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probability and statistics>regression analysis> Standard error of the regression slope

Standard error of regression slope: overview

The standard errors for regression are measures of how spread out your y variable is about the mean μ. The standard error of the regression slope,S(aka Standard Error of Estimate) represents the average distance your observations deviate from the regression line. The smaller the “s” value, the closer your values ​​are to the regression line.

Watch the video for an overview of the standard errors inlinear regression, including SE for coefficients and slopes. The video also shows how to calculate standard error for slope/coefficient in Excel:

on YoutubeClick here

Standard error of the regression slopeis a term you may come acrossAP stats. In fact, find the recipe aboveStatistical formula APThe list will be given to you on the day of the exam.

Standard Error of Slope Regression Formula / Guide TI-83

SE of regression slope = sb1 = sqrt[Σ(yi – ŷi)2 / (n – 2)] / sqrt[Σ(xi – x)2].

The equation looks a bit ugly, but the secret isYou don’t need to manually run the formula in the test. Even if you think you know how to use the formula, it will be so time consuming that you’ll waste about 20-30 minutes with one question trying to do the calculations by hand! The TI-83 calculator is approved for use on the test and can help you find the standard error of the regression slope.

Note: TI83 does not directly find the SE of the regression slope; The “s” given in the output is the SE of the residual, not the SE of the regression slope. However, you can use the output to find it with a simple division.

Step 1:Enter your data in L1 and L2 lists. If you don’t know how to enter data into a list, see:Scatterplot TI-83.)

Step 2:PressSTAT, scroll rightEXAMand then selectE: LinRegTTest

Step 3:Enter the name of your playlistxlistandYliste. For example, enter L1 and L2 if you entered your data in List L1 and List L2 in step 1.

Step 4:Choose your word characteralternative hypothesis. For example, select (≠ 0) and then pressINPUT.

Step 5:highlightscalculationand then pressINPUT.

Step 6:Find the “t” value and the “b” value. You may need to scroll down using the arrow keys to see the results. Suppose your t-value is -2.51 and your b-value is -0.067.

Step 7:Divide b by t. For this example, -0.67 / -2.51 = 0.027.

The standard error of the regression slope for this example is 0.027.

That’s it!

moderator

Beyer, W.H.CRC Standard Mathematical Table, 31st Edition.Boca Raton, FL: CRC Press, pp. 536 and 571, 2002.
Everitt, BS; Skrondal, A. (2010),Cambridge Statistical Dictionary, Cambridge University Press.
Koetz, S.; et al., eds. (2006),Encyclopedia of Statistical Science, Wiley.
Wheelan, C. (2014).Nudist statistics. W.W. Norton

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An example of how to calculate the standard error of the estimate (Mean Square Error) used in simple linear regression analysis. This typically taught in statistics.

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A simple (two-variable) regression has three standard errors: one for each coefficient (slope, intercept) and one for the predicted Y (standard error of regression). While the population regression function (PRF) is singular, sample regression functions (SRF) are plural. Each sample produces a (slightly?) different SRF. So, the coefficients exhibit dispersion (sampling distribution). The standard error is the measure of this dispersion: it is the standard deviation of the coefficient. For more great Financial Risk Management videos, visit the Bionic Turtle website!

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