Answer to Question #166068 in Economics for Lulu

Question

Explain what côv (X, Y) and r measure. What is the dissimilarity between the two?

Answer 1

The cov (x,y) function calculates the covariance matrix.

The covariance of two samples (two random variables) is a measure of their linear dependence, which is defined as follows:

$$cov(x,y)=M(X-MX))Y-MY)$$

In statistics, the coefficient of determination, denoted by R or r and pronounced "R squared", is the fraction of the variance in the dependent variable that can be predicted from the explanatory variables.

It is a statistic used in the context of statistical models whose main purpose is either to predict future outcomes or to test hypotheses based on other related information. It provides a measure of how well the observed results are reproduced by the model based on the proportion of the overall variation in the results explained by the model.

There are several definitions of R that are only occasionally equivalent. One class of such cases includes the simple linear regression case where r is used instead of R. When a bar is included, then r is just the square of the sample's correlation. the coefficient (i.e., r) between the observed results and the observed values ​​of the predictor. If additional regressors are included, R is the square of the multiple correlation coefficient. In both such cases, the coefficient of determination is usually in the range from 0 to 1. Wikipedia site: wikichi.ru