Hi,

If analysing the relationship means estimating a regression model, my opinion is that  relationship can be established only between option price data & stock data. Open interest reveals an aggregate of both bought open positions & sold open positions, without any sign assigned, so determining how it influences stock price is not possible, as both bought & sold positions outstanding may have opposite pulls on the price. 

Secondly, volume has no relationship with price, per se. It is change in volume that causes change in price. So, relationship should be based on 'del v' & not just volume. I hope that introducing the necessary changes in your model may help.

Sorry for deviating from your question regarding using continuous option series instead of using OTM options only but I thought these could be the reasons for your problem.

Hemlata

It's a well-documented finding that there's no correlation between market volatility and future stock returns...it's flat. Daily, monthly, OTM, ATM, historical, implied. So, looking for better volatility metrics won't show anything. 

OTM options and ATM options would have comparatively more information content. So, instead of aggregating the entire trading data, you can consider  data relating to OTM options or ATM options by comparing the relative predictive power of the two types of options.