A student runs an experiment six times in an attempt to obtain an equation relating two physical quantities x and y. For x = 1,2,4, 6, 8, 10 units, the experiments result in corresponding y values of 3, 3, 4, 6, 7, 8 units. Find and graph the following:
(a) The least squares line;
(b) The least squares quadratic polynomial;
(c) The interpolating polynomial.
(d) Which do you think is the most likely theoretical model for this data?