How to find out Standard Deviation from FIT

I fitting my data by y =a*x, and I need to find out the standard deviation.

From fit I have these parametres:

sse: 0.0290

rsquare: 0.9998

dfe: 64

adjrsquare: 0.9998

rmse: 0.0213

Can I get standard deviation from it?

Than you!

[Jaroslav Zadnik]

x data: [0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 124 128 132 136 140 144 148 152 156 160 164 168 172 176 180 184 188 192 196 200 204 208 212 216 220 224 228 232 236 240 244 248 252 255

y data: [0 0.0835832255570885 0.174154840956123 0.257738066513212 0.346668397145368 0.415453324421146 0.509560044586318 0.574699512626839 0.656700786156504 0.722509560430464 0.787321101372576 0.895127344627839 0.972376065620929 1.04165387296938 1.12997554323061 1.18782589580150 1.24830429670128 1.34049566423218 1.41637708439414 1.50555559037856 1.59593383517466 1.67029245291320 1.74409261660216 1.82653357465703 1.91758841382921 1.99232695666526 2.07462101757454 2.15923082788446 2.25467523953401 2.32101347334403 2.40342916226982 2.48178590261877 2.59314062501480 2.68174487905133 2.75802220563721 2.84190019778286 2.93021630190423 2.99493958142691 3.08708931485714 3.17866751685460 3.23623118738817 3.32918373207880 0 3.47101103952780 3.56608879092851 3.63677067521487 3.72085524693018 3.80233518715071 3.86578999967953 3.94281396858961 4.00812989450695 4.09544793153269 4.15617433865030 4.24345123392614 4.31395155561104 4.41607818144872 4.49347983457683 4.57443478922387 4.67025111105206 4.76924871138654 4.84059582234540 4.92751239994652 5.03195453161929 5.12673734778607 5.10441047575048]

Answer 1

[Adam Danz]

Do you want the standard deviation of the residuals? If so, compute the residulas and apply std().

Or maybe you're looking for a way to compute standard deviation from the sum of squared errors:

• SD is standard deviation
• S^2 is variance
• SS is sum of squared error
• N is number of values

[Jaroslav Zadnik]

If I want both of them, what numbers should I substitute?

[Adam Danz]

I don't know what fitting function you used but it might provide you with the residuals. You need to read the documentation for that function (1 page). If the fitting function does not prodive the residuals, you need to calculate them yourself which is fairly easy. Use the original x values and the fitted line to compute the estimated y values. Then subtract the original y values from the y-estimates to compute the residuals. The appy std to the residuals.

As for the equations I shared, the variables are defined in my answer in a bulleted list and you've already supplied all of the variables needed to solve it.

[Jaroslav Zadnik]

Fitting function is y =a*x where a = 0.02756. I need find out standard deviation, but I don't know how..

[Adam Danz]

Standard deviation of what? That's still not clear.

If you want the std of the residuals, you need to compute the residuals first, unelss the fitting function you're using provides them.

If you compute

a = 0.02756;
 y = a*x;

you'll have the y-estimates at each x. The residuals are just the y-estimate minus the actual y value of the data. You'll have a vector of residuals the same size as y and you can apply std() to the residuals.

If that still doesn't make sense, you'll need to search for a tutorial.

[Adam Danz]

Jaroslav Zadnik's answer moved here as a comment

Ok, thank you. Can I say that rmse is standard deviation?

[Adam Danz]

The equations are similar but std divides by N-1 while RMSE divides by N. They also have conceptual differences. I found a 1.5 pg paper that explaines this well:

Root Mean Square Error Compared to, and Contrasted with, Standard Deviation