Question

Describe: (1) every component of the equation for calculating a correlation coefficient; (2) the purpose of each component; (3) what kind of data you would use this equation on; and (4) how to use the equation on raw data.

Answer 1

Solution: The formula or equation for correlation coefficient is given by r =[ Cov X,Y)/ {sqrt(Var X) * sqrt(Var Y)}]

Answer of (1) and (2) r denotes the correlation coefficient between two variables X and Y

Cov(X,Y) denotes the covariance between X and Y; which measures the joint variability between two variables.

Var(X) denotes Variance or variability of X values

and Var (Y) denotes variance or variability of Y values

(3) this equation is used for bivariate data i.e. data on two variables preferably measured in interval or ratio scale.

(4) Starting with the raw data; first calculate the sum total and mean for both variables x and y; the calculate the variance of both the variables which is obtained on diving by total no. of observations the squared value obtained on subtracting the mean from each value. then calculate the covariance which is given by the formula 1/n *sum(xi*yi) - xbar*ybar

where x bar and y bar denoted the means.

then we have to put the values of covariance and variance in the equation of r given above. hence we will get the result.