method of nonlinear estimation

1. method of nonlinear estimation Imagine, you conducted an experiment and got information. For example, interests you, what exists dependence between Charges on exploitation of bus from his age. Then accept age an Х, charges - an Y.

2. Open the menu of Analysis and choose one of variants • User-specified regression is a function, set an user. • regression it is logistic regression ( for the variants of yes/no). • Exponential growth regression is regression of exponential growth. • Piecewise linear regression – is a linear function with the point of break. For example, to the point of break of у= 2 to increase on Х, after the point of break of y= 3 minus of x • A formula is set as v1=b0+b1*v1+b2*v1**2. Try to describe it as possible wider, for example, for free variation at description a sine set a variant v1=b0+b1*sin(b2+b3*v2). • It is possible to describe a function as a set of terms, for example • v2=(b0+b1*v1+b2*sin(b3+v1))*(v3=1)+(b4*v1)*(v3=0) • ifv3=1 ifv3=0 • If v3=1, the value of the left expression is equal to 1, otherwise 0. Like with right part of expression.

3. Missing date – case wise to take into account only the complete line of information or to replace the expected value (mean). Press the button Function to be estimation and enter a formula for the search of functional dependence. How to define, what dependence to choose? Linear, quadratic, sine or logarithm…

4. First we will build a chart in Excel. Open a menu Insert / Diagram and choose a variant Point. It is the unique diagram in Excel, which takes into account numerical values on an AxisХ.

5. Next step. Press the button Next. Open a page Row and press on the button to Add. In the line of value select the interval of valuesY, in the line of Name of ax Х are values Х. Button Ready means an end. You will get the chart of experimental values of function. We try linear dependence first. Its equation.v5=bo+b1*v6 Press the button OK Passed to the next step. Choice of method of decision of task.

6. Estimation Method : quasi-Newton-most widespread and rapid. A method is rapid, but depends on a starting value. Simplex – slow, but does not depend on a start. It is a iteration method, built on the calculation of m+1 point on m previous Max number of iteration –Max number of iteration – to set the maximal number of possible iterations . Set, for example, three hundred first. Asymptotic standard errors- to mark this block, if it is necessary to get the standard error of estimation of parameters. Start values – initial value for first iteration . You can set independence or to define by program. If on the screen report of parametersestimationprocessconverged - a decision is found.

7. Press the button OK. Next window Parameters estimates- coefficients of formula. Residual–differences Yit- Yiэ Predicted– forecast values. Observed -Initial values. Press the button OK. Next window Parameters estimates- coefficients of formula. Residual–differences Yit- Yiэ Predicted– forecast values. Observed -Initial values.

8. Open the forecast values and copy them in Excel/ Add information to the chart. Use command Copy Raw. For addition of information will select a mouse click a diagram / and will execute a command Diagram / Basic data. Click on the button to Add and enter a new row. You will compare information by sight. Does a line describe information well ?