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 xaxis shows the temperature measured by the outdoor gauge. The yaxis shows the temperature measured by the indoor gauge. The zaxis 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.
