pls explain pearson correlation?

Question

has a variation from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation)....pls explain to me the meaning of these. thanks!

Answer 1

The pearson correlation coefficient measures the strength of the linear relationship between two variables. Using human height and weight as an example, you would expect that taller people would weigh more than short people - that weight should increase linearly with height.

If you plotted people's weight on the Y-axis, and people's height on the X-axis, the points would more or less fall into a line if there is a linear relationship. If all of the points fell exactly on a straight line where weight increases with height, and the line formed a perfect 45 degree slope on normal graph paper, pearsons correlation would be +1. If weight increased only slightly with height, the slope of the line would be less steep, and yield a coefficient somewhere less than one, but greater than 0.

A negative coefficient occurs when there is an inverse relationship between two variables: where on variable decreases as the other increases. This type of relationship would yield a negative coefficient.

When there is no correlation, a plot of two variables shows no discernible pattern, and the pearson coefficient is zero. An example of this is something like shoe size and a person's income - you would expect there is no relationship between the two.

Answer 2

It can be defined for both, but for ungrouped, individual data, it will be more accurate. The coefficient is only a figure of merit. If you group and average out data in each group, you are actually creating a different form of the data. Remember that averages are not very good representatives of the actuals and hence a lot of information is lost in finding the correlation coefficient for such data.

Answer 3

Read this it should help.

Values of the Pearson Correlation
http://cnx.org/content/m10950/latest/