Can i study correlation and linear regression for only one group that answered my questionnaire? the two variables of my research are "gamification" and "motivation" but how can i study the relationship between those two without the need to give the questionnaire to two groups? (most of questions in the questionnaire concern motivation only)
OK based on your last comment, you have two somewhat different things going on here: (1) research design and (2) choice of analysis. In order to investigate the effect of gamification on motivation, your research design might be for instance the following:
-2 groups of individuals
-You measure their motivation (time 1)
-one group goes through gamification, one does not (the latter maybe goes through some event that is otherwise similar, but lacks the "gamification" element)
-you measure their motivation again (time 2)
Choice of analysis is a different issue. If you chose to use some version of the above suggested design, you could use multilevel regression or repeated measures ANOVA with time x group interaction predicting motivation. Correlation does not seem to be a relevant analysis with your research questions.
If you only have data on some group's motivation after they went through a gamification event, you can't say anything about the possible effects of gamification on motivation, and actually not run any analyses either (at least no correlations or regressions, if you only have one variable measured once).