HWK 8: Regression 1. For the questions below answer first by techniques that do NOT use the R linear model function (lm) and then compare to what is gotten from the lm() function. You may use R for the calculations not including lm but show how you do them. X = [ -2, 1, 2, -1, 0] Y = [25, 18, 13, 23, 16] a) Find the slope and intercept of the line b) Find the residuals, the average of the absolute value of the residuals, and the standard deviation of the residuals using the appropriate number of degrees of freedom. c) Calculate the correlation coefficient d) Calculate the F-value and explain what it means 2. Find the best fit of the data sets below using log or semilog (whichever works best) and from that fit produce the equation in the form y = f(x). Using the R lm function and plotting will be helpful. a) x = [0, 1, 2, 3, 4] y = [0, 0.45, 2.8, 7.9, 15.5] b) x = [0, 1, 2, 3, 4] y = [0.55, 1.20, 3.3, 7.8, 19.6] c) x = [1, 2, 3, 4, 5] y = [0, 1.04, 1.65, 2.08, 2.40] 3. In the below data, y is a polynomial of x. Find the formula by using multi variable regression on powers of x. x = [ -2, 1, 2, -1, 0, 3 ] y = [ -2, 2.5, 2.0, -2.5, 0.1, -4.5 ]