Why is correlation useful in determining the strength of the link between two variables
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In correlation analysis, we estimate a sample correlation coefficient, more specifically the Pearson Product Moment correlation coefficient. The sample correlation coefficient, denoted r, Show ranges between -1 and +1 and quantifies the direction and strength of the linear association between the two variables. The correlation between two variables can be positive (i.e., higher levels of one variable are associated with higher levels of the other) or negative (i.e., higher levels of one variable are associated with lower levels of the other). The sign of the correlation coefficient indicates the direction of the association. The magnitude of the correlation coefficient indicates the strength of the association. For example, a correlation of r = 0.9 suggests a strong, positive association between two variables, whereas a correlation of r = -0.2 suggest a weak, negative association. A correlation close to zero suggests no linear association between two continuous variables. It is important to note that there may be a non-linear association between two continuous variables, but computation of a correlation coefficient does not detect this. Therefore, it is always important to evaluate the data carefully before computing a correlation coefficient. Graphical displays are particularly useful to explore associations between variables. The figure below shows four hypothetical scenarios in which one continuous variable is plotted along the X-axis and the other along the Y-axis. 
Example - Correlation of Gestational Age and Birth WeightA small study is conducted involving 17 infants to investigate the association between gestational age at birth, measured in weeks, and birth weight, measured in grams.
We wish to estimate the association between gestational age and infant birth weight. In this example, birth weight is the dependent variable and gestational age is the independent variable. Thus y=birth weight and x=gestational age. The data are displayed in a scatter diagram in the figure below. Each point represents an (x,y) pair (in this case the gestational age, measured in weeks, and the birth weight, measured in grams). Note that the independent variable, gestational age) is on the horizontal axis (or X-axis), and the dependent variable (birth weight) is on the vertical axis (or Y-axis). The scatter plot shows a positive or direct association between gestational age and birth weight. Infants with shorter gestational ages are more likely to be born with lower weights and infants with longer gestational ages are more likely to be born with higher weights. return to top | previous page | next page What determines the strength of correlation between two variables?A correlation coefficient measures the strength of that relationship. Calculating a Pearson correlation coefficient requires the assumption that the relationship between the two variables is linear. The relationship between two variables is generally considered strong when their r value is larger than 0.7.
Why is establishing a correlation between two variables useful?Once correlation is known it can be used to make predictions. When we know a score on one measure we can make a more accurate prediction of another measure that is highly related to it. The stronger the relationship between/among variables the more accurate the prediction.
What is correlation and why is it useful?In statistical terms, correlation is a method of assessing a possible two-way linear association between two continuous variables. Correlation is measured by a statistic called the correlation coefficient, which represents the strength of the putative linear association between the variables in question.
What is the relationship between the strength of the correlation?The correlation coefficient (expressed as r ) shows the direction and strength of a relationship between two variables. The closer the r value is to +1 or -1, the stronger the linear relationship between the two variables is.
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