USE JAVA CODE:
Write a procedure that ts a straight line to Table (1). Use this procedure to nd the constants in the equation S = aT + b for the table in the example that begins this chapter (p. 426). Also, verify the results obtained for Example 1 (p. 429).
y=ax + b Table (1) Surface tension S in a liquid is known to be a linear function of tempera- ture T. Fora particular liquid, measurements have been made of the surface tension at certain temperatures. The results were as follows: pg. 426 TL0 110 120 30 140 80 190 19 S 68.0 67.166.4 65.6 64.6 618 61.0 60.0 How can the most probable values of the constants in the equation S=aT + b be deternined? Methods for solving such problerns are developed in this chapter. p429 EXAMPLE 1 Asaconcrete example, find the linear least-squares solution for the following table of values: x |47|13 | 17 y 20 267 Plot the original data points and the line using a finer set of grid points. Solution The equations in Algorithm 1 lead to this system of two equations: 644a + 52b = 227 52a + 5b= 17 whose solution is a = 0.4864 and b =-1.6589. By Equation (3), we obtain the value (a, b) = 10.7810. Figure 9.2 is a plot of the given data and the linear least-squares straight line. 10 y -ax +b FIGURE 9.2 least squares 0 2 46 8 10 12 14 16 18 20 y=ax + b Table (1) Surface tension S in a liquid is known to be a linear function of tempera- ture T. Fora particular liquid, measurements have been made of the surface tension at certain temperatures. The results were as follows: pg. 426 TL0 110 120 30 140 80 190 19 S 68.0 67.166.4 65.6 64.6 618 61.0 60.0 How can the most probable values of the constants in the equation S=aT + b be deternined? Methods for solving such problerns are developed in this chapter. p429 EXAMPLE 1 Asaconcrete example, find the linear least-squares solution for the following table of values: x |47|13 | 17 y 20 267 Plot the original data points and the line using a finer set of grid points. Solution The equations in Algorithm 1 lead to this system of two equations: 644a + 52b = 227 52a + 5b= 17 whose solution is a = 0.4864 and b =-1.6589. By Equation (3), we obtain the value (a, b) = 10.7810. Figure 9.2 is a plot of the given data and the linear least-squares straight line. 10 y -ax +b FIGURE 9.2 least squares 0 2 46 8 10 12 14 16 18 20
