I am being tortured with the following problem...

I have a set of crude mortality rates for ages 0 to 60. Let's call them

**Observed Rates**.

I use a smoothing technique (cubic spline regression) on the crude mortality rates and so smoothed mortality rates are produced for ages 0 to 60. Let's call them

**Estimated Rates**.

I want to know whether the

**Estimated Rates are a good representation of the Observed Rates.**I have calculated the R-square, however I am also looking to confirm this with a statistical test.

I am puzzled with which test I should pick, can you please help me out?