To fit a linear regression model you don't need the variables to be normally distributed. The residuals have to be normally distributed. So, you fit the model and check goodness of fit Here there are several assumptions you should test. You may need to read some theory for regression before you apply it.

I agree with Eliana

Hello Uzma,

Eliana Ibrahimi 's response is correct. Should you find that your model residuals do not meet the usual assumptions (and you are unable to transform scores in such a way as to ameliorate the situation), you could use the bootstrap method to estimate the standard errors of any model parameter (e.g., a regression coefficient), that should be legitimate for the specific data set with which you are working.

As a side note, the principal reason for opting for Spearman over Pearson correlations as a measure of (linear) association would be if you believed the scores were only of ordinal strength (and not interval or ratio strength). Both S & P quantify linear association: P = linear association of scores; S = linear association of ranks of scores (and is nothing but a Pearson correlation performed on the rank values).

Good luck with your work.

I agree that regression is relatively "robust" with regard to violations of normality, but this may not be the case if your variables are heavily skewed toward one tail or the other. In that case, you may want to explore transformations that can create a more symmetrical distribution.

I agree with Eliana, except that she says that "The residuals have to be normally distributed," and I would not put it so strongly. It might be desirable, but not so important.

Heteroscedasticity should be expected, but there may be model and/or data issues which might reduce (but possibly increase) the effect. You can consider the level of heteroscedasticity by using this tool:

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

You might consider this for regression of form y = y* + e:  

https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression

By the way, with regard to highly skewed data distributions for the variables, mentioned above, that is to be expected for establishment surveys. I worked for many years developing linear regression for use at a statistical agency producing massive amounts of Official Statistics from the US energy industry, for economic use. I was invited back, after retirement, to give the following presentation to a luncheon for mathematical statisticians working at that agency:

https://www.researchgate.net/publication/319914742_Quasi-Cutoff_Sampling_and_the_Classical_Ratio_Estimator_-_Application_to_Establishment_Surveys_for_Official_Statistics_at_the_US_Energy_Information_Administration_-_Historical_Development