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Thursday, January 27, 2011

Simple Linear Correlation (Pearson r)

In the previous chapter, we have discuss about the meaning of Correlation (What is correlation?). Now we will further discuss about Simple Linear Correlation (in Bahasa it means Korelasi Linear Sederhana), known as Pearson r, because it was found by Carl Pearson, thus named Pearson Correlation. I post and publish this article to my blog, as a content of quantitative and statistical methods for management and distance learning business and management.

This article I quoted from statsoft... for further information you could visit their site, or maybe you have to is just take a sit, relax and try to understand about the topics...

Simple Linear Correlation (Pearson r). Pearson correlation (hereafter called correlation), assumes that the two variables are measured on at least interval scales (see Elementary Concepts), and it determines the extent to which values of the two variables are "proportional" to each other. The value of correlation (i.e., correlation coefficient) does not depend on the specific measurement units used; for example, the correlation between height and weight will be identical regardless of whether inches and pounds, or centimeters and kilograms are used as measurement units. Proportional means linearly related; that is, the correlation is high if it can be "summarized" by a straight line (sloped upwards or downwards).

Look at the picture below:

This line is called the regression line or least squares line, because it is determined such that the sum of the squared distances of all the data points from the line is the lowest possible. Note that the concept of squared distances will have important functional consequences on how the value of the correlation coefficient reacts to various specific arrangements of data (as we will later see).

How to Interpret the Values of Correlations. As mentioned before, the correlation coefficient (r) represents the linear relationship between two variables. If the correlation coefficient is squared, then the resulting value (r2, the coefficient of determination) will represent the proportion of common variation in the two variables (i.e., the "strength" or "magnitude" of the relationship). In order to evaluate the correlation between variables, it is important to know this "magnitude" or "strength" as well as the significance of the correlation.

Significance of Correlations. The significance level calculated for each correlation is a primary source of information about the reliability of the correlation. As explained before (see Elementary Concepts), the significance of a correlation coefficient of a particular magnitude will change depending on the size of the sample from which it was computed. The test of significance is based on the assumption that the distribution of the residual values (i.e., the deviations from the regression line) for the dependent variable y follows the normal distribution, and that the variability of the residual values is the same for all values of the independent variable x. However, Monte Carlo studies suggest that meeting those assumptions closely is not absolutely crucial if your sample size is not very small and when the departure from normality is not very large. It is impossible to formulate precise recommendations based on those Monte- Carlo results, but many researchers follow a rule of thumb that if your sample size is 50 or more then serious biases are unlikely, and if your sample size is over 100 then you should not be concerned at all with the normality assumptions. There are, however, much more common and serious threats to the validity of information that a correlation coefficient can provide; they are briefly discussed in the following paragraphs.

Okay my friends, I think enough for this time and I will continue it next time. Hopefully it can help you easily understand about simple linear correlation (Korelasi Linear Sederhana)... This is just a little notes about quantitative and statistical methods for management and distance learning business and management

1 comment:

Blog Dasista said...

Makasih boedita....
Saya cba terjemahkan dan sya udah tau artinya...
maklum Saya lOm lncar bhsa inggris...