Business Statistics - Term Paper Example

Business Statistics – Correlation and Regression I. Introduction a. Correlation and regression have applications in various fields and business management is no exception.b. Regression, which identifies the numeric connection between the variables, is discussed in detail along with the method to formulate a straight line regression equation using the Least Squares methodc. Hence the method to compute the coefficient of determination which gives a numeric value of the goodness of fit is included in the reportII.

Correlation refers to the degree of association between two variables. When two variables are said to be correlated, it indicates that there is a relationship or a pattern in the movement of the two variables.a. The Pearson’s correlation coefficient (R) is computed using the formula: R = Covariance of X and Y / (Std. Dev. of X times Std. Dev. of Y)b. Values of Rc. The association of the two variables depends on the sign and magnitude of the R value calculated. III. Correlation does not indicate causation.

Only the degree of association can be established with the help of correlation measures and the direction of relationship or causation cannot be determined.a. Limitation of correlation is that it can only be applied to proper numeric data.b. It is imperative to note that there might be extra variables which cause movement in the observed variables and these are not taken into account when analyzing the correlation between the two variablesIV. Correlation establishes the association between two variables, whereas regression is to establish a numerical connection between the two variables.

In other words, correlation answers the questions if two variables X and Y are related whereas regression gives the numerical connection between them.a) Straight Line Regression: The regression line is of the form: Y = a + b X, where Y is the dependent variable X is the independent variable a represents the y- intercept, i.e., the value of Y when X is equal to zero b represents the slope of the regression line indicating the sensitivity of Y to changes in Xb) Least Squares Method: The regression line can be estimated based on the Least Squares Method.

The method is based on the concept that the best regression line is the line which is at a minimum distance possible from all the data pointsc) The regression line gives the relationship between the two variables in the form of an equation.d) The least squares method gives us the equation of the line of best fit. It is however essential to estimate the reliability or ‘goodness of fit’ of this regression equatione) The coefficient of determination is the square of the value of R (R2). The coefficient of determination is expressed as a percentage.

In case R is +1 or -1, the R2 value is 1 indicating a perfect fit or a 100 % fit. V. Conclusions