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Lecture8bc

# Lecture8bc - Welcome to Math 122 Lecture 8 Survey of...

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Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009 Welcome to Math 122 Lecture 8 Survey of Calculus and its Applications I1 ! Partial Derivatives ! Finding Relative Maxima and Minima ! Lagrange Multipliers and Constrained Optimization

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§ 7.5 ! Least Squares Error ! Least Squares Line (Regression Line) ! Determining a Least Squares Line Definition Example Least Squares Error : The total error in approximating the data points ( x 1 , y 1 ), .... , ( x N , y N ) by a line y = Ax + B , measured by the sum E of the squares of the vertical distances from the points to the line, Example is forthcoming.
Definition Example Least Squares Line ( Regression Line ): A straight line y = Ax + B for which the error E is 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.

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