How can I get an R-squared value of 1 (fit 100%)? I have a set of data and plotted it in a graph (in Microsoft Excel) and then added a trendline. The equation I got is $y=833.71x^{-1.448}$ with $R^2=0.9511$. What should I do to get $R^2=1$ (100% fit)? 
 A: An $R^2 = 1$ indicates perfect fit.  That is, you've explained all of the variance that there is to explain.  In ordinary least squares (OLS) regression (the most typical type), your coefficients are already optimized to maximize the degree of model fit ($R^2$) for your variables and all linear transforms of your variables.  Your model appears to be a little odd in that x is being raised to a particular exponent, so your mileage may vary.  But in response to your general question, you can always get $R^2 = 1$ if you have a number of predicting variables equal to the number of observations, or if you've estimated an intercept the number of observations - 1.  Either way, 20 parameters perfectly describes 20 data points.  Such a model is called just-identified.  Although this gives you the highly desirable perfect fit... it is essentially meaningless.  
A: If you REALLY want to get 100% R^2, just construct an nth degree polynomial, where n is the sample size. Each degree adds a new kink through one observation. You'll get the 100%, but the model will be meaningless. 
