Explanation:

The coefficient of determination is a statistical measure that represents the proportion of the total variation in one variable that is explained by the variation in the other variable. It is also known as the R-squared value.

The coefficient of correlation, denoted by r, is a statistical measure that represents the strength and direction of the linear relationship between two variables. It ranges from -1 to 1. A value of -1 indicates a perfect negative correlation, a value of 0 indicates no correlation, and a value of 1 indicates a perfect positive correlation.

When the coefficient of correlation between two variables is -0.9, it indicates a strong negative correlation between the two variables. This means that as one variable increases, the other variable decreases and vice versa.

Formula:

The formula for the coefficient of determination, denoted by R^2, is as follows:

R^2 = r^2

where r is the coefficient of correlation.

Calculation:

Using the formula above, the coefficient of determination can be calculated as follows:

R^2 = (-0.9)^2 = 0.81

Therefore, the coefficient of determination is 0.81 or 81%.

Interpretation:

The coefficient of determination of 0.81 means that 81% of the total variation in one variable is explained by the variation in the other variable. The remaining 19% of the variation is due to other factors not included in the analysis. This indicates a strong relationship between the two variables.

In other words, the value of one variable can be predicted with 81% accuracy based on the value of the other variable. However, it is important to note that correlation does not imply causation, and further analysis may be required to establish causality between the two variables.