Write programs that use Least-Squares regression to fit this data with (a) a straight line and (b) a power equation based on log transformations. Compute the correlation coefficient and provide an analysis of the results explaining which approach is more appropriate for this experiment.

In many studies, we measure more than one variable for each individual. For example, we measure precipitation and plant growth, or number of young with nesting habitat, or soil erosion and volume of water. We collect pairs of data and instead of examining each variable separately (univariate data), we want to find ways to describe bivariate data, in which two variables are measured on each subject in our sample. Given such data, we begin by determining if there is a relationship between these two variables. As the values of one variable change, do we see corresponding changes in the other variable?

We can describe the relationship between these two variables graphically and numerically. We begin by considering the concept of correlation.

Correlation is defined as the statistical association between two variables.

A correlation exists between two variables when one of them is related to the other in some way. A scatterplot is the best place to start. A scatterplot (or scatter diagram) is a graph of the paired (x, y) sample data with a horizontal x-axis and a vertical y-axis. Each individual (x, y) pair is plotted as a single point.

Explanation: