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.
