Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009Welcome toMath 122 Lecture 8 Survey of Calculus and its Applications I1 !Partial Derivatives !Finding Relative Maxima and Minima !Lagrange Multipliers and Constrained Optimization
§ 7.5 !Least Squares Error !Least Squares Line (Regression Line) !Determining a Least Squares LineDefinition Example Least Squares Error: The total error in approximating the data points (x1, y1),...., (xN, yN) by a line y= Ax+ B, measured by the sum Eof the squares of the vertical distances from the points to the line, Example is forthcoming.
Definition Example Least Squares Line(Regression Line): straight line y= Ax+ for which the error Eis as small as possible. Example is forthcoming. Table 5 shows the 1994 price of a gallon (in U.S. dollars) of fuel and the average miles driven per automobile for several countries. (a) Find the straight line that provides the best least-squares fit to these data. A B
