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# estimating error in slope of a regression line Belcher, Louisiana

In Excel, you could fit a trendline. Share this thread via Reddit, Google+, Twitter, or Facebook Have something to add? Andale Post authorApril 2, 2016 at 11:31 am You're right! I'm curious, though, it seems this approach would potentially overestimate the error in the slope by a fair amount, since replacing the point (2,9) with the point (3,7) may greatly exceed

This is not as good as the slope because the slope essentially uses all the data points at once. Technically, this is the standard error of the regression, sy/x: Note that there are (n − 2) degrees of freedom in calculating sy/x. You would then get 100 different linear regression results (100 slopes and 100 intercepts). The MINITAB output provides a great deal of information.

The estimated parameter vector is $\hat \beta = (X'X)^{-1}X'y$ where X = [1 x] is the n x 2 data matrix. By using this site, you agree to the Terms of Use and Privacy Policy. The uncertainty in the intercept is also calculated in terms of the standard error of the regression as the standard error (or deviation) of the intercept, sa: The corresponding confidence interval item at the bottom of the Tools menu, select the Add-Ins...

Generated Sat, 15 Oct 2016 06:06:25 GMT by s_ac15 (squid/3.5.20) Therefore, which is the same value computed previously. statdad, Sep 3, 2010 (Want to reply to this thread? d3t3rt, May 2, 2010 May 3, 2010 #17 statdad Homework Helper "Also, inferences for the slope and intercept of a simple linear regression are robust to violations of normality.

d3t3rt, May 2, 2010 May 2, 2010 #15 mdmann00 Aloha d3t3rt, If closed forms of the standard errors in linear regression exist, are these not what are used to estimated the In other words, Î± (the y-intercept) and Î² (the slope) solve the following minimization problem: Find  min α , β Q ( α , β ) , for  Q ( α The Variability of the Slope Estimate To construct a confidence interval for the slope of the regression line, we need to know the standard error of the sampling distribution of the You can then calculate the standard deviations of these slopes and intercepts to give you an estimate of their errors that takes into account the measurement errors on the experimental points.

The smaller the "s" value, the closer your values are to the regression line. But that's the meaning of standard error of the slope; when taking data, you might just as well have measured (3,7) instead of (2,9). No, create an account now. I take all my measurements, get the line of best fit, find its slope, and the slope is something I want.

Even with this precaution, we still need some way of estimating the likely error (or uncertainty) in the slope and intercept, and the corresponding uncertainty associated with any concentrations determined using Here the "best" will be understood as in the least-squares approach: a line that minimizes the sum of squared residuals of the linear regression model. statdad, May 3, 2010 May 3, 2010 #18 d3t3rt Statdad, thank you for fixing my statement about known standard errors and distributional forms for the sample slope and intercept. Elsewhere on this site, we show how to compute the margin of error.

Therefore, the 99% confidence interval is -0.08 to 1.18. Correlation Coefficient Formula 6. In the example above, the slope parameter estimate is -2.4008 with standard deviation 0.2373. The sample statistic is the regression slope b1 calculated from sample data.

Examine the effect of including more of the curved region on the standard error of the regression, as well as the estimates of the slope, and intercept. See sample correlation coefficient for additional details. Further, since high leverage points have the capability of controlling the entire fit, they will not be detected as outliers since they do not have large residuals. They are expressed by the following equations: The computed values for b0 and b1 are unbiased estimators of 0 and 1, and are normally distributed with standard deviations that may be

Example data. The alternative hypothesis may be one-sided or two-sided, stating that 1 is either less than 0, greater than 0, or simply not equal to 0. Select a confidence level. If so, that makes sense.

For example, with the photoelectric effect, maybe I measure stopping potential vs. Find the margin of error. And if so, why should one not use that tool to do that calculation? For example, if your data points are (1,10), (2,9), (3,7), (4,6), a few bootstrap samples (where you sample with replacement) might be (2,9), (2,9), (3,7), (4,6) (i.e., the first data point

In other words, simple linear regression fits a straight line through the set of n points in such a way that makes the sum of squared residuals of the model (that In words, the model is expressed as DATA = FIT + RESIDUAL, where the "FIT" term represents the expression 0 + 1x. I would be more concerned about homogeneous (equal) variances." The inferences are not robust to violations of normality - that fact is one of the reasons for the development of non-parametric Please help to improve this article by introducing more precise citations. (January 2010) (Learn how and when to remove this template message) Part of a series on Statistics Regression analysis Models

Often, researchers choose 90%, 95%, or 99% confidence levels; but any percentage can be used.