4. (a) Suppose that (x1, yı), (x2, y2), ..., (In, yn) are n numerical data points on the xy-plane. When we try to fit a

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4 A Suppose That X1 Yi X2 Y2 In Yn Are N Numerical Data Points On The Xy Plane When We Try To Fit A 1 (186.3 KiB) Viewed 29 times

4. (a) Suppose that (x1, yı), (x2, y2), ..., (In, yn) are n numerical data points on the xy-plane. When we try to fit a line L: y = mx + c to the above data points so that the sum of squares of the vertical distances from the points to L is minimized, i.e. (mxi +c- — yi) W = *มี i=1 is minimized. L is called the regression line and this linear approach to model the relationship between two variables is called the linear regression. Show that n yi - n Xiyi i=1 n i=1 m (E-) ( i=1 2 and 1 C= n syi – m ) n n i=1 i=1 - n i=1 i=1 (b) Using (a), find the regression line for the data points (0,0), (2, 3), (4,7), (6,11). Hence, predict the value of y that would correspond to x = 5.
5. Show that the system xy2 + xzu + yv2 = 3 X’yz + 2xv – u?y2 = 2 can be solved for (u, v) as a function of (x, y, z) near the point (X, Y, Z, U, V) = (1,1,1, 1, 1), and find the value of au for the solution at (x, y, z) = (1,1,1). ду