
Regardless of the number of independent variables, regression only looks at correlation and relationships. Regression CANNOT establish cause and effect. Regression results are normally written up as x is associated with y: associated, not caused. Regression gives hints about the validity of a hypothesis or can predict the likely effect of a change, but a regression NEVER can test a hypothesis. Regressions on longitudinal data from a randomized trial with adequate power and a well-matched control group (RCT) or more weakly, with a propensity-score-matched synthetic comparison group, tighten the causative chain by narrowing the plausible range of alternate explanations of the association between the intervention and outcome variables. Statistician's also have been moving to SEM or other models, which draw them CLOSER (still not definitive) to causation by showing that each of a set of hypothesized changes along a causal chain occurred. Even then, it's not a true hypothesis test.
On the contrary, when the hypotheses (OLS) are verified, it gives support to the regression analysis using the (OLS) method, especially if the sample is medium-sized. But if the data sample is large, it is achieved by the central theory.
I'm not sure, would my answer be helpful or not, from my point of view, it is neccessary to understand, are 2 factors so different? If they are not so different, it is possible to use uni-variate regression. Also, I think, you can use uni-variate regression separately with each factor, and analyze the resuts for clairifing the case.
Yuko -
As I said regarding another of your recent questions, https://www.researchgate.net/post/Is_it_possible_to_validate_hypothesis_testing_based_on_OLS_regression_with_2_indep_variables_only, if you are looking for the best predictions, you need the best set of variables, not too many, not too few, and ones which work together well in a function which provides the best predicted-y values. A "graphical residual analysis" will check this, including heteroscedasticity, for your sample, and a "cross-validation" is used to try to avoid overfitting to your sample, when you need to predict well for the entire population or subpopulation you are trying to model.
OLS is a special case of WLS regression, and often not a very good option, just a more convenient option. See https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity, as bounded by Ken Brewer,
https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity,
and
https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and the various updates there, in reverse chronological order.
Cheers - Jim
I an amateur in research . I think I will answer yes.
Oops. Above I referenced this question, https://www.researchgate.net/post/Is_it_possible_to_validate_hypothesis_testing_based_on_OLS_regression_with_2_indep_variables_only,
when I meant to reference my response to
https://www.researchgate.net/post/OLS_regression_variables_changing_sign_eventhough_VIF_is_below_2_0
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