TI-BASIC:Linreg Error - Revision history

Maintenance script: Automated internal link correction

2016-02-24T23:54:15Z

Automated internal link correction

← Older revision		Revision as of 23:54, 24 February 2016
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	The routine returns a two-element list; σ,,''a'',, is the first element, and σ,,''b'',, is the second element.		The routine returns a two-element list; σ,,''a'',, is the first element, and σ,,''b'',, is the second element.

	If one prefers to use the function [[TI-BASIC:LinReg_A_Bx\|LinReg(a+bx)]] instead of [[TI-BASIC:~~LinReg_Ax_B~~\|LinReg(ax+b)]], the appropriate routine is:		If one prefers to use the function [[TI-BASIC:LinReg_A_Bx\|LinReg(a+bx)]] instead of [[TI-BASIC:Linreg_Ax_B\|LinReg(ax+b)]], the appropriate routine is:

	:2-Var Stats		:2-Var Stats

KermMartian at 19:49, 24 February 2016

2016-02-24T19:49:31Z

← Older revision		Revision as of 19:49, 24 February 2016
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	{{Template:TI-BASIC:Routine		{{Template:TI-BASIC:Routine
	\|picture=@@		\|picture=
	\|summary=Calculates the standard error associated with linear regression coefficients.		\|summary=Calculates the standard error associated with linear regression coefficients.
	\|input=''L₁'' - values of the independent variable		\|input=''L₁'' - values of the independent variable
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	\|variable=L₁, L₂,		\|variable=L₁, L₂,
	\|compatibility=TI-83/84/+/SE		\|compatibility=TI-83/84/+/SE
	\|author=@@		\|author=
	\|authors=@@		\|authors=
	\|url=@@		\|url=
	\|download=@@		\|download=
	}}		}}

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	The routine returns a two-element list; σ,,''a'',, is the first element, and σ,,''b'',, is the second element.		The routine returns a two-element list; σ,,''a'',, is the first element, and σ,,''b'',, is the second element.

	If one prefers to use the function [[TI-BASIC:~~LinReg(a+bx)~~\|LinReg(a+bx)]] instead of [[TI-BASIC:~~LinReg(ax+b)~~\|LinReg(ax+b)]], the appropriate routine is:		If one prefers to use the function [[TI-BASIC:LinReg_A_Bx\|LinReg(a+bx)]] instead of [[TI-BASIC:LinReg_Ax_B\|LinReg(ax+b)]], the appropriate routine is:

	:2-Var Stats		:2-Var Stats

KermMartian at 19:17, 24 February 2016

2016-02-24T19:17:59Z

← Older revision		Revision as of 19:17, 24 February 2016
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	For the fitting equation ''y''=''a''//x''+''b'',		For the fitting equation ''y''=''a''//x''+''b'',

	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}		\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}
	\begin{align*}		\begin{align*}
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	\sigma_b&=\sigma_a\sqrt{\frac{\Sigma x^2}{n}}		\sigma_b&=\sigma_a\sqrt{\frac{\Sigma x^2}{n}}
	\end{align*}		\end{align*}
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>

	where ''n'' is the number of data points, ''r''² is the coefficient of determination, and Σ''x''² is the sum of squares of the independent variable values.		where ''n'' is the number of data points, ''r''² is the coefficient of determination, and Σ''x''² is the sum of squares of the independent variable values.
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	= Reference =		= Reference =

	Lichten, William. ''Data and Error Analysis''., 2nd. ed., Prentice Hall: Upper Saddle River, NJ, 1999.[[Category:TI-BASIC]]		Lichten, William. ''Data and Error Analysis''., 2nd. ed., Prentice Hall: Upper Saddle River, NJ, 1999.
			[[Category:TI-BASIC]]
	[[Category:TIBD]]		[[Category:TIBD]]

Maintenance script: Initial automated import

2016-02-24T18:18:16Z

Initial automated import

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{{Template:TI-BASIC:Routine
|picture=@@
|summary=Calculates the standard error associated with linear regression coefficients.
|input=''L₁'' - values of the independent variable
''L₂'' - values of the dependent variable
|output=''Ans'' - a 2-element list containing the standard errors
|variable=L₁, L₂,
|compatibility=TI-83/84/+/SE
|author=@@
|authors=@@
|url=@@
|download=@@
}}

:2-Var Stats
:LinReg(ax+b)
:a√((r²ֿ¹−1)/(n-2)){1,√(Σx²/n)}

This routine computes the standard error (uncertainty) associated with the linear regression coefficients ''a'' and ''b'' (σ,,''a'',, and σ,,''b'',,, respectively) for the regression equation ''y''=''a''//x''+''b''. Precisely stated, the true value of the coefficient ''a'' is expected to be within the interval ''a''±σ,,''a'',,, and similarly for ''b''.

The routine returns a two-element list; σ,,''a'',, is the first element, and σ,,''b'',, is the second element.

If one prefers to use the function [[TI-BASIC:LinReg(a+bx)|LinReg(a+bx)]] instead of [[TI-BASIC:LinReg(ax+b)|LinReg(ax+b)]], the appropriate routine is:

:2-Var Stats
:LinReg(a+bx)
:b√((r²ֿ¹−1)/(n-2)){√(Σx²/n),1}

(note that the meanings of σ,,''a'',, and σ,,''b'',, have now interchanged).

In both routines, r², a, b, n, and Σx² are statistical variables.

= Formulas =

For the fitting equation ''y''=''a''//x''+''b'',

[[TI-BASIC:Math|Math]]
\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}
\begin{align*}
\sigma_a&=a\sqrt{\frac{\frac1{r^2}-1}{n-2}} \\
\sigma_b&=\sigma_a\sqrt{\frac{\Sigma x^2}{n}}
\end{align*}
[[TI-BASIC:/math|/math]]

where ''n'' is the number of data points, ''r''² is the coefficient of determination, and Σ''x''² is the sum of squares of the independent variable values.

= Error Conditions =

* '''[[TI-BASIC:Errors#dimmismatch|ERR:DIM MISMATCH]]''' is thrown if the two lists' sizes are not the same.

= Reference =

Lichten, William. ''Data and Error Analysis''., 2nd. ed., Prentice Hall: Upper Saddle River, NJ, 1999.[[Category:TI-BASIC]]
[[Category:TIBD]]