Manuals/calci/LOGEST

LOGEST(Y, X, C , stats)

where,

• $Y$ is a set of Y values,
• $X$ is an optional set of X values,
• $C$ 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 'Y' is dependent variable, 'X' is 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 $X$ and $Y$ should be numeric, else Calci displays NaN error message.
• The length of array of X values should be equal to length of array of Y values, else Calci displays #NULL error message.
• $C$ is a logical value that decides whether to make constant 'b' equal to 1.
• If $C$ = TRUE or omitted, 'b' is calculated normally. If $C$ = 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 -

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle Yintercept(b)=INDEX(LOGEST(Y,X),2)}

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m_n}	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m_{n-1}}	---	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m_1}	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle se_n}	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle se_{n-1}}	---	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle se_1}	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle se_b}
$r_{2}$	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle se_y}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F}	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d_f}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ss_{reg}}	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ss_{resld}}

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m_n} is an array of constant base values for curve equation
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} is the constant value of Y when X=0
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle se_1} is the standard error value for m1
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle se_b} is the standard error value for constant b
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r_2} is the coefficient of determination
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle se_y} is the standard error value for Y estimate
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F} is the observed F value
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d_f} is the number of degrees of freedom
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ss_{reg}} is the regression sum of squares
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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

See Also

• LINEST

References

• Curve
• Curve Fitting
• Linear Equation