Hi,why do we take log of stock returns in regressions? does the results differ in this case from the results of a regression without log?

Not sure if I got your question correctly, but it is better to use the log return than the spot price due to the fact that stock prices (and any asset price) tend to exhibit serial correlation. As the returns don't have this problem, it is better to use the return.

The key difference is log RETURN versus price, not log versus non-log. You could also regress price returns.So if you're asking why people regress returns rather than prices, VolMaster gave you the answer.If you're asking why people use log returns instead of simple price returns, the answer is that logs have better mathematical properties but that it usually makes little practical difference.

First of all we never do any regression analysis (or possibly any statistical analysis) on the raw Price. Price is non-stationary therefore having regression will lead to to Spurious Regression like, the distribution of the estimated beta coefficient will no longer be t-distribution. Therefore if this fact is unknown to the analyst then he would make false inference on the true Beta. Therefore you need to **kill** this non-stationarity hence take 1st difference and apply regression (or any Statistical toll) on that transformed series.Another way to say that, any Statistical inference is based on Sample. Therefore more sample point you have more robust (in terms of Consistency in estimated parameters) inference you will make. Therefore if you work with non-stationary figures then past values will no more relevant for your current analysis as, non-stationary means, in loose term, property of the DGP for price is changing.On the other way once you make your price-data stationary by taking 1st diff. then you can use historical data for your analysis, assuming historical realized diff-ed values are the possible realizations for Next random variable of the underlying stochastic process. You can assume, as in this case properties of the underlying DGP is not changing.Having said that you should work with diff-ed series, you must take Logarithmic price. There are many reasons for that, however most important is that, generally a price series grows exponentially (see any time series plot). If you take log then, the growth becomes linear. As Statistical tools are generally for "linear world", you then use Statistical tools conveniently on that transformed data. Additionally, logarithmic transformation is good for Variance Stabilization.Combining these two points, I think it is now clear why to work with Log-return not with Price or even with log-priceThanks,