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Regression and Correlation Coefficient

One of the most usual applications of Statistics is describing a set of data using regression and correlation coefficient. Given a set of data, for instance, the data in study 1 to check the correlation coefficient between Brain Weight and Body Weight in study 2 between Water Temperature and Length of Fish in study 3 between Age Systolic and Blood Pressure. By analyzing and examining the raw data, we can make and draw logical conclusions or even compare, contrast or rank on this data based on the specified attribute.

The use of various descriptive statistical measures is one of the most effective ways to examine properly these business attributes. To name some, one needs to employ the application of measures of central tendencies, linear regression, measures of variability, and positions, estimation and even correlation.

This paper will focus on linear regression and correlation between two variables. (Walpole, 1982).

Excel Tab Study 1: Correlation between Brain Weight and Body Weight.

From the regression out put the correlation determination between Brain Weight and Body Weight is R Square is equal to 0.873, this shows that the goodness fit of the model is 87.3%. The correlation is the square root of the R-squared value so the correlation coefficient between Brain Weight and Body Weight is 0.934. From the correlation coefficient (0.934) and the slope between Brain Weight and Body Weight is positive (0.9665), we can conclude that there is strong positive relationship exist between Brain Weight and Body Weight.

Excel Tab Study 2: Correlation between Water Temperature and Length of Fish.

From the regression output:

From the correlation coefficient (0.181) and the slope between Water Temperature and Length of Fish is negative (-106.414), we can conclude that there is very low negative relationship exist or even we can say there is no relationship exist between Water Temperature and Length of Fish.

Excel Tab Study 3: Correlation between Age and Systolic Blood Pressure

From the regression output:

From the correlation coefficient (0.656) and the slope between Age and Systolic Blood Pressure is positive (0.9709), we can conclude that there is low positive relationship exist between Age and Systolic Blood Pressure

References

Walpole, R. (1982). Introduction to Statistics. (3rd ed.). Prentice Hall Publication.