How to calculate 95% confidence interval using regression analysis?

I have a timeseries dataset of measured lengths of some lines. The dataset consists of dates from oct of one year to march of next year. How do I calculate the 95% confidence interval values using regression analysis for each season (e.g. oct 2003 to March 2004 and so on). Something like this as shown below (CI = 95% confidence interval).

[dpb]

Which toolboxes do you have available? regress in the Statistics TB returns the coefficients and the 95% CI (upper and lower) for each. The table above would use (one presumes) half the difference if the values presented are to be interpreted as "Rate +/- CI".

Alternatively, fit in the Curve Fitting TB has the same statistics and doesn't need the manual insertion of the column of ones to estimate the intercept term if needed.

The easiest way to do this will be to put your data into a timetable and create a grouping variable for the seasons by year; your selection from Oct to March (Is this inclusive or exclusive of March?) isn't a built in grouping so you'll have to create it.

[Anwesha Sharma]

Thank you so much. This worked perfectly.

Answer 1

[Sulaymon Eshkabilov]

If there is a linear fit model for x vs. y(x), then fitlm() can be used, e.g.:

x = (0:.1:13)';
Noise = 35*randn(size(x));
y = @(x)3*x.^2-5*x+3;
Y =y(x)+Noise; 
YT=table(x);
YT.Y=Y;
FM =fitlm(YT, 'Y~x^2+x+1')

FM = 
Linear regression model:
    Y ~ 1 + x + x^2

Estimated Coefficients:
                   Estimate      SE        tStat       pValue  
                   ________    _______    _______    __________

    (Intercept)     5.1654      8.6403    0.59783       0.55101
    x              -7.3628      3.0713    -2.3973      0.017962
    x^2             3.2304     0.22865     14.128    6.7796e-28


Number of observations: 131, Error degrees of freedom: 128
Root Mean Squared Error: 33.5
R-squared: 0.945,  Adjusted R-Squared: 0.944
F-statistic vs. constant model: 1.1e+03, p-value = 2.04e-81

plot(FM)

[Anwesha Sharma]

This is so great, that you so much.

[Sulaymon Eshkabilov]

Most welcome. Glad to help.