Consider the following data x = [1, 3, 4, 6, 9, 12, 14]: y = [2, 4, 5, 6, 7, 9, 11]: a) Use linear regression to model the data (you may use the technique of your choice to implement linear regression). Your answer should be the coefficients of the first order model b) Model the data using linear regression, but force the line through the origin (y = 0 when x = 0). Use the technique of your choice - your answer should be the coefficient of this model. c) Plot the data and your models from part a and b on the same graph. Plot the data as blue circles, the model from part a as a green line and The model from part b as a red line. Adjust the range of your plot to include x = 0. Your plot should include the usual labels and a legend. d) Fit the data from problem 1 to a third order polynomial. Your answer should be the coefficients e) Add your model to the plot from problem 1, in black. You should calculate enough values of y so that your graph is a smooth line. f) Predict the y value at an x value of 10, using the model you think best represents the data. Identify which model you chose and your reasons using the disp function