Final answer:
Approximately 30.01% of the variation in y can be explained by the variation in x using the provided regression equation, with a correlation coefficient of r = -0.548.
Step-by-step explanation:
To determine what proportion of the variation in y can be explained by the variation in the values of x using the regression equation y = -55.29x + 10.05 and the correlation coefficient r = -0.548, you need to calculate the coefficient of determination, which is denoted as r². The coefficient of determination is the square of the correlation coefficient and represents the proportion of the variance in the dependent variable that is predictable from the independent variable.
To compute this, you square the correlation coefficient:
r² = (-0.548)² = 0.3001
Expressed as a percentage, this coefficient of determination is:
r² = 30.01%
Therefore, approximately 30.01% of the variation in y can be explained by the variation in the values of x using the provided regression equation. This means that 30.01% of the variation in the dependent variable (y) can be accounted for by the relationship with the independent variable (x), as captured by the linear regression model.
Looking at the remaining proportion, which is 1 - r², we can deduce that approximately 69.99% of the variation in y is due to factors other than x, or is simply unexplained by this model.