taking the average of each person and then run a regression I have a very large data frame with 14000 rows and 4 columns.
In the data frame, every Person (2000 in total) stated for one week,(one day has one row, so in total every person has 7 rows) how often they used the car to go to work.
This will be my dependent variable.
So one row is basically one day.
Additional to that I have the independent variables, age, temperature, precipitation, and km they drove.
I am thinking, do take the average values for every person, so that I will have a data frame with 2000 rows and then run a regression, as I am struggling with the huge data set.
And I find it extremely messy to look at the scatterplot and find any relationships.
Does this make sense or will I run into difficulties ?
Is there anything I need to take into consideration ?

By averaging you may hide important day-of-week effects, and you will lose a small to moderate amount of statistical information otherwise, which will somewhat decrease power and precision.  This appears to be an application suited to a random effects model, i.e., random person-specific intercepts.   This assumes an equal correlation pattern, i.e., the correlation within person for days s and t where s $\neq$ t is the same no matter what s and t.
You're right, scatterplots are hard to read when the signal:noise ratio is small (low $R^2$).  You can plot trends though, using nonparametric smoothers or regression splines.  But this only helps with bivariate relationships.
