Exercise 3: Linear regression and correlation on bivariate earth science data.

A) Find a data set with potential x, y pairs. A bonus point towards this exercise if you find your own. If you can't find one in the literature or on the web, come see me and I can assign one. Attach a copy of the data set to your report.

B) Describe which variable will be the x (independent) and y (dependent) variables, and what type of relationship you might expect between the two.

Independent variable =

Dependent variable =

expected nature of relationship?

C) Use Excel or other software package to create a scatter plot. Attach a printout copy to this report. To your eye do the points trace out a line or curve. Intuitively estimate the value of r, remembering that it should be 1 for a perfect fit and 0 for no fit.

apparent nature of mathematical relationship (linear, curved, other)?

estimate for r =

If curved, try a log or power law transformation to see if that helps. Include a scatter plot of the transformed data.

D) Use Excel to compute your best fit line (Regression under Data Analysis under Data), the correlation coefficient, the percentage of variation explained by the mathematical relationship, and the standard estimate of error for your data or transformed data. Attach to this sheet a printout of the scatter plot and the computed curve. You may want to explore other fits, if your data does not follow a line.

 b = intercept m = slope r = correlation coefficient r-squared = variability explained SSE = standard error of estimate

E) Explain the potential geologic significance of your results, including ways the mathematical model might be used.