Standard deviation between two vector

Hi there,

Can anybody help me to find out standard deviation between two vector? first vector shows data points and other vector shows fitting curve for it. I want to see based on std which curve fitting function has best fit

68.3306790117463	68.0583000000000
69.7661166036220	69.7895000000000
72.1123677003504	71.5207000000000
73.0939315719700	73.2519000000000
73.9225823385832	74.9831000000000
76.4566931111904	76.7143000000000
77.5042095769199	78.4455000000000
78.8703468364576	80.1767000000000
81.7629172086221	81.9079000000000
84.5119789972035	83.6391000000000
85.6904259495530	85.3703000000000
86.9839371938436	87.1015000000000
88.1731382924858	88.8327000000000
88.5525994121150	90.5639000000000
93.3274107768681	92.2951000000000
94.3898044222140	94.0263000000000
96.4532553644749	95.7575000000000
98.6474654885060	97.4887000000000
99.9741525141648	99.2199000000000
101.980636557984	100.951100000000
104.675296906708	102.682300000000
106.750596607465	104.413500000000
106.199133595364	106.144700000000
108.657750373732	107.875900000000
109.234571173461	109.607100000000
109.976002830055	111.338300000000
111.845164723014	113.069500000000
114.282169520428	114.800700000000
114.789373580927	116.531900000000
117.538189964372	118.263100000000
119.854576650875	119.994300000000
122.247310933277	121.725500000000

Thank you in advance to all

Answer 1

[Star Strider]

I suspect that what you want are confidence intervals for the fitted regression line, since ‘standard deviation’ does not make sense in this context. Without the independent variable (x) data, it is not possible for me to do it.

With your original (x,y) data, use the fitlm function to repeat the fit, then use the predict function to create the confidence intervals. Plotting the confidence limits as lines is then straightforward. You can also use the errorbar function to plot the error bars at each point on the regression line as an alternative.

[Ill ch]

Hello Star,

thank you very much... you are always there to help ....I really appreciated. yes i want to find confidence interval also errorbar. I do not know but i can process. Could you please give me one example then i will follow same for my further data set also. here is my x data:

function which i have used: y=ax+b where a,b=0.8656 7.4663 with leastsquarefit

70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
100
102
104
106
108
110
112
114
116
118
120
122
124
126
128
130
132

[Ill ch]

I read the link which have given in your explanaion. I have one small question: my models are already ready with different mathematical functions. I want to check which function is more suitable. I can not use fitlm again to generate mdl and then check the confidence interval. Here my supervisior suggest me to check with std. suppose:

i have two mathematical functions which i have fitted on the data:

one model has: std for measurement data=0.1822 ; std of fitted curve= 0.1834

similarly with another mathematical function std=0.1934 .

Now here i do not know how i can select which one is better?

[Star Strider]

This works:

Data = [                70          68.3306790117463
                        72           69.766116603622
                        74          72.1123677003504
                        76            73.09393157197
                        78          73.9225823385832
                        80          76.4566931111904
                        82          77.5042095769199
                        84          78.8703468364576
                        86          81.7629172086221
                        88          84.5119789972035
                        90           85.690425949553
                        92          86.9839371938436
                        94          88.1731382924858
                        96           88.552599412115
                        98          93.3274107768681
                       100           94.389804422214
                       102          96.4532553644749
                       104           98.647465488506
                       106          99.9741525141648
                       108          101.980636557984
                       110          104.675296906708
                       112          106.750596607465
                       114          106.199133595364
                       116          108.657750373732
                       118          109.234571173461
                       120          109.976002830055
                       122          111.845164723014
                       124          114.282169520428
                       126          114.789373580927
                       128          117.538189964372
                       130          119.854576650875
                       132          122.247310933277];
                   
model = fitlm(Data(:,1), Data(:,2), 'linear');
[ypred,yci] = predict(model, Data(:,1));

figure
plot(Data(:,1), Data(:,2), '.')
hold on
plot(Data(:,1), ypred, '-r')
plot(Data(:,1), yci(:,1), '-g')
plot(Data(:,1), yci(:,2), '-g')
hold off
grid
legend('Data', 'Linear Fit', '95% Confidence Limits',  'Location','SE')

Add the title and appropriate xlabel and ylabel strings.

[Ill ch]

Thank you very very much

[Star Strider]

As always, my pleasure!

[Ill ch]

Hello Star,

Could you please help me for the following problem? Thank you very very very much in advance

https://www.mathworks.com/matlabcentral/answers/497191-gaussien-distribution-histogram-plot