Multiple Linear Regression Analysis

Regression analysis involving only one independent variable is called simple linear regression analysis. The major limitation of this analysis is that it is applicable only to the cases with one independent variable. Regression analysis involving more than one independent variable is called multiple regression analysis. When all the independent variable are assumed to affect the dependent variable in a linear fashion and independently of one another, the procedure is called multiple regression analysis. A multiple linear regression analysis is said to operate if the relationship of dependent variable say (Y) to k independent variable say X1,X2,X3, . . . . Xk can be expressed as

            Y = b0 + b1X1 + b2X2 + . . . . + bkXk + e

Where b0, b1, b2…. bk are regression coefficients.The above equation can be represented

    The following statistic can be computed using OPSTAT. These are

Correlation Analysis:

    Correlation is a measure of association between two variables. The variables are not designated as dependent or independent. The two most popular correlation coefficients are: Spearman's correlation coefficient rho and Pearson's product-moment correlation coefficient.

When calculating a correlation coefficient for ordinal data, select Spearman's technique. For interval or ratio-type data, use Pearson's technique. The value of a correlation coefficient can vary from minus one to plus one. A minus one indicates a perfect negative correlation, while a plus one indicates a perfect positive correlation. A correlation of zero means there is no relationship between the two variables. When there is a negative correlation between two variables, as the value of one variable increases, the value of the other variable decreases, and vise versa. In other words, for a negative correlation, the variables work opposite each other. When there is a positive correlation between two variables, as the value of one variable increases, the value of the other variable also increases. The variables move together.

The standard error of a correlation coefficient is used to determine the confidence intervals around a true correlation of zero. If your correlation coefficient falls outside of this range, then it is significantly different than zero. The standard error can be calculated for interval or ratio-type data (i.e., only for Pearson's product-moment correlation).

The significance (probability) of the correlation coefficient is determined from the t-statistic. The probability of the t-statistic indicates whether the observed correlation coefficient occurred by chance if the true correlation is zero. In other words, it asks if the correlation is significantly different than zero. When the t-statistic is calculated for Spearman's rank-difference correlation coefficient, there must be at least 30 cases before the t-distribution can be used to determine the probability. If there are fewer than 30 cases, you must refer to a special table to find the probability of the correlation coefficient. The package OPSTAT computes the correlation matrix and their significance.

Data Arrangement

    The variables are laid down horizontally and their observations are vertically downward in a columnar fashion i.e. the first line contains the first observations of all the variables separated by space or tab. The second line will contain the second observation of all the variables and so on.

Procedure of Analysis