Least Squares Estimation of the Temperature on My Walk to School.
A gauge in my home measures the indoor temperature. A remote gauge outside my window measures temperature and sends it, via radio transmitter, to the indoor gauge.
Problem: The outdoor gauge is inside a thermal boundary layer surrounding my building, so it doesn't get an accurate measurement of the true outdoor temperature.
Bad solution: Look up the real temperature downtown on the internet.
My solution: Collect 36 triplets of data for the Downtown temp, the Home temp and the Outdoor (wrong) temp (D,H,O). According to heat conduction/convection theory, O is a linear function (or nearly a linear function) of D and H. Attempt to fit the data to a function of the form O=xD+yH using a least squares minimization to find the coefficients x and y.
The graph shows the plane which minimizes the squares of the errors. Click it for a larger view. The x-axis shows the temperature measured by the outdoor gauge. The y-axis shows the temperature measured by the indoor gauge. The z-axis is the true outdoor temperature found from the National Weather Service Website. Stars show the 36 data points that I collected. This plot can be used to estimate the real outdoor temperature from the two pieces of data that my gauge collects. Predictions so far are within 1 or 2 degrees fahrenheit of accuracy. Errors are likely due to variability in wind speeds.