1. Use least-square regression to fit a straight line to the following data:

X 0 2 4 6 9 11 12 15 17 19 y 5 6 7 6 9 8 8 10 12 12

(a) Along with the slope and intercept, compute the correlation coefficient.

(b) Compute the standard error of the estimate Sy/x, which is given by the equation:

/ = 2

where Sr is the sum of the squares of errors.

(c) Plot the data and the regression line using MATLAB.

(d) Repeat the problem, but regress x versus y, that is, switch the variables. Interpret your results.

2. Fit a cubic polynomial to the following data:

X 3 4 5 7 8 9 11 12 y 1.6 3.6 4.4 3.4 2.2 2.8 3.8 4.6