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My master thesis investigates the relation between stock raw returns and sentiment scores.

To make a conclusion there is a multiple linear regression with the mean sentiment, the variance of the sentiment and the variance of the raw returns (of the stocks) as independent variables and average raw return as dependent variable. Something like:

raw return = constant + (average sentiment * x1) + (variance sentiment * x2) + (variance raw return * x3)

a snap shot of the data: enter image description here

When I the multiple linear regression. SPSS gives me following output. My problem is that I don't know if I can use this.. the ANOVA test is significant (but what does it mean with this data?) and the only coefficient that is significant is the variance of the raw returns. As this is the final result I need to explain the results.

This is the SPSS output: enter image description here

This is the scatterplot of the residuals and raw returns: (if this could be useful)

enter image description here

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In linear models (like ANOVA) we can get a significant model with no significant predictors when some predictors are correlated and they carry the same information.

p-value of each individual predictor just tests the model with all predictors against a model without that particular predictor. If predictors are correlated, another predictor (or set of predictors) may carry the same information and therefore removing one predictor doesn't make any different, and the predictor is reported as not significant.

I suggest trying variable selection. Removing some predictors may cause the remaining ones to become significant.

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  • $\begingroup$ Thank you for the information. However removing predictors has no effects on the significant values. If the sentiment scores are in any case significant, does this inclusion in the model make any sense? $\endgroup$ – belgiums May 11 at 16:48
  • $\begingroup$ not significant* $\endgroup$ – belgiums May 11 at 17:11
  • $\begingroup$ In this case all the VIFs are close to 1 so multicollinearity doesn't seem to be an issue $\endgroup$ – Glen_b May 12 at 10:06
  • $\begingroup$ @Glen_b - Yes, I'm afraid you are right. $\endgroup$ – Pere May 13 at 8:33

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