I'm assuming you used dummy coding in multiple linear regression to test a nominal predictor variable with 5 groups. Then, each dummy regression coefficient reflects the mean difference (or adjusted mean difference if you have other covariates/predictors in the model) between a specific group and the reference group. The p value(s) depend on whether a specific (adjusted) mean difference is significantly different from zero. Normally, you wouldn't look at significance tests (p values) for individual predictors if you found a non-significant overall F statistic (exception: if you had specific a priori theory-driven hypotheses about specific contrasts/mean differences).

If you don't have other covariates/predictors in the model, this regression analysis is identical to a oneway analysis of variance (ANOVA). In an ANOVA, you would also look at the omnibus F statistic first and conduct post hoc tests (pairwise comparisons of mean differences, typically with adjustment for Type-I error inflation) only if you found a significant F statistic (again with the exception being if you had specific a priori theory-driven hypotheses about individual contrasts).

It is difficult to say for a nominal variable with > 2 categories that the predictor as a whole is "significant" (or not) because the predictor isn't a single one: It is broken down into multiple separate dummy predictor variables (four in this case). Since the coding of the reference category is mathematically arbitrary (it does not change the fit of the overall regression model [R-squared] or the F statistic), the p values can change when you select a different reference category because the types of contrasts would change. The overall F statistic merely tells you that one or more group mean differences may be statistically significant.

Thank you so much, Christian, for your help, time and great explanation. And sorry, I should have mentioned the categorical variable is ordinal (1-5), and I did include that as a categorical variable in the linear regression model (both adjusted regression and unadjusted regression), and after I sent the results, I see in the manuscript they mentioned that:

The objective is to identify whether this categorical independent variable could predict the continuous outcome variable.

But since at the beginning they asked me to consider this variable as a categorical in 5 categories, I think this regression analysis with including the categorical independent variable cannot answer this objective.

The objective should be changed like is there any difference among categories when adjusted for other variable? not true to talk about the predictor, am I correct?

I don't want to consider this categorical variable as a continuous variable, as they confirmed to include that as a categorical variable. I know that if I consider that as a continuous variable, then I can answer that objective. My question is for independent categorical(ordinal)variable

Thank you so much for your help

Or would it better to ask my question this way?

Since the overall p-value for this categorical independent variable in linear regression (both adjusted and unadjusted models) is not statistically significant, can we conclude that this variable is not a significant predictor even though one category is significant?

Or not — as you mentioned, since the variable is broken down into multiple separate dummy predictors (four in this case), we cannot say whether the variable is a significant predictor or not. Instead, we can only conclude that there is no statistically significant difference among the categories (in both adjusted and unadjusted models), even though one level is significant- because the overall F-test is not significant.

Sorry for the long message, and thanks so much for any input you have

My recommendation would be to not dummy-code the variable if it is truly ordinal and to simply include it "as is" (i.e., in its original form) as a single predictor. That gets you around this whole issue I think because then there's just a single regression coefficient and p-value for the predictor variable in question.

Thanks so much for your suggestion. Since they wanted to include that as a category (as I have also run the Kruskal-Wallis test for this categorical variable along the box plot), and I am in the interpretation step, I am trying to fix the interpretation in the regression analyses.

In general, I wondered how we can determine whether a categorical independent variable (more than two categories) is not a significant predictor ( or is a significant predictor)of a continuous outcome in a linear regression model?

I would appreciate if you had any input on this