(a) (3 marks) We collect experimental data on two quantities a: and'y. W. believe that y depends on a: as follows: y = a+b:1; for some constants a and I) (this is the equation of a line in R2). Our data consists of the following points (5%, yk): i, (230):('1,1),(011);(1,5),(2,8)- Use the least squares method to find the line of best fit for this data. Also calculate the error for this line. , _ x . (b) (3 marks) Recent theory causes us to adjust our hypothesis from part (a). '~ We now believe that y depends on a: as follows: y = a F (xv + 0:52 for some ' constants a, b, and c (this is the equation of a parabola in R2). Using the 7 same data points from part (a), use the least Squares method to nd the parabola of best t for this data. Also calculate the error for this parabola. /