linear regression for non normal data


Some of my variables are not normally distributed (with Kolmogorov-Smirnov and Shapiro-Wilk tests). So I used Spearman's correlations. But I also did a linear regression, which shouldn't be the best fit for my data. My question is: if I have significant results using a linear regression, are these findings spurious? Or, knowing that ma data are not linear, if something is significant with a linear regression analysis, it is likely that it would be even more significant with a model that better fits my data? Is this idea correct or totally wrong? And if so, do you have any references to support this?

Thank you


Ambassador to the humans
Are the variables you are talking about dependent variables or independent variables? We typically don't care about the distribution of the independent variables. We also typically only care if the residuals are normally distributed.
I'm not sure.
I looked at a measure of personality trait in people, which would be my dependent variable. I made people do a task of reasoning and their scores are not normally distributed: this task would be my independent variable.
The idea was to see if the task results correlated with the personality trait (Spearman's correlations). And then how the task results and some emotional measures predict the personality trait (linear regression)...