# Calculating R-squared with duplicate data

I have the following question regarding the proper usage of R-squared value.

Say I have an equation, that predicts energy consumption for the month of a building. One of the input variables accounts for time, so 1 would be for January, 2 would be for February, etc. and 12 would be for December

For one year, I would have 12 numbers for predicted data points. Say also at the end of the year I am able to get the exact energy consumption from my Electric company. So now I have 12 predicted data points and 12 exact data points which were measured without any error.

Would it be an accurate analysis to take these data points, and perform a regression analysis using excel? Could I then interpret the R-squared value as the telling me how similar the two sets of data are, and overall tell me whether or not the equation that predicts energy consumption is a good enough approximation of the true energy consumption?

Also, if there's a some statistics genius who could tell me the proper way to interpret R-squared, I would really appreciate it. Thanks

$R^2$ is good for showing correlation, but you need more. For example, if your prediction is always twice higher than the actual consumption, then you get perfect correlation $R=1$ but this is clearly unacceptable.
I think, the average (Mean) square error of prediction $MSE = \frac{1}{n} \sum_{i=1}^n (Actual_i - Predicted_i)^2$ should be a better measure.