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With any number of random variables in excess of 1, the variables can be stacked into a random vector whose i th element is the i th random variable. Then the variances and covariances can be placed in a covariance matrix, in which the (i, j) element is the covariance between the i th random variable and the j th one.
The sign of the covariance, therefore, shows the tendency in the linear relationship between the variables. If greater values of one variable mainly correspond with greater values of the other variable, and the same holds for lesser values (that is, the variables tend to show similar behavior), the covariance is positive. [ 2 ]
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
Financial correlations measure the relationship between the changes of two or more financial variables over time. For example, the prices of equity stocks and fixed interest bonds often move in opposite directions: when investors sell stocks, they often use the proceeds to buy bonds and vice versa.
One of the many variables lenders use when deciding whether or not to loan you money is your debt-to-income ratio or DTI. Your DTI reveals how much debt you owe compared to the income you earn ...
For this example, divide your monthly debt payments ($2,400) by your total monthly gross income ($6,000). In this case, your total DTI would be 0.40, or 40 percent. To confirm your number, use a ...
The total-debt-to-total-assets ratio is one of many financial metrics used to measure a company’s performance. In this case, the ratio shows how much of a company’s operations are funded by debt.
The nomenclature in this article's title parallels the phrase law of total variance. Some writers on probability call this the "conditional covariance formula" [2] or use other names. Note: The conditional expected values E( X | Z) and E( Y | Z) are random variables whose values depend on the value of Z.