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I am running a regression model in R and I want to interpret the variance explained percentage, as well as, R-squared value.

result1<- lme(values~ gas*price, random = ~1|ID, data=dt)
r2beta(model=result1,partial=TRUE,method='sgv')
MuMIn::r.squaredGLMM(result1)
       Effect      Rsq upper.CL lower.CL
       Model       0.15    0.312    0.032
       gas         0.08    0.323    0.003
       gas:price   0.063   0.123    0.001
       price       0.001   0.234    0.000
       R2m       R2c
       0.0596562 0.7687985  

I am not quite sure if I understand the output correctly. To my understanding, this whole model can explain 15% of the variance. Furthermore, gas can only explain 8% of variance. On the other hand, when we look at the conditional r2c, which is the percentage of both fixed and random effect, we see high percentage, 0.76. May I ask if someone can explain how to interpret these two different output? I would also like to ask why do Model and R2c result also differ while both are using whole model?

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