Showing posts with label Correlation Regression. Show all posts
Showing posts with label Correlation Regression. Show all posts

Saturday, September 4, 2010

ACCA Paper F2 free course note | Correlation & Regression | Correlation

Correlation analysis is the study of the relationship between two or more than two variables. It is the statistical tool we can use to describe the relationships between two or more than two variables. It is also defined as group of techniques to measure the association between two or more than two variables.
To explain, suppose the sales manager of Square Pharmaceuticals Ltd. wants to determine whether there is a relationship between the medicine sold in a month and advertisement.

Correlation analyses are based on the relationship between two (or more) variables. The known variable (or variables) is called the independent variable(s). The variable we are trying to predict is the dependent variable. Let’s take an example. Bankers might base their predictions of customer satisfaction on the interest rate. Thus, the interest rate is the independent variable and the customer satisfaction is the dependent variable. Bankers, for example, may add a second independent variable, environment, to improve their estimate of the customer satisfaction.

Coefficient of Correlation

The measure of correlation called the coefficient of correlation (denoted by the symbol r) summarizes in the figure the direction and degree of correlation.
Coefficient of Correlation is a measure of the strength of the linear relationship between two variables. It requires interval or ratio-scaled data.

Features of Correlation Coefficient

l  It can range from -1 to 1
l  Values of -1 or 1 indicate perfect and strong correlation.
l  The closer to -1, the stronger the negative linear relationship
l  The closer to 1, the stronger the positive linear relationship
l  Values close to 0 indicate weak correlation.
l  Negative values indicate an inverse relationship and positive values indicate a direct relationship.

ACCA Paper F2 free course note | Correlation & Regression | Regression Equation

Regression equation is an equation that expresses the linear relationship between two variables. It is an algebraic expression of the regression line. Since there are two regression lines, there are two regression equations—the regression equation of X on Y is used to describe the variations in the values of X for given changes in Y and the regression equation of Y on X is used to describe the variations in the values of Y for given changes in X.

Regression equation of Y on X

The regression equation of Y on X is expressed as follows:
                Y= a + bX
Where Y is the dependent variable to be estimated and X is the independent variable. The parameter ‘a’ determines the level of the fitted line. The parameter ‘b’ determines the slope of the line, i.e., the change in Y for unit change in X.
                b =
               
                a = - b


Regression equation of X on Y

The regression equation of X on Y is expressed as follows:
                X= a+ bY
 The parameter ‘a’ determines the level of the fitted line. The parameter ‘b’ determines the slope of the line, i.e., the change in X for unit change in Y.
                b =
               
                a = - b


Illustration: Calculate the regression equation of Profit on Capital and Capital on Profit from the following data.

Capital (X)
Profit (Y)
5
2
10
3
15
5
20
8
25
12

ACCA Paper F2 free course note | Correlation & Regression | What is Regression

The dictionary meaning of the term “regression” is the act of returning or going back. The term “regression” was first used in 1877 by Francis Galton while studying the relationship between the height of fathers and sons.
Regression analysis is the technique used to develop the equation and provide the estimate. In regression, we develop an equation to express the linear relationship between two variables. In addition, we are able to estimate the value of the dependent variable Y based on a selected value of the independent variable X.
The statistical tool with the help of which we are in a position to estimate (or predict) the unknown values of one variable from known values of another variable is called regression.
With the help of regression analysis we are in a position to find out the average probable change in one variable given a certain amount of change in another variable.
For example, if we know that advertisement and sales are correlated, we may find out the expected amount of sales for a given advertisement expenditure or the required amount of expenditure for achieving a fixed sales target.

Differences between correlation and regression analysis

There are two important points of difference between correlation and regression analysis. These are
v  Correlation coefficient measures the degree of association between two or more than two variables, whereas regression analysis measures the nature of relationship between the variables.
v  In case of correlation analysis, it never measure cause and effect relationship whereas regression analysis specially measures this.


Regression Line

Regression line is the graphical presentation of equation. It is a line drawn through a scatter plot of two variables If we take the case of two variables X and Y, we shall have two regression lines as the regression line of X on Y and the regression line of Y on X.