Definition: The Coefficient of determination is the square of the coefficient of correlation r2 which is calculated to interpret the value of the correlation. It is useful because it explains the level of variance in the dependent variable caused or explained by its relationship with the independent variable. The coefficient of determination explains the proportion of the … [Read more...] about Coefficient of Determination
Probable Error of Correlation Coefficient
Definition: The Probable Error of Correlation Coefficient helps in determining the accuracy and reliability of the value of the coefficient that in so far depends on the random sampling. In other words, the probable error (P.E.) is the value which is added or subtracted from the coefficient of correlation (r) to get the upper limit and the lower limit respectively, within … [Read more...] about Probable Error of Correlation Coefficient
Standard Error of Estimate
Definition: The Standard Error of Estimate is the measure of variation of an observation made around the computed regression line. Simply, it is used to check the accuracy of predictions made with the regression line. Likewise, a standard deviation which measures the variation in the set of data from its mean, the standard error of estimate also measures the variation in the … [Read more...] about Standard Error of Estimate
Properties of Regression Coefficient
Definition: The constant ‘b’ in the regression equation (Ye = a + bX) is called as the Regression Coefficient. It determines the slope of the line, i.e. the change in the value of Y corresponding to the unit change in X and therefore, it is also called as a “Slope Coefficient.” Properties of Regression Coefficient The correlation coefficient is the geometric mean … [Read more...] about Properties of Regression Coefficient
Regression Equation
Definition: The Regression Equation is the algebraic expression of the regression lines. It is used to predict the values of the dependent variable from the given values of independent variables. If we take two regression lines, say Y on X and X on Y, then there will be two regression equations: Regression Equation of Y on X: This is used to describe the variations in … [Read more...] about Regression Equation
Regression Coefficient
Definition: The Regression Coefficient is the constant ‘b’ in the regression equation that tells about the change in the value of dependent variable corresponding to the unit change in the independent variable. If there are two regression equations, then there will be two regression coefficients: Regression Coefficient of X on Y: The regression coefficient of X on Y is … [Read more...] about Regression Coefficient
Regression Line
Definition: The Regression Line is the line that best fits the data, such that the overall distance from the line to the points (variable values) plotted on a graph is the smallest. In other words, a line used to minimize the squared deviations of predictions is called as the regression line. There are as many numbers of regression lines as variables. Suppose we take two … [Read more...] about Regression Line
Regression Analysis
Definition: The Regression Analysis is a statistical tool used to determine the probable change in one variable for the given amount of change in another. This means, the value of the unknown variable can be estimated from the known value of another variable. The degree to which the variables are correlated to each other depends on the Regression Line. The regression line is … [Read more...] about Regression Analysis
Method of Least Squares
Definition: The Method of Least Squares is another mathematical method that tells the degree of correlation between the variables by using the square root of the product of two regression coefficient that of x on y and y on x. The numerical notation of the formula to calculate the correlation by the coefficient method of least squares is given below: Lag and Lead in … [Read more...] about Method of Least Squares
Spearman’s Rank Correlation Coefficient
Definition: The Spearman’s Rank Correlation Coefficient is the non-parametric statistical measure used to study the strength of association between the two ranked variables. This method is applied to the ordinal set of numbers, which can be arranged in order, i.e. one after the other so that ranks can be given to each. In the rank correlation coefficient method, the ranks … [Read more...] about Spearman’s Rank Correlation Coefficient