[6] Consider the following data generated in R for a generic (x, y) data set of 10 values. > round (rbind (x, y), 2) [1] [2] [3] [4] x 1.00 6.00 9.00 12.00 y 3.06 7.23 19.34 29.29 30.76 36.5 39.24 40.54 52.19 46.98 [5] [6] [7] [8] 14.00 15.0 17.00 18.00 [9] [10] 19.00 20.00 In the following, you may use software, to confirm. You may also use software to develop the estimates requested, BUT, I want to see the formulas used, either written with intermediate values shown or code showing the computation process. You don't have to be extreme with this, but I need to see enough to know you know the relevant equations and are not merely relying on regression software to provide each result. [a] Fit the simple linear model and report the estimates for intercept (a) and slope (b). [b] Conduct a t-test (a = 0.05) for the slope coefficient being equal to zero. [c] Develop a 95% confidence interval for the intercept. [d] Determine a confidence interval for the regression line when x = 5. [e] Determine a 95% prediction interval for a new observation collected at x = 5.