The relationship between the number of square feet and the selling price (in dollars) of a sample of homes for sale in Cincinnati, Ohio, is observed to be linear, with a correlation of r = 0.58. A regression equation is subsequently constructed in order to predict selling price based on number of square feet. What percentage of the variability in selling price can be explained by this regression equation?

The percentage of variability in selling price explained by the regression equation is 33.64%.

To determine the percentage of variability in selling price explained by the regression equation, we need to square the correlation coefficient (r) to get the coefficient of determination (r^2). In this case, r = 0.58, so r^2 = 0.58^2 = 0.3364. To convert this to a percentage, we multiply by 100, giving us 33.64%.

Therefore, the regression equation can explain approximately 33.64% of the variability in selling price. This means that about 33.64% of the variation in selling price can be attributed to the variation in the number of square feet in the homes for sale in Cincinnati, Ohio. It's important to note that the remaining percentage (around 66.36%) is attributed to other factors not accounted for in the regression equation.

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