# TI-BASIC:Linreg Error

**Routine Summary**

Calculates the standard error associated with linear regression coefficients.

**Inputs**

*L₁* - values of the independent variable
*L₂* - values of the dependent variable

**Outputs**

*Ans* - a 2-element list containing the standard errors

**Variables Used**

L₁, L₂,

**Calculator Compatibility**

TI-83/84/+/SE

**Download**

No download provided.

: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 LinReg(a+bx) instead of 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*,*

<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*} </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

**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.