The coefficient of correlation, denoted by r, represents the strength and direction of a linear relationship between two variables. The value of r ranges from -1 to +1. The closer the absolute value of r is to 1, the stronger the linear relationship between the variables.
The coefficient of determination, denoted by r^2, represents the proportion of the variation in one variable that can be explained by the other variable in a linear regression model.
The proportion of the variation in hours of sleep that cannot be explained by the time spent on social media is equal to 1 - r^2.
Given the coefficient of correlation, r = -0.73, we can find the coefficient of determination:
r^2 = (-0.73)^2 = 0.5329
So, the proportion of the variation in hours of sleep that can be explained by the time spent on social media is 0.5329.
Therefore, the proportion of the variation in hours of sleep that cannot be explained by the time spent on social media is:
1 - 0.5329 = 0.4671
Multiplying this by 100, we get:
0.4671 x 100 = 46.71%
So, approximately 46.71% of the variation in hours of sleep cannot be explained by the time spent on social media.