Univ have sent us a *Newsletter & Roll of Donors*, presumably meaning to prod us into action of some kind. Since this brochure contains a listing of the percentage of surviving ex-students who gave a donation in the academic year 2012/13 by year of matriculation, we suppose we are meant to do a regression.

That gives us the results plotted above, or the model is:

*Call:* * lm(formula = PERCENT ~ YEAR, data = univ)*

*Residuals:* * Min 1Q Median 3Q Max**-16.5684 -3.3648 -0.8145 4.1408 11.8245* *Coefficients:* * Estimate Std. Error t value Pr(>|t|)* * (Intercept) 1368.28941 112.48351 12.16 2.85e-16 **** * YEAR -0.67092 0.05668 -11.84 7.65e-16 **** * —* * Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1* *Residual standard error: 5.784 on 48 degrees of freedom* * Multiple R-squared: 0.7448, Adjusted R-squared: 0.7395* * F-statistic: 140.1 on 1 and 48 DF, p-value: 7.648e-16*

I don’t really feel like trying a quadratic term here…

Presumably the simplest explanation is that the older year groups just have more disposable income and so they give more to their old college. Generally speaking, charitable giving is more prevalent among older people even among normal human beings, never mind this population, characterised as it is by excessive personal wealth (see for instance here). Of course, and especially for this population, a great deal of the value is contained in a few high-value donations, so participation rate doesn’t necessarily tell you very much.

Anyway, we could also ask about the performance of particular years against the model prediction. The figure below shows residuals against year. We see that 1980 is quite significantly–indeed 1 standard deviation–below the predicted value, while 1982 is less frugal.

A friend writes: * I was looking for a pattern in the residuals for significant anniversaries e.g. 25th since graduating, but need more data. It would be interesting to look at the data for previous years to see percentage donating by year since matriculation for different cohorts. Is the class of 82 consistently more generous or is it that in the 20th year after graduating every cohort donates more?*

In the absence of more data, we can look at the autocorrelations, as below:

Clearly there is nothing significant here (though we may question the wisdom of going up to lag = 20 with only 50 data points).

Logically, one might expect some effect connected with ‘gaudies’, where those who matriculated in a given period are invited back to the college to engage in donating money and in self-congratulation. So there might be a quasi-significant-anniversary effect, since recent years (like 1980) tend to get invited back every ten years or so, but this would not show up in the autocorrelations.

Then there’s the question of displacement: are the same people giving what they would have given anyway but at a different time?