Polynomial Fit Intervals VI

Owning Palette: Advanced Curve Fitting VIs

Requires: Full Development System

Calculates statistical intervals of the best polynomial fit for a data set (X, Y).

You must manually select the polymorphic instance to use.

Details  

Use the pull-down menu to select an instance of this VI.

Select an instance Confidence Interval (Polynomial)Prediction Interval (Polynomial)

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Confidence Interval (Polynomial)

	confidence level specifies the level of certainty for the confidence interval. The default is 0.95, which means the probability that the best fit falls between Lower Bound and Upper Bound is 95%. confidence level must be greater than 0 and less than 1.
	Y is the array of dependent values. The number of sample points in Y must be greater than the number of elements in Polynomial Coefficients.
	X is the array of independent values. X must be the same size as Y.
	Weight is the array of weights for the observations (X, Y). Weight must be the same size as Y. Weight also must contain non-zero elements. If an element in Weight is less than 0, the VI uses the absolute value of the element. If you do not wire an input to Weight, the VI sets all elements of Weight to 1.
	Polynomial Coefficients specifies coefficients of the fitted model in ascending order of power. If the total number of elements in Polynomial Coefficients is m, the polynomial order is m – 1.
	Upper Bound returns the upper bound of the confidence interval.
	Lower Bound returns the lower bound of the confidence interval.
	Delta Polynomial Coefficients returns the confidence radius of Polynomial Coefficients.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Prediction Interval (Polynomial)

	confidence level specifies the level of certainty for the prediction interval. The default is 0.95, which means the probability that a new dependent value falls between Lower Bound and Upper Bound is 95%. confidence level must be greater than 0 and less than 1.
	Y is the array of dependent values. The number of sample points in Y must be greater than the number of elements in Polynomial Coefficients.
	X is the array of independent values. X must be the same size as Y.
	Weight is the array of weights for the observations (X, Y). Weight must be the same size as Y. Weight also must contain non-zero elements. If an element in Weight is less than 0, the VI uses the absolute value of the element. If you do not wire an input to Weight, the VI sets all elements of Weight to 1.
	Polynomial Coefficients specifies coefficients of the fitted model in ascending order of power. If the total number of elements in Polynomial Coefficients is m, the polynomial order is m – 1.
	Upper Bound returns the upper bound of the prediction interval.
	Lower Bound returns the lower bound of the prediction interval.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Polynomial Fit Intervals Details

Confidence Interval

In the following illustration, the region between the upper and lower confidence bounds is the confidence interval.

Prediction Interval

In the following illustration, the region between the upper and lower prediction bounds is the prediction interval.

If the noise of Y is Gaussian distributed, use both instances of the polymorphic VI to calculate the confidence interval and prediction interval. The following block diagram illustrates the calculation of the confidence interval and the prediction interval using the Polynomial Fit Intervals VI. You must fit the observations with the General Polynomial Fit VI, using the Least Square method to obtain the Polynomial Coefficients.