Statistical Analysis Of Key And Semi-Key Lincoln Cents

I did a multi-variable linear regression to try to relate log(mintage) to log(price) and year for Mercury dimes and came up with a much better model than one that just used mintage. However, it still wasn't a very good predictor of price at the grades I tried it at. It suggested that certain mid-20s dates like 1925-D were overpriced by more than twice, and some teen dates and late-20s/early-30s dates were under-priced by similar factors (interestingly, 1.8ish million mintage '30-S and '31-S were much more under-priced than 1.5ish million mintage '31-D).

The under-priced dates seem to correspond to recessions, so I may try plugging in an economic-activity factor into the model to see if that will improve the fit at all. E.g. something like GDP over the 5 years following the release of each issue. I may also get a better fit by only looking at very low grades or only looking at uncirculated grades, which would be less dependent on amount of circulation.

And this is a great thread. I really like the idea.

Is there a way to compare keys from one denomination to another?

Mainly to see what keys of what denominations are more rare than the other?

Trashy,

Biggfreds point was the price for a good 1931-s is only half of a ms60. Look at any other "key date" coin of almost any other denomination and you'll see a condition multiplier well in excess of 2. For instance the 1914-D Good to MS60 multiplier is around 12. Nobody hoarded 1914-D's like they did 1931-S's so they are relatiely rarer. The "No Cent" nickle is a classic example of this also...

Paddy

It was OLS. I think. Adjusted R was 0.85. That was after excluding the worst outliers, 1916 and 1916-S. I think excluding them is justified because they were saved in large numbers and well known to be particularly common as a result.

Keep in mind the wise words of Chemistry Dog, I am new to this kind of analysis. My independent variables were the year of issue and the log of the mintage. The dependent variable was the log of the Numismedia XF40 price. This is the output of my statistics package (I'm using R).

Residuals:
     Min       1Q   Median       3Q      Max 
-1.01520 -0.45579  0.07489  0.38104  1.11649 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 364.68854   38.02047   9.592 1.41e-11 ***
log_Mintage  -1.05848    0.07352 -14.398  < 2e-16 ***
Year         -0.17902    0.01958  -9.144 4.96e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.5449 on 37 degrees of freedom
Multiple R-squared: 0.8636,	Adjusted R-squared: 0.8562 
F-statistic: 117.1 on 2 and 37 DF,  p-value: < 2.2e-16

Also any reason why you took the log of the price?

Ok, I think I'm getting the idea Paddy and Bigg Fredd, thank you! The bottom line is the shorter mintages are usually hoarded and the higher mintages not so much, therefore the higher mintage old coins will be tougher to find high end quality survivors.

This is what I have been thinking all along, but got caught up in statistics! (grin) I put together this image bringing together some key historical aspects to the Lincoln Mintages just for kicks, to see if any areas might be better than others. I did NOT include proofs or steel pennies. Hope this helps in the food for thought area! :)

I'm not sure if the following adds anything to the discussion or not. Of what I hve understood I began to wonder about the availability of what is available (assuming what I have found roll hunting in the last 9 months is indicative of the available distribution.) I have kept every 1938 - 1959 nickel I have found and this is the distribution. I did not include 1938 and 1939 since some of those were given to me.

P D S

1940 9 5 4
1941 10 4 4
1942 5 1
1942 3 2 silver
1943 3 1 2 silver
1944 4 1 2 silver
1945 2 2 1 silver
1946 12 2 1
1947 7 2 3
1948 6 6 1
1949 4 5 2
1950 1 0
1951 6 2 2
1952 9 1 2
1953 7 7 2
1954 12 11 2
1955 3 7
1956 6 6
1957 10 12
1958 4 15
1959 4 13

I live in WV so that may account for an over supply of P minted nickels.