A helpful worksheet for Exercise 3.4.1.

Here is the data for Exercise 3.4.1:

data = {{0.1, 0.11}, {0.6, 0.5}, {1.1, 0.6}, {1.4, 0.5}}

A plot

ListPlot[data]

To fit a function u(a,t) = a*t to this data by adjusting "a", define

u[t_,a_] = a*t

and form sum of squares

SS = Sum[(u[data[[i,1]],a]-data[[i,2]])^2,{i,1,4}]

Then minimize the resulting expression SS as a function of a.

For parts b, c, and d, do the same but with appropriate modifications to u.