• Write a subroutine that will perform a linear regression(linear least square analysis) of the input data set. Copy the data set file datahw61.dat form /home/h4/fort1/fortran/hw. Plot the data and the best fit line on one set of axis for comparison. Help for plotting is available here.

• The second data set, datahw62.dat, has an additive exponential trend trace(j) = data(j) + a*exp(b*j). write a subroutine which will transform this data set (take the natural logarithm of the data), then call your linear least square analysis subroutine to determine the parameters of the exponential trend. Plot the original data and exponential function you determine.Detrend the data trace.

• The data also has a mean value. Demean the data. Plot the trace after you have detrended and demeaned the data.

Turn in:
 

• Your least square subrouine, and the plot of the data of problem 1 with the best fit line plotted.

• Your subroutine to transform the data values, a plot of the original daya and exponential trend function. turn in the best fit values of the amplitude "a" and the exponent term "b" which describe the trend.

• Turn in the value of mean of the data and a plot of demeaned, detrended data trace.

The formulas for calculating the least suares best fit of some data are:

where
y_i = a + b*x_i