Correlation is the degree and type of relationship between 2 or more quantities or variables in which they vary together over a period of time. Correlation is represented by 'r'.
Importance or uses:
1.The degree of variation between the variables is to be known for an effective evaluation.
2.It is very much used in forecasts.
3.Correlation analysis is used to understand the economic behaviour.
Types :
Positive and negative correlation.
Linear and non-linear correlation.
Simple and partial correlation.
Positive correlation is when the value of 2 variables change in the same direction.
Negative correlation is when the value of 2 variables change in the opposite direction.
Linear correlation is when there is a constant change in one variable due to a unit change in other variable over the entire range of values.
Non-linear correlation is when there is no constant change due to unit change in other variable over the entire range of values.
Simple correlation is when only 2 variables vary.
Partial correlation or multiple correlation is when more than 2 variables vary.
Main methods of correlation analysis:
1. Scatter diagram
2. Karl Pearson's coefficient of correlation
3. Spearman's rank correlation coefficient
Scatter diagram is the simplest method to calculate the correlation. Under this method, the values for each pair of a variable is plotted on a graph in the form of dots.
Looking at the scatter of several points, the degree of correlation is ascertained, the following are the different degrees correlation:
1.Perfect positive correlation; it is when the value of r = +1.
2.Perfect negative correlation; it is when the value of r = -1.
3.High degree positive correlation; it is when the value of r is positively high.
4.High degree of negative correlation; it is when the value of r is negatively high.
5.No correlation; when the value of r is equal to 0. This happens when the points are haphazardly scattered over the graph and do not show a specific pattern.
Karl Pearson, a British statistician, has given two main formulae to calculate the correlation.
One as a direct method and another which is known as the assumed mean method.
where;
dx = deviation from assumed mean = x - A
The third method of computing correlation(Spearman's rank correlation) is developed by a British psychologist named Charles Edward Spearman. Here, correlation is calculated under 2 situations:
1.When the ranks are given
2.When equal ranks are given
Regression analysis is a statistical technique used to examine the relationship between one dependent and one independent variable. It can be used to predict the dependent variable when the independent variable is known.
When we talk about the uses of regression analysis;
1.It mainly focuses on business activities and forecasts.
2.To find any unknown variable.
3.The analysis is used to have a check on the quality control.
Before we go into detail, we must know the differences between correlation and regression.
Correlation is used to determine the degree of relationship; whereas regression is used to study the cause and effect of relationship.
When it comes to the correlation analysis, there is no need of independent and dependent variables; whereas in the case of regression analysis, identification of independent and dependent variables is a must.
There are 2 sets of regression equations:
1.x on y; this equation is used to find out the values of x for the given values of y.
x = a + by
Σx = na + bΣy
Σxy = aΣy + bΣy2
2.y on x; this equation is used to find out the values of y for the given values of x.
y = a + bx
Σy = na + bΣx
Σxy = aΣx + bΣx2
Regression coefficients
2 cases;
1.x on y
(x - x̄) = bxy(y - ȳ)
2.y on x
(y - ȳ) = byx(x - x̄)
Regression coefficient using correlation
2 cases again;
1.x on y
2.y on x
Importance or uses:
1.The degree of variation between the variables is to be known for an effective evaluation.
2.It is very much used in forecasts.
3.Correlation analysis is used to understand the economic behaviour.
Types :
Positive and negative correlation.
Linear and non-linear correlation.
Simple and partial correlation.
Positive correlation is when the value of 2 variables change in the same direction.
Negative correlation is when the value of 2 variables change in the opposite direction.
Linear correlation is when there is a constant change in one variable due to a unit change in other variable over the entire range of values.
Non-linear correlation is when there is no constant change due to unit change in other variable over the entire range of values.
Simple correlation is when only 2 variables vary.
Partial correlation or multiple correlation is when more than 2 variables vary.
Main methods of correlation analysis:
1. Scatter diagram
2. Karl Pearson's coefficient of correlation
3. Spearman's rank correlation coefficient
Scatter diagram is the simplest method to calculate the correlation. Under this method, the values for each pair of a variable is plotted on a graph in the form of dots.
Looking at the scatter of several points, the degree of correlation is ascertained, the following are the different degrees correlation:
1.Perfect positive correlation; it is when the value of r = +1.
2.Perfect negative correlation; it is when the value of r = -1.
3.High degree positive correlation; it is when the value of r is positively high.
4.High degree of negative correlation; it is when the value of r is negatively high.
5.No correlation; when the value of r is equal to 0. This happens when the points are haphazardly scattered over the graph and do not show a specific pattern.
Karl Pearson, a British statistician, has given two main formulae to calculate the correlation.
One as a direct method and another which is known as the assumed mean method.
where;
dx = deviation from assumed mean = x - A
The third method of computing correlation(Spearman's rank correlation) is developed by a British psychologist named Charles Edward Spearman. Here, correlation is calculated under 2 situations:
1.When the ranks are given
2.When equal ranks are given
Regression analysis is a statistical technique used to examine the relationship between one dependent and one independent variable. It can be used to predict the dependent variable when the independent variable is known.
When we talk about the uses of regression analysis;
1.It mainly focuses on business activities and forecasts.
2.To find any unknown variable.
3.The analysis is used to have a check on the quality control.
Before we go into detail, we must know the differences between correlation and regression.
Correlation is used to determine the degree of relationship; whereas regression is used to study the cause and effect of relationship.
When it comes to the correlation analysis, there is no need of independent and dependent variables; whereas in the case of regression analysis, identification of independent and dependent variables is a must.
There are 2 sets of regression equations:
1.x on y; this equation is used to find out the values of x for the given values of y.
x = a + by
Σx = na + bΣy
Σxy = aΣy + bΣy2
2.y on x; this equation is used to find out the values of y for the given values of x.
y = a + bx
Σy = na + bΣx
Σxy = aΣx + bΣx2
 |
| Where dx = x - A; dy = y - A |
2 cases;
1.x on y
(x - x̄) = bxy(y - ȳ)
2.y on x
(y - ȳ) = byx(x - x̄)
Regression coefficient using correlation
2 cases again;
1.x on y
2.y on x
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