I work in aviation and we are having a problem with a certain system on a fleet of aircraft. Preliminary research has shown that these problems tend to crop up in the winter time in sporadic intervals, only to disappear or greatly diminish in frequency in the spring and summer.
I suspect that when the temperature is cold and we use deicing fluid to get rid of ice and frost on the aircraft skin, that fluid is penetrating various electrical connectors and wreaking havoc. This is more so than ordinary rain because of the high volume and concentration of the fluid.
I have dates, station location, and weather temps for each departure location. Would a linear regression be sufficient to show a correlation between weather temps and this problem? If not, what sort of modeling could I use to show the validity (or lack thereof) that the weather (and thereby our use of deicing equipment) is influencing the frequency of said problems?
If all you care about is whether two variables are positively correlated but you have no theoretical expectation as to the graph's shape (linear, quadratic etc.), I recommend rank correlation. If on the other hand you need to be able to make quantitative predictions, you may wish to add a line/curve of best for in Excel, which lets you try a few options. (It's with displaying the equation and $R^2$, and try to get a large $R^2$, but don't set the degree to high with a polynomial fit or it's liable to be spurious.)