Difference between revisions of "Manuals/calci/LOGEST"

Latest revision as of 16:19, 22 August 2018

LOGEST (YRange,XRange,Constant,Stats)

where,

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 YRange} is a set of Y values,
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 XRange} is an optional set of X values,
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 Constant} is a logical value TRUE or FALSE, that decides whether to force the constant 'b' to 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 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 -

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 Y= b*m^X}

For multiple ranges of X-values,

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

Argument values 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 XRange} and 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 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.
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 Constant} is a logical value that decides whether to make constant 'b' equal to 1.
If 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 Constant} = TRUE or omitted, 'b' is calculated normally. If 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 Constant} = FALSE, 'b' is made equal to 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 Stats} is a logical value that decides whether to display additional regression statistics.
If $Stats$ = TRUE, calci returns additional regresstion statistics. If 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 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 (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 Y intercept (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}}	---	$se_{1}$	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}
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}	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

References

List of Main Z Functions

Z3 home

@@ Line 1: / Line 1: @@
-=LOGEST(Y, X, C , stats)=
+<div style="font-size:30px">'''LOGEST (YRange,XRange,Constant,Stats)'''</div><br/>
 where,
-*<math>Y</math> is a set of Y  values,
+*<math>YRange</math> is a set of Y  values,
-*<math>X</math> is an optional set of X  values,
+*<math>XRange</math> is an optional set of X  values,
-*<math>C</math> is a logical value TRUE or FALSE, that decides whether to force the constant 'b' to 1,
+*<math>Constant</math> is a logical value TRUE or FALSE, that decides whether to force the constant 'b' to 1,
-*<math>stats</math> is a logical value TRUE or FALSE, that decides whether to return additional regression statistics.
+*<math>Stats</math> 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.
-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),
+*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 -
@@ Line 18: / Line 17: @@
 *For multiple ranges of X-values,
-  <math>Y = (b*(m1^X1)*(m2^X2)*......)</math>
+  <math>Y = (b*(m1^{X1})*(m2^{X2})*......)</math>
-*Argument values <math>X</math> and <math>Y</math> should be numeric, else Calci displays an error message.
+*Argument values <math>XRange</math> and <math>YRange</math> 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 an 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.
-*<math>C</math> is  a logical value that decides whether to make constant 'b' equal to 1.
+*<math>Constant</math> is  a logical value that decides whether to make constant 'b' equal to 1.
-*If <math>C</math> = TRUE or omitted, 'b' is calculated normally. If <math>C</math> = FALSE, 'b' is made equal to 1.
+*If <math>Constant</math> = TRUE or omitted, 'b' is calculated normally. If <math>Constant</math> = FALSE, 'b' is made equal to 1.
-*<math>stats</math> is a logical value that decides whether to display additional regression statistics.
+*<math>Stats</math> is a logical value that decides whether to display additional regression statistics.
-*If <math>stats</math> = TRUE, calci returns additional regresstion statistics. If <math>stats</math> = FALSE or omitted, Calci returns the values of 'm coefficients' and the constant 'b'.
+*If <math>Stats</math> = TRUE, calci returns additional regresstion statistics. If <math>Stats</math> = FALSE or omitted, Calci returns the values of 'm coefficients' and the constant 'b'.
-*When there is only one independent X variable, Slope(m) and Y intercept (b) can be calculated using following formulas -
+*When there is only one independent X variable, Y intercept (b) can be calculated using following formulas -
   <math>Y intercept (b) = INDEX(LOGEST(Y, X),2) </math>
-*The additional regression
+*The additional regression is displayed in the following format where each statistic value is described as below-
 {| class="wikitable"
 |-
-| <math>m_n</math> || <math>m_(n-1)</math> || --- || <math>m_1</math> || <math>b</math>
+| <math>m_n</math> || <math>m_{n-1}</math> || --- || <math>m_1</math> || <math>b</math>
 |-
-| <math>se_n</math> || <math>se_(n-1)</math> || --- || <math>se_1</math> || <math>se_b</math>
+| <math>se_n</math> || <math>se_{n-1}</math> || --- || <math>se_1</math> || <math>se_b</math>
 |-
 | <math>r_2</math> || <math>se_y</math> ||  || ||
@@ Line 40: / Line 39: @@
 | <math>F</math> || <math>d_f</math> ||  ||  ||
 |-
-| <math>ss_(reg)</math> || <math>ss_(resld)</math> || ||  ||
+| <math>ss_{reg}</math> || <math>ss_{resld}</math> || ||  ||
 |}
-where each statistic value is described below-
+*<math>m_n</math> is an array of constant base values for curve equation
-<math>m_n</math> is an array of constant base values for curve equation
+*<math>b</math> is the constant value of Y when X=0
-<math>b</math> is the constant value of Y when X=0
+*<math>se_1</math> is the standard error value for m1
-<math>se_1</math> is the standard error value for m1
+*<math>se_b</math> is the standard error value for constant b
-<math>se_b</math> is the standard error value for constant b
+*<math>r_2</math> is the coefficient of determination
-<math>r_2</math> is the coefficient of determination
+*<math>se_y</math> is the standard error value for Y estimate
-<math>se_y</math> is the standard error value for Y estimate
+*<math>F</math> is the observed F value
-<math>F</math> is the observed F value
+*<math>d_f</math> is the number of degrees of freedom
-<math>d_f</math> is the number of degrees of freedom
+*<math>ss_{reg}</math> is the regression sum of squares
-<math>ss_(reg)</math> is the regression sum of squares
+*<math>ss_{resld}</math> is the residual sum of squares
-<math>ss_(resld)</math> is the residual sum of squares
 == Examples ==
@@ Line 97: / Line 95: @@
 |}
-Example with single range of X values:
+'''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 cell range C2 to C6 and X values in the cell range A2 to A6.
+  =LOGEST(C2:C6,A2:A6,TRUE,TRUE)  : Displays all the regression statistics for curve <br />with Y values in cells C2 to C6 and X values in cells A2 to A6.
 <div id="5SpaceContent" class="zcontent" align="left">
@@ Line 122: / Line 120: @@
 |}
-Example with multiple range of X values:
-  =LOGEST(C2:C6,A2:B6,TRUE,TRUE) : Displays all the regression statistics for curve with Y values in cell range C2 to C6 and X values in the cell range A2 to B6.
+'''Example 2''': With multiple range of X values -
+  =LOGEST(C2:C6,A2:B6,TRUE,TRUE) : Displays all the regression statistics for curve <br />with Y values in cells C2 to C6 and X values in  cells A2 to B6.
 <div id="5SpaceContent" class="zcontent" align="left">
@@ Line 145: / Line 144: @@
 |}
+==Related Videos==
+{{#ev:youtube|fp5yFpzAJ7g|280|center|LOGEST}}
 == See Also ==
-*[[Manuals/calci/LOGEST| LOGEST]]
+*[[Manuals/calci/LINEST| LINEST]]
 == References ==
@@ Line 153: / Line 156: @@
 *[http://en.wikipedia.org/wiki/Curve_fitting Curve Fitting]
 *[http://en.wikipedia.org/wiki/Linear_equation Linear Equation]
+*[[Z_API_Functions | List of Main Z Functions]]
+*[[ Z3 |   Z3 home ]]

Difference between revisions of "Manuals/calci/LOGEST"

Latest revision as of 16:19, 22 August 2018

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Description

Examples

Related Videos

See Also

References

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