I have a conspiracy-prone friend who believes that people are controlling the weather to ensure good weather for a large, annual festival (last weekend in June in San Francisco). As a scientist, (not earth science), I was interested in testing this hypothesis. So..I built 2 linear models--one representing the days leading up to the festival, one representing the days following the festival-- where the I regressed max daily temperature onto the number of days away from the festival. Lo and behold, indeed the temperature did appear to rise, peak on the weekend of the festival, and then drop afterwards! Next I figured, it must just be a natural trend, irrespective of local festivities (and weather-controlling overlords). So next, I included data from the years before the festival began (1972), made two groups (pre-festival and post-festival) and included a days_away_from_festival*group interaction term. To my great surprise, the interaction was significant! Testing only the group dated before the festival began, did not yield significant results.
And so! My question is... can any of you experts explain this by means other than a statistical coincidence/wealthy weather gods? Why might the temperature in San Francisco tend to rise in the week leading up to the last weekend in June, and then fall afterwards--but for this effect not to be present in the years before 1970'sish?
EDIT: Here are my two models.
The first model represents the days leading up to the festival and days are indicated by the countdown variable, (e.g. Friday = -1, Saturday = 0) There are 5 days prior included in the model. The group variable refers to the fact that I split the years into two groups, old:(1942-1971) and new:(1972-2017). TMAX is the maximum temperature of the day.
The second model is the same except it represents the days following the festival.
As you can see, after 1972 the temperature seems to rise, peak during the festival in the last weekend in June, and then fall immediately after. However, this effect was not present prior to 1972.
EDIT2: The data came from https://www.ncei.noaa.gov and the station is San Francisco Downtown