[gjm11]

(Not the author.)

D is a vector of input data. If it's more than a single number, then beta D needs to be interpreted as a dot product.

There's no guarantee that in any specific case a linear function of D will be a good approximation to the log odds. (In the present instance, where D is the temperature, it won't be -- there'll be a narrow range of good temperatures and the further away you get from that range, the worse the coffee is likely to be.)

But a linear approximation is at least simple and log odds (unlike e.g. probability) at least can take any value from -oo to +oo. Sometimes you get lucky.