# LogFitInterval

Advanced Analysis Library Only

AnalysisLibErrType LogFitInterval (double arrayX[], double arrayY[], double weight[], int numberOfElements, double logBase, int intervalType, double confidenceLevel, double amplitude, double scale, double upperBound[], double lowerBound[], double *deltaAmplitude, double *deltaScale);

## Purpose

Calculates the confidence interval for the best logarithm fitting function or the prediction interval for the observations. The confidence interval refers to the interval within which the actual function is expected to fall. The prediction interval refers to the interval within which the arrayY values are expected to fall in repeated measurements.

## Parameters

Input
Name | Type | Description
arrayX | double-precision array | The x value of the data set (x, y).
arrayY | double-precision array | The y value of the data set (x, y).
weight | double-precision array | The weight of each data point. If weight is NULL, the function assumes all the weights are 1.
numberOfElements | integer | The length of arrayX, arrayY, and weight.
logBase | double-precision | The base of the logarithm. If logBase is less than or equal to 0, the function uses the natural logarithm.
intervalType | integer | The type of interval. intervalType must be one of the following values: CONFIDENCE_INTVL (0) PREDICTION_INTVL (1) deltaAmplitude and deltaScale are not referenced if intervalType is PREDICTION_INTVL.
confidenceLevel | double-precision | The level of certainty for the confidence interval or prediction interval. For the confidence interval, confidenceLevel specifies the probability that the actual function lies within the confidence interval. For the prediction interval, confidenceLevel specifies the probability that the arrayY values lie within the prediction interval in repeated measurements. confidenceLevel must be between 0 and 1.
amplitude | double-precision | The amplitude of the fitted logarithm model calculated using the Least Square method.
scale | double-precision | The scale of the fitted logarithm model calculated using the Least Square method.
Output
Name | Type | Description
upperBound | double-precision array | The upper bound for the confidence interval or prediction interval.
lowerBound | double-precision array | The lower bound for the confidence interval or prediction interval.
deltaAmplitude | double-precision | The uncertainty radius of amplitude. deltaAmplitude is available only when intervalType is CONFIDENCE_INTVL.
deltaScale | double-precision | The uncertainty radius of scale. deltaScale is available only when intervalType is CONFIDENCE_INTVL.

## Return Value

Name | Type | Description
status | AnalysisLibErrType | A value that specifies the type of error that occurred. Refer to analysis.h for definitions of these constants.