Making Maps: Lab 10 - Introductory Statistics, Correlation, and Bivariate Regression

Statistics-something I know nothing about, or knew nothing about until now. It was one of those labs where I was a tiny bit exciting in the beginning as I felt I was grasping it, then it was just frustrating by the end when I started thinking maybe I didn't really get it. Regardless, it was a very valuable lab for me to at least learn the terminology and try to understand the equations, methods, and results.

The lab itself consisted of 3 parts: descriptive statistics, correlation, and regression. Using Excel, I carried out various statistical functions on provided tabular data: mean, median, standard deviation, weighted mean, rates and averages, correlation, scatterplots, and a correlation matrix. Part C focused on linear bivariate regression. First calculating slope, intercept, and using the regression analysis function in Excel, along with interpreting the results. Then I used regression analysis for prediction of values.

I was given the tabular data for annual rainfall amounts for two Stations (A, B) from 1931-2004, unfortunately there was no data for Station A from 1931-1949. To predict the missing rainfall values I created a scatterplot for the two stations rainfall data, then carried out the regression analysis (intercept was not set to zero) with Excel's Data Analysis tool. The results gave me the slope (0.846), which is the rate of change in Station A in relation to Station B, and the intercept (162.342), which represents where the regression line crosses the Y axis. I plugged those values into the regression equation y = a * x + b , and used the arrays for rainfall data for Station B, independent variable, to calculate the rainfall values for Station A, the dependent value in this case.

There are a few different assumptions to consider about this regression analysis. First is that Station A and Station B are in a similar geographic area where you can assume that the rainfall at B has a realistic relationship to the rainfall at Station A. Second we are assuming that what correlation exists between Station B and A for rainfall from 1950-2004 is the same correlation pattern from 1931-1949, when in reality, it is possible that the stations could have variation during that period. However, that would suggest a geographical distance or environmental circumstance between the two stations that we are saying doesn't exist in our first assumption.