# Calculating of Pearson Product-Moment Correlation Coefficient and Simple Linear Regression example

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Calculating of Pearson Product-Moment Correlation Coefficient and Simple Linear Regression

Pearson product-moment correlation coefficient (PPMCC) is a measure of the linear dependence between two variables (X and Y). PPMCC can take values between -1 and +1 inclusive, where -1 is perfect negative linear correlation, 0 shows the absence of linear correlation, and 1 is total positive linear correlation (Pearson, 1895). This coefficient was developed by Karl Pearson and has been widely used in many sciences, including nursing research.

PPMCC is the most commonly used correlation index in nursing studies (Polit, 2010). The interpretation of the coefficient strongly depends on the nature of the input variables. For example, X is the patient’s body temperature measured orally and Y is his temperature measured rectally. In this case, PPMCC of .65 would be considered rather low. However, if the variables depict psychological state of the person (e.g., anxiety and level of stress), PPMCC of .65 is quite high. Correlations of -1 and +1 are very rare.

Simple linear regression is a linear regression model with a single explanatory variable. It means that one variable is always fixed (measured), and the value of the dependent variable is predicted by the function of the fixed variable. In other words, simple linear regression predicts the values of the dependent variable Y based on values of the independent variable X (Kenney, 1962).

The simple linear regression is widely used in nursing studies. For example, it can be used to predict the weight of a new-born baby (Y variable) based on the age of the mother and alcohol consumprion during pregnancy. There are, however, a few important assumptions that ensure the accuracy of such prediction. These essential assumptions include: variables are measured without errors, the selection from the population of interest is random, independent variables have to be mutually exclusive (not to be the subsets or combinations of other independent variables).

References

Kenney, J. F. (1962). Linear Regression and Correlation. Ch. 15 in Mathematics of Statistics. Princeton, New Jersey: Van Nostrand, pp. 252–285.

Pearson, K. (1895). Notes on regression and inheritance in the case of two parents. Proceedings of the Royal Society of London, 58, 240-242.

Polit, D. (2010). Essentials of Nursing Research: Appraising Evidence for Nursing Practice. Philadelphia, Pennsylvania: Lippincott-Raven …

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