# Statistical Procedures of Simple Linear Correlation and Regression

## This article discusses the statistical procedures and processes of correlation and regression analysis and statistical inferences.

In real life at least most of the time one factor or number of factors influences the other. That may happen due to mere luck or due to actual or real existing relationship between the factors. For example, a person’s ability to concentrate on a task may depend on many factors such as his interest, his level of psychological state of mind, his physical health, fatigue, physical conditions, skill and knowledge factors, social factors etc. In statistical terms some variables are related to other variables in a mathematical way but not exactly but at varying degrees. That is, to mathematically measure the degree of variability between given variables. Normally the simple linear correlation studies the relationship between two variables. As well, as mentioned above they also have a statistical method to verify whether the relationship exist due to chance or due to real relationship given a probability level of confidence level. In the following paragraphs I will discuss the method of measuring and the meaning of these measures and the method of analysis and processes.

### Correlations

Say if an x variable influences another variable y then the variable which can be varied irrespective of y is called an independent variable. The variable y, which is influenced by x, is called a dependent variable. For example, say one measure the percentage of high school students taking a difficult exam in several states and the states publish such results then the exam results do not influence the percentage of high school students taking the exam. There fore, the exam scores are not dependent variable as it is influenced by the percentage students taking the exams. In this situation, percentage students taking the exam are independent variable and the sores are dependent variable.

To study statistically, to determine the degree of relationship one has to first graphically plot these on a Cartesian graph known as a scatter plot in its initial stage to verify visually there is any relationship particularly  a linear relationship. By visual examination one can see there is a linear relationship between the percentage students taking the exam and the average sores. It is also clear that the linear relationship is not positive but negative. That is, when the x variable increases the y variable reduces. This is a negative relationship because the ratio of the change in y variable divided by the change in x variable is negative given the direction of change. However, the diagram does not give any information regarding the degree of relationship between the variables.

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