To calculate the correlation coefficient, we need to first find the slope of each regression line.



2y = -9x + 5

y = (-9/2)x + (5/2)

Slope = -9/2



2x = -4y + 6

y = (-1/2)x + (3/2)

Slope = -1/2



r = (Slope of regression line of x on y) * (Slope of regression line of y on x)

r = (-9/2) * (-1/2)

r = 9/4

Therefore, the correlation coefficient is 9/4.



The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

In this case, the correlation coefficient is positive, which indicates a positive linear relationship between x and y. As the correlation coefficient is greater than zero but less than 1, the relationship is not very strong but still significant.

The slope of each regression line tells us how much one variable changes for a unit change in the other variable. For example, the slope of the regression line of x on y tells us that for every unit increase in y, x decreases by 4.5 units.

Overall, the correlation coefficient and the regression lines provide useful information about the relationship between two variables, allowing us to make predictions and gain insights into the data.