You can try the Weighted Least squares, which is a special case of Generalized least squares, in this situation.

Debopam Ghosh Thanks for your answer. I have been doubting for a while so I have now also statistically tested for heteroscedasticity. I do get rather contradictory results in my opinion. When looking at the scatterplots (see attachments), does any of them show heteroscedasticity?

Ellen Kroon, an alternative would be to estimate/use Heteroskedasticity Robust Standard Errors in your significance testing. This can be done easily in Stata or R. See the link below for more: https://www.r-econometrics.com/methods/hcrobusterrors/

Mehmet Mehmetoglu is there also a possibility to do that in SPSS? I am only familiar with SPSS. I‘m doubting whether the scatterplots are in fact showing signs of heterscedasticity or not and if I really do need to do something additionally.

Ellen Kroon, here is a video explaining how to perform linear regression with robust standard error in SPSS: https://www.youtube.com/watch?v=WurjrwzRpOg

Transforming will not improve anything. If you can send me the data, I could have a look...

Ellen -

You do not want a transformation to do weighted least squares regression. See https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and the various updates there.   

Studentized residuals are best, but you can even use raw residuals through graphical analysis to estimate the coefficient of heteroscedasticity. Below are references, including an Excel tool for doing this:

https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity, as determined by Ken Brewer,

and

https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity

with 

https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx

Also, for a more complete picture, see https://www.researchgate.net/publication/354854317_WHEN_WOULD_HETEROSCEDASTICITY_IN_REGRESSION_OCCUR.

Cheers - Jim

Ellen - Also, robust standard errors, by the way, only patch the standard errors. Yes the regression coefficients are unbiased over infinitely many cases for OLS when you have heteroscedasticity, but for each case it is different. That is, using a robust standard error will not change the fact that your model predictions, though often close, are not the best you can do. Sometimes the difference is substantial, more likely with a small sample, so you might be OK. - Jim