Practise Problem Set
ECSE 443- introduction to Numerical Methods in EE
Practice Problem Set – Chapter 4
(Note: This problem set is for extra practice. It is not for credit, and not to be handed in) Question 1: Suppose that in a study, several measurements were made to determine a particular quantity for different values of . The collected data are summarized in the following table:
1.0000 5.8823 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 4.5000 5.0000 5.5000 6.0000 8.8823 17.8821 11.8822 14.8826 26.8825 24.8822 28.8822 45.8826 50.8821 59.8829
a) For the
values, determine the measures of central tendency: (a)- Arithmetic mean, (b)- Median, (c)- Mode and the measures of spread: (d)- Range, (e)- Standard deviation, (f)-Variance (g)- Coefficient of variation. Answer: (a)- 26.9733, (b)- 24.8822, (c)- No Mode (d)- 54.0006, (e)- 18.0248, (f)- 324.8950, (g)- 66.8248
b) Apply the least-square regression and fit a first-order line to the given points. Determine the standard error of estimate and the coefficient of determination. Compare the fitting accuracy of this linear model with the model in part (a) that only uses the arithmetic mean of the variable . Answer: < 0.8964 , c) Apply the least-square regression and fit a second-order curve to the given points. Determine the standard error of estimate and the coefficient of determination. Compare the accuracy of this polynomial fit with the linear model in part (b). Answer: < 0.9567, > 324.8950
d) Apply the general linear least-square to fit the model , where , and are three basis functions as follow: , , Compute the corresponding matrix system by employing the method of normal equation. Determine the standard error of estimate and the coefficient of determination. Compare the fitting accuracy with part (c). Answer: < 0.9998, >
ECSE 443- introduction to Numerical Methods in EE
Practice Problem Set – Chapter 4
Question 2: The goal of a two dimensional quadratic regression is to find the best values for the coefficients
Practice Problem Set – Chapter 4
(Note: This problem set is for extra practice. It is not for credit, and not to be handed in) Question 1: Suppose that in a study, several measurements were made to determine a particular quantity for different values of . The collected data are summarized in the following table:
1.0000 5.8823 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 4.5000 5.0000 5.5000 6.0000 8.8823 17.8821 11.8822 14.8826 26.8825 24.8822 28.8822 45.8826 50.8821 59.8829
a) For the
values, determine the measures of central tendency: (a)- Arithmetic mean, (b)- Median, (c)- Mode and the measures of spread: (d)- Range, (e)- Standard deviation, (f)-Variance (g)- Coefficient of variation. Answer: (a)- 26.9733, (b)- 24.8822, (c)- No Mode (d)- 54.0006, (e)- 18.0248, (f)- 324.8950, (g)- 66.8248
b) Apply the least-square regression and fit a first-order line to the given points. Determine the standard error of estimate and the coefficient of determination. Compare the fitting accuracy of this linear model with the model in part (a) that only uses the arithmetic mean of the variable . Answer: < 0.8964 , c) Apply the least-square regression and fit a second-order curve to the given points. Determine the standard error of estimate and the coefficient of determination. Compare the accuracy of this polynomial fit with the linear model in part (b). Answer: < 0.9567, > 324.8950
d) Apply the general linear least-square to fit the model , where , and are three basis functions as follow: , , Compute the corresponding matrix system by employing the method of normal equation. Determine the standard error of estimate and the coefficient of determination. Compare the fitting accuracy with part (c). Answer: < 0.9998, >
ECSE 443- introduction to Numerical Methods in EE
Practice Problem Set – Chapter 4
Question 2: The goal of a two dimensional quadratic regression is to find the best values for the coefficients