Manuals/calci/LOGEST

LOGEST (YRange,XRange,Constant,Stats)

where,

• $YRange$ is a set of Y values,
• $XRange$ is an optional set of X values,
• $Constant$ is a logical value TRUE or FALSE, that decides whether to force the constant 'b' to 1,
• $Stats$ is a logical value TRUE or FALSE, that decides whether to return additional regression statistics.
  • LOGEST() is an array function that calculates the exponential curve that fits the data values and returns an array of values that describes the curve.

Description

• If 'YRange' is the set of dependent variable, 'XRange' is the set of independent variable, 'm' is a constant base for X value and 'b' is constant (Y-intercept),

then equation for curve is -

$Y=b*m^{X}$

• For multiple ranges of X-values,

$Y=(b*(m1^{X1})*(m2^{X2})*......)$

• Argument values $XRange$ and $YRange$ should be numeric, else Calci displays NaN error message.
• The length of array of XRange values should be equal to length of array of YRange values, else Calci displays #NULL error message.
• $Constant$ is a logical value that decides whether to make constant 'b' equal to 1.
• If $Constant$ = TRUE or omitted, 'b' is calculated normally. If $Constant$ = FALSE, 'b' is made equal to 1.
• $Stats$ is a logical value that decides whether to display additional regression statistics.
• If $Stats$ = TRUE, calci returns additional regresstion statistics. If $Stats$ = FALSE or omitted, Calci returns the values of 'm coefficients' and the constant 'b'.
• When there is only one independent X variable, Y intercept (b) can be calculated using following formulas -

$Yintercept(b)=INDEX(LOGEST(Y,X),2)$

• The additional regression is displayed in the following format where each statistic value is described as below-

$m_{n}$	$m_{n-1}$	---	$m_{1}$	$b$
$se_{n}$	$se_{n-1}$	---	$se_{1}$	$se_{b}$
$r_{2}$	$se_{y}$
$F$	$d_{f}$
$ss_{reg}$	$ss_{resld}$

• $m_{n}$ is an array of constant base values for curve equation
• $b$ is the constant value of Y when X=0
• $se_{1}$ is the standard error value for m1
• $se_{b}$ is the standard error value for constant b
• $r_{2}$ is the coefficient of determination
• $se_{y}$ is the standard error value for Y estimate
• $F$ is the observed F value
• $d_{f}$ is the number of degrees of freedom
• $ss_{reg}$ is the regression sum of squares
• $ss_{resld}$ is the residual sum of squares

Examples

X1 values	X2 values	Y values
1	15	5
2	17	9
3	23	11
4	28	16
5	30	20

Example 1: With single range of X values -

=LOGEST(C2:C6,A2:A6,TRUE,TRUE)  : Displays all the regression statistics for curve 
with Y values in cells C2 to C6 and X values in cells A2 to A6.

1.3976542375431584	4.015612511401349
0.035964826100314505	0.11928183382512401
0.9665390759484563	0.11373076612886521
86.65681866342828	3
1.1208788400613339	0.038804061492775904

Example 2: With multiple range of X values -

=LOGEST(C2:C6,A2:B6,TRUE,TRUE) : Displays all the regression statistics for curve 
with Y values in cells C2 to C6 and X values in  cells A2 to B6.

0.9684996526566505	1.593646236498643
0.05737674420683413	0.23878654115432985
0.9710443899207976	0.12957493182116453
33.53562184546261	2
1.1261035756411908	0.03357932591291887

Related Videos

LOGEST

See Also

• LINEST

References

• Curve
• Curve Fitting
• Linear Equation

• List of Main Z Functions

• Z3 home