Question 2: (Everything to be done by hand expect if otherwise is stated) The following data are provided: X Y a/a 1 2 3 4 5 6 7 8 9 10 11 12 13 35.3 29.7 30.8 58.8 61.4 71.3 74.4 76.7 70.7 57.5 46.4 28.9 28.1 10.98 11.13 12.51 8.40 9.27 8.73 6.36 8.50 7.82 9.14 8.24 12.19 11.88 a/a X 14 15 16 17 18 39.1 46.8 48.5 59.3 19 20 21 22 23 24 25 70 70 74.5 72.1 58.1 44.6 33.4 28.6 Y 9.57 10.94 9.58 10.09 8.11 6.83 8.88 7.68 8.47 8.86 10.36 11.08| Where X represent the steam in pounds per months and Y is the mean atmosphere temperature measured in Fahrenheit. Calculate the followings: a) Fit a linear regression model and give the least square estimates for the constant and the slope. b) Calculate the residuals for each of the 25 observations. c) Make the ANOVA table and complete it by performing all the required calculations. What is the ANOVA table used for? d) Find the coefficient of determination and the correlation coefficient. Explain its value. e) Calculate the std for the error, the std for the slope and the std for the constant. f) Test whether the slope and the constant are significant. State the needed hypotheses and explain your results. g) Construct the confidence intervals for the slope and for the constant. (8+4+6+4+6+4+6=38)