Error In Slope Calculator
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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 that I have not really addressed much. However, it is important enough that I talk about it. how to calculate error in slope excel In many labs, you will collect data, make a graph, find the slope of a function
Calculate Error In Slope From R2
that fits that data and use it for something. Well, what if need to find the uncertainty in the slope? How do you do slope equation calculator that? There are a couple of ways 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.
Slope Intercept Form Calculator
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 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 slope calculator 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 data pair with the largest uncertainty (to be safe) - although hopefully, it won’t matter much. For this case, I will pick d= 0.06+/-0.002 m and C = 0.183 +/- 0.004 m. This would give an uncertainty in the slope of 0.2. I would write: (there are no units - they canceled) Method 2 The next method is better but a little tricky. Basically, if you draw a best fit line you could “wiggle” the line and still have it fit. This would give a minimum and a maximum slope. If you do the trendline in Exce
known or estimated uncertainties. The calculations may involve algebraic operations
Slope Graph Calculator
such as: Z = X + Y ; Z
Slope Percentage Calculator
= X - Y ; Z = X x Y ; Z = X/Y ; how to find slope Z = XY or mathematical functions of the type: Z = 1/X ; Z = ln(X) ; Z = log10(X) ; Z = 10X https://www2.southeastern.edu/Academics/Faculty/rallain/plab193/page1/page35/page36/page36.html ; Z = eX ; Z = sqrt(X) . If uncertainties (dX, dY) are provided for the input quantities (X,Y), the program will perform the operation or function to calculate the answer (Z) and will also calculate the uncertainty in the answer (dZ). The program will assume the value has no http://web.mst.edu/~gbert/JAVA/uncertainty.HTML uncertainty if an uncertainty is not provided. Operation: Position the cursor on the blank under "X", click the mouse, and type a value. Alternately, press the TAB key until the cursor appears in this blank, then type the number. In case of an error, use normal text-editing procedures. Enter values for X and dX, and possibly for Y and dY. (The TAB key moves the cursor through the blanks in the order: X, dX, Y, dY). Click on the button for the desired operation or function. The equation for the calculation appears in the central blank, and the values of Z and dZ appear in their respective blanks. There are buttons for transferring values from Z to a MEMory location, or to the blanks for X or Y; or from the MEMory to X or Y. top
the picture below, the data points are shown by small, filled, black circles; each datum has error http://spiff.rit.edu/classes/phys369/workshops/w2c/slope_uncert.html bars to indicate the uncertainty in each measurement. It appears that current is measured to +/- 2.5 milliamps, and voltage to about +/- 0.1 volts. The hollow triangles http://web.centre.edu/james.kelly/p210l_fa10/LINEST.pdf 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, error in 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 error in slope 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.