I am interested in performing a multiple linear regression in order to determine if levels of my protein of interest is associated with cognitive decline in pre-symptomatic Alzheimer's disease. However, based on the literature I have decided to add several covariates/ confounders (such as age, gender, years of education and ApoE4 carrier status) to the model. When I run the analysis, the overall model (F-statistic from ANOVA table) is not significant (p = 0.069). From what I understand, this suggests that none of the regression coefficients differ from 0. However, when I look at the significance of the regression coefficient for my protein of interest, it is highly significant (p = 0.008) when adjusting for the covariates/confounders.
Is it possible that the non-significance of the overall model is due to the the non-significance of the regression coefficients of some of these confounders? For instance, the significance of the regression coefficients are: ApoE4 (p = 0.855), age (p = 0.180), gender (p = 0.085) education (p = 0.469).
I am only interested in the effects of my protein (p = 0.008) on my dependent variable (cognitive decline) while controlling for these covariates/ confounders. I am not necessarily interested in the individual regression coefficients of these covariates/ confounders.
Can I still say that there is a significant relationship between my protein and cognitive decline? Multicollinearity and heteroskedasticity do not appear to be present