st: Multiple linear regression the right approach?

[Simon Hauburger <simonhauburger@gmail.com>]

Dear potential helpers,

I have a problem figuring out the right regression for my model:

- It has a interval dependent variable (costs in $)  that looks
normally distributed, but according to shapiro-wilk test isn't
- a number of independent variables which are categorial (scale from
1-6) and interval (assets in $)

My first guess was to use a multiple linear regression, but not all of
the independent variables are linearly related to the dependent
variable (tested with cprplot lowess), even after having tried the
common transformation techniques (log, square...)

Any reommendations for my next steps? Keep trying to transform the
variables and use the multiple linear regression or try an alternative
method? If so, which method could it be? Logistic regression?
(Transformation of the dependent variable to a binary variable is
possible)

I am really confused, statistics will never become my best friend....

Thank you for your help!

Best
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