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A textbook of Computer Based Numerical and Statiscal Techniques part 43

A textbook of Computer Based Numerical and Statiscal Techniques part 43. By joining statistical analysis with computer-based numerical methods, this book bridges the gap between theory and practice with software-based examples, flow charts, and applications. Designed for engineering students as well as practicing engineers and scientists, the book has numerous examples with in-text solutions. | 406 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 7. Fit a parabola y a bx cx2 to the folliwng data x 2 4 6 8 10 y 3.07 12.85 31.47 57.38 91.29 Ans. y 0.34 - 0.78x 0.99x2 8. Determine the constants a and b by the method of least squares such that y aebx fits the following data x 2 4 6 8 10 y 4.077 11.084 30.128 81.897 222.62 Ans. y 1.49989e0 50001x 9. Fit a least square geometric curve y axb to the following data x 1 2 3 4 5 y 0.5 2 4.5 8 12.5 Ans. y 0.5012X1 9977 1 10. A person runs the same race track for five consecutive days and is timed as follows Day x 1 2 3 4 5 Time y 15.3 15.1 15 14.5 14 b c Make a least square fit to the above data using a function a ---- . 6.7512 4.4738 Ans. y 13.0065 x----1 X2 1 11. Use the method of least squares to fit the curve y - c- y x to the following table of values x 0.1 0.2 0.4 0.5 1 2 y 21 11 7 6 5 6 1.97327 Ans. y ------- 3.2818 X x 12. Using the method of least square to fit a parabola y a bx cx2 in the following data x y -1 2 0 0 0 1 1 2 Ans. y 1 3x2 CURVE FITTING 407 13. The pressure of the gas corresponding to various volumes V is measured given by the following data V cm3 50 60 70 90 100 p kgcm- 64.7 51.3 40.5 25.9 78 Fit the data to the equation pVY c. Ans. pV0.28997 167.78765 9.3 REGRESSION We know that in a functional relation between two variables if we know the value of one variable then the corresponding value of the other variable can be determined exactly. But in a statistical relationship between the two variables when the value of one variable is known we can simply estimate the corresponding value of another variable. Regression analysis is the method used for estimating the unknown values of one variable corresponding to the known values of another variable. 9.3.1 Dependent and Independent Variables Suppose there is a relation between two variables. The variable whose values are known is known as independent variable while another one is called the dependent variable. 9.3.2 Line of Regression Let x y 1