Error Slope Line
Contents |
Springs Charge of an Electron Video Analysis Torque Rolling Objects Mechanical Energy Human Performance Old labs Extra Stuff Slope uncertainty Reports How to find the uncertainty in the slope This is an issue standard error of slope of regression line that I have not really addressed much. However, it is important enough that
Error In Slope Linear Regression
I talk about it. In many labs, you will collect data, make a graph, find the slope of a
Error In Slope Of Linear Fit
function that fits that data and use it for something. Well, what if need to find the uncertainty in the slope? How do you do that? There are a couple of ways
Percent Error Slope
you can do this, neither are absolutely correct. However, if you write a formal lab report and you find the slope you MUST find the uncertainty in it. Here is some sample data. Suppose I measure the diameter and the circumference of several roundish objects. Here is my data. So, I want to plot this and find a functional relationship between these two. With error in slope calculator error bars, this is what it should look like: Now, I want to fit a linear function to this data. That should be ok, but what about the uncertainty? Method 1 - use uncertainty of data points I could get the ratio of C/d by just looking at each data point. This is not as good as the slope because the slope essentially uses all the data points at once. In this method, I am going to find the slope as normal. In Excel, you could fit a trendline. Or, you could draw a best fit line. Either way, I would get something like this (I did this in Logger Pro): This gives a slope of 3.28 (compare to pi = 3.14). I could get a better slope if I required the fitting function to go through the origin (0,0), but I am not going to do that. In essence, the slope is: But, what if I just use one set of data points? Then I could use propagation of error as usual. This would give Where the delta - slope represents the uncertainty in the slope. For this metho
Community Forums > Mathematics > Set Theory, Logic, Probability, Statistics > Dismiss Notice Join Physics Forums Today! The friendliest, high quality science and math community on the planet! Everyone who loves science error in slope excel is here! Estimating error in slope of a regression line Page 1 of 2 how to find standard error of slope 1 2 Next > Oct 29, 2007 #1 Signifier OK, I have a question I have no idea how to standard error of slope formula answer (and all my awful undergrad stats books are useless on the matter). Say I make a number of pairs of measurements (x,y). I plot the data, and it looks strongly positively correlated. I https://www2.southeastern.edu/Academics/Faculty/rallain/plab193/page1/page35/page36/page36.html do a linear regression and get an equation for a line of best fit, say y = 0.3x + 0.1 or something. The Pearson coefficient is very close to one, IE 0.9995 or so. Now, say that the quantity I am interested in is the slope of this line, that is (for the above equation) 0.3. I take all my measurements, get the line of best fit, find its https://www.physicsforums.com/threads/estimating-error-in-slope-of-a-regression-line.194616/ slope, and the slope is something I want. For example, with the photoelectric effect, maybe I measure stopping potential vs. frequency of light; the slope can be related to Planck's constant. Or something similar. The question I have is: how do I estimate the error (uncertainty) in this slope value I get? My professor said to use the "standard deviation in the slope," which doesn't sound sensible to me. I thought to myself: well, maybe it has to do with using the uncertainty in x and the uncertainty in y. But how would you combine these uncertainties to find the uncertainty in dy/dx? How does one estimate the error range for a parameter obtained from the slope of a line of best fit on a set of (x,y) data? Thank you so much, this one seems really important and I'm a bit disturbed I haven't the slightest idea what to do. Signifier, Oct 29, 2007 Phys.org - latest science and technology news stories on Phys.org •Game over? Computer beats human champ in ancient Chinese game •Simplifying solar cells with a new mix of materials •Imaged 'jets' reveal cerium's post-shock inner strength Oct 29, 2007 #2 EnumaElish Science Advisor Homework Helper The
treated statistically in terms of the mean and standard deviation. The same phenomenon applies to each measurement taken in the course of constructing a calibration curve, causing a variation in the slope and intercept of the calculated http://www.chem.utoronto.ca/coursenotes/analsci/stats/ErrRegr.html regression line. This can be reduced - though never completely eliminated - by making http://stattrek.com/regression/slope-confidence-interval.aspx?Tutorial=AP replicate measurements for each standard. Multiple calibrations with single values compared to the mean of all three trials. Note how all the regression lines pass close to the centroid of the data. Even with this precaution, we still need some way of estimating the likely error (or uncertainty) in the slope and intercept, and the corresponding error in uncertainty associated with any concentrations determined using the regression line as a calibration function. Tips & links: Skip to uncertainty of the regression Skip to uncertainty of the slope Skip to uncertainty of the intercept Skip to the suggested exercise Skip to Using Excel’s functions Download a specimen Excel file for this section Navigation: Introduction Bibliography Contact Info Copyright How to Use Concept Map Site Map Excel™ Basics Entering Data Formulas error in slope Plotting Functions Trendlines Basic Statistics Stats in Anal Chem Mean and Variance Error and Residuals Probability Confidence Levels Degrees of Freedom Linear Regression Calibration Correlation Linear Portions Regression Equation Regression Errors Using the Calibration Limits of Detection Outliers in Regression Evaluation & Comparison Hypotheses t-test 1- and 2-tailed Tests F-test Summary Quick Links: Site Map Concept Map Next Page Previous Page Next Topic Previous Topic The Uncertainty of the Regression: We saw earlier that the spread of the actual calibration points either side of the line of regression of y on x (which we are using as our calibration function) can be expressed in terms of the regression residuals, (yi − ): The greater these resdiuals, the greater the uncertainty in where the true regression line actually lies. The uncertainty in the regression is therefore calculated in terms of these residuals. Technically, this is the standard error of the regression, sy/x: Note that there are (n − 2) degrees of freedom in calculating sy/x. This is because we are making two assumptions in this equation: a) that the sample population is representative of the entire population, and b) that the values are representative of the true y-values. For each assumption, we remove one degree of freedom, and our estimated standard deviatio
test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes rule Combinations/permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Regression Slope: Confidence Interval This lesson describes how to construct a confidence interval around the slope of a regression line. We focus on the equation for simple linear regression, which is: ŷ = b0 + b1x where b0 is a constant, b1 is the slope (also called the regression coefficient), x is the value of the independent variable, and ŷ is the predicted value of the dependent variable. Estimation Requirements The approach described in this lesson is valid whenever the standard requirements for simple linear regression are met. The dependent variable Y has a linear relationship to the independent variable X. For each value of X, the probability distribution of Y has the same standard deviation σ. For any given value of X, The Y values are independent. The Y values are roughly normally distributed (i.e., symmetric and unimodal). A little skewness is ok if the sample size is large. Previously, we described how to verify that regression requirements are met. 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 slope. Many statistical software packages and some graphing calculators provide the standard error of the slope as a regression analysis output. The table below shows hypothetical output for the following regression equation: y = 76 + 35x . Predictor Coef SE Coef T P Constant 76 30 2.53 0.01 X 35 20 1.75 0.04 In the output above, the standard error of the slope (shaded in gray) is equal to 20. In this example, the standard error is referred to as "SE Coeff". However, other software packages might use a different label for the standard error. It might be "StDev", "SE", "Std Dev", or something else. If you need to calculate the standard error of the slope (SE) by hand, use the following formula: SE = sb1 = sqrt [ Σ(yi - ŷi)2 / (n - 2) ] / sqrt [ Σ(xi - x)2 ] where yi is the value of the dependent variable for observation i, ŷi is estima