A Couple of Comments About Ch. 3 Material Covered Week 3
Notice that the footnote on p. 63 of the text has "we seldom believe that the true relationship is linear." And I believe that one of the Ch. 3 videos of the
HTOC suggests that it never is. However, sometimes scientific laws provide linear relationships. E.g., Gay-Lussac's law gives us that for a fixed amount of
gas in a fixed volume, the pressue is directly proportional to the temperature (Kelvin). This gives us that if ti is the
ith temperature (Kelvin) considered, and
Yi is the measured pressure
for the ith temperature, then the model
Yi = β
ti +
εi,
where εi is an error term due to measurement error, might be accurate.
I think that the shark / ice cream example in the last paragraph of p. 74 of the text is particularly cute. It indicates that one might have a relationship
due to what is known as a "spurious dependence" and serves to warn us that we need to be careful about making claims of causality. (In the example,
shark attacks are related to ice cream sales. But because both of these are related to temperature, we shouldn't conclude that ice cream sales in any way
"drives" shark attacks ... it would be foolish to think that banning the sale of ice cream will reduce shark attacks. It's more reasonable to believe that
when the temperature is high, both ice cream sales and shark attacks increase (with the latter being due to when the temperature is high, more people use
the beaches, and thus supply a greater number of potential shark attack victims).)