# Slope Error Equation

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 uncertainty in slope excel that I have not really addressed much. However, it is important enough that

## Error In Slope Of Linear Fit

I talk about it. In many labs, you will collect data, make a graph, find the slope of a function how to calculate uncertainty from a graph 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 you

## Uncertainty In Slope Of Best Fit Line

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 formula for calculating error in slope 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 method, just pick

the picture below, the data points are shown by small, filled, black circles; each datum has error

## Uncertainty In Y Intercept

bars to indicate the uncertainty in each measurement. It appears that

## How To Find The Maximum And Minimum Slope Of A Graph

current is measured to +/- 2.5 milliamps, and voltage to about +/- 0.1 volts. The hollow triangles standard error of slope calculator represent points used to calculate slopes. Notice how I picked points near the ends of the lines to calculate the slopes! Draw the "best" line through all the points, https://www2.southeastern.edu/Academics/Faculty/rallain/plab193/page1/page35/page36/page36.html taking into account the error bars. Measure the slope of this line. Draw the "min" line -- the one with as small a slope as you think reasonable (taking into account error bars), while still doing a fair job of representing all the data. Measure the slope of this line. Draw the "max" line -- the one with http://spiff.rit.edu/classes/phys369/workshops/w2c/slope_uncert.html as large a slope as you think reasonable (taking into account error bars), while still doing a fair job of representing all the data. Measure the slope of this line. Calculate the uncertainty in the slope as one-half of the difference between max and min slopes. In the example above, I find 147 mA - 107 mA mA "best" slope = ------------------ = 7.27 ---- 10 V - 4.5 V V 145 mA - 115 mA mA "min" slope = ------------------ = 5.45 ---- 10.5 V - 5.0 V V 152 mA - 106 mA mA "max" slope = ------------------ = 9.20 ---- 10 V - 5.0 V V mA Uncertainty in slope is 0.5 * (9.20 - 5.45) = 1.875 ---- V There are at most two significant digits in the slope, based on the uncertainty. So, I would say the graph shows mA slope = 7.3 +/- 1.9 ---- V Last modified 7/31/2007 by MWR. Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might http://stats.stackexchange.com/questions/91750/how-is-the-formula-for-the-standard-error-of-the-slope-in-linear-regression-deri have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting http://www.fiz-ix.com/2013/01/finding-standard-error-of-slope-and-y-intercept-using-linest-in-excel-linear-regression-in-physics-lab/ ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, in slope data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How is the formula for the Standard error of the slope in linear regression derived? [duplicate] up uncertainty in slope vote 3 down vote favorite This question already has an answer here: Derive Variance of regression coefficient in simple linear regression 2 answers As stated in many textbooks, the Standard error of the slope in linear regression with one variable is $\sqrt{\frac{s^2}{SSX}}$ or some rewrite, ${s^2}$ being the error variance and ${SSX}$ being the sum of the ${x}$-squares. Can anybody help with an explicit proof? regression standard-error share|improve this question edited Apr 14 '14 at 7:05 asked Mar 28 '14 at 20:11 user3451767 11319 marked as duplicate by gung, Nick Stauner, Momo, COOLSerdash, Glen_b♦ Mar 29 '14 at 8:00 This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question. 1 see stats.stackexchange.com/questions/88461/… –TooTone Mar 28 '14 at 23:19 It's reasonably straightforward if you start from the fact that the line goes through $(\bar x,\bar y)$ and write the slope estimator as a kind of average. –Glen_b♦ Mar

in Excel (Linear Regression in Physics Lab) January 4, 2013 by Jeff Finding Standard Error of Slope and Y-Intercept using LINEST in Excel (Linear Regression in Physics Lab) In Excel, you can apply a line-of-best fit to any scatterplot. The equation for the fit can be displayed but the standard error of the slope and y-intercept are not give. To find these statistics, use the LINEST function instead. The LINEST function performs linear regression calculations and is an array function, which means that it returns more than one value. Let's do an example to see how it works. Let's say you did an experiment to measure the spring constant of a spring. You systematically varied the force exerted on the spring (F) and measured the amount the spring stretched (s). Hooke's law states the F=-ks (let's ignore the negative sign since it only tells us that the direction of F is opposite the direction of s). Because linear regression aims to minimize the total squared error in the vertical direction, it assumes that all of the error is in the y-variable. Let's assume that since you control the force used, there is no error in this quantity. That makes F the independent value and it should be plotted on the x-axis. Therefore, s is the dependent variable and should be plotted on the y-axis. Notice that the slope of the fit will be equal to 1/k and we expect the y-intercept to be zero. (As an aside, in physics we would rarely force the y-intercept to be zero in the fit even if we expect it to be zero because if the y-intercept is not zero, it may reveal a systematic error in our experiment.) The images below and the following text summarize the mechanics of using LINEST in Excel. Since it is an array function, select 6 cells (2 columns, 3 rows). You can select up to 5 rows (10 cells) and get even more statistics, but we usually only need the first six. Hit the equal sign key to tell Excel you are about to enter a function. Type LINEST(, use the mouse to select your y-data, type a comma, use the mouse to select your x-data, type another comma, then type true twice separated by a comma and cl

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slope error excel

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Slope Error Formula p Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings uncertainty in slope excel and policies of this site About Us Learn more about Stack Overflow the p Error In Slope Of Linear Fit p company Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags Users Badges p How To Calculate Uncertainty From A Graph p Unanswered Ask Question Cross Validated is a question and answer site for people interested in statistics machine learning data analysis

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standard error of a slope excel

Standard Error Of A Slope Excel p in Excel Linear Regression in Physics Lab January by Jeff Finding Standard Error of Slope and Y-Intercept using LINEST in Excel Linear Regression in Physics Lab In Excel you can apply a line-of-best fit to any scatterplot The equation for the fit can be displayed but the standard error of the slope and how to calculate error in slope y-intercept are not give To find these statistics use the LINEST function instead The LINEST function standard deviation of slope formula performs linear regression calculations and is an array function which means that it

standard error of the slope excel

Standard Error Of The Slope Excel p in Excel Linear Regression in Physics Lab January by Jeff Finding Standard Error of Slope and Y-Intercept using LINEST in Excel Linear Regression in Physics Lab In Excel you can apply a line-of-best fit to any scatterplot The equation for the fit can be displayed but the standard error of the slope and y-intercept how to calculate error in slope are not give To find these statistics use the LINEST function instead The LINEST function performs linear standard deviation of slope formula regression calculations and is an array function which means that it

standard error slope excel

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using linest to calculate error

Using Linest To Calculate Error p The error in slope excel Linest function in Excel gives the error or uncertainty how to calculate error in slope for data in the lab It calculates the statistics for a line error in slope of linear fit by using the least squares method to calculate a straight line that best fits your data and returns an array that standard error of slope calculator describes the line Because this function returns an array of values it must be entered as an array formula An array should be entered in the four boxes The array