Figure 1: The results of multiple linear regression depend on the correlation of the predictors, as measured here by the Pearson correlation coefficient r (ref. 2).

The correlation calculation simply takes the covariance and divides it by the product of the standard deviation of the two variables. This will bind the correlation between a value of -1 and +1.

If one variable goes up in tandem with the other, then that is a positive correlation. If there doesn't seem to be any clear trend in the variables, then we say that there is no correlation.

The envelope model allows efficient estimation in multivariate linear regression. In this paper, we propose the sparse envelope model, which is motivated by applications where some response variables ...

The Pearson coefficient is a mathematical correlation coefficient representing the relationship between two variables, denoted as X and Y. Pearson coefficients range from +1 to -1, with +1 ...

James K. Binkley, The Effect of Variable Correlation on the Efficiency of Seemingly Unrelated Regression in a Two-Equation Model, Journal of the American Statistical Association, Vol. 77, No. 380 (Dec ...

I ran 20,000 sets of random sequences of the numbers 1 through 10 and sorted them by correlation to the sequence 1,2,3,4,5,6,7,8,9,10. 2,483 sequences out of the 20,000 had a correlation between 0 ...