Rafael is analyzing data about the price of a certain stock in his finance class. He finds the linear regression line for the data to be f(x) = 0.76x + 42.39, where x is the number of days since Rafael started observing the stock's price and f(x) is the price in dollars of the stock after x days of observation. If the point (15, 52.04) is in the original data set, what is the residual for when x = 15?

For this case, the first thing to do is to use the equation of the given line.
 We have then:
 f (x) = 0.76x + 42.39
 We substitute the value of x = 15:
 f (15) = 0.76 * (15) + 42.39
 f (15) = 53.79
 Then, subtracting with the original value we have:
 53.79-52.04 = 1.75
 Answer:
 the residual for when x = 15 is:
 1.75