- X LY 2 9.16 7.28 11.53 10.86 4 10.03 9.93 7.53 6.06 6 9.16 8.3 7.8 8.16 8 11.82 10.64 9.75 8.47 10 11.8 9.23 11 10.34 11.08 12 9.37 6.11 13 5.72 4.79 14 11.47 10.73 15 10.1 10.46 16 9.63 9.46 17 9.49 9.38 18 10.13 8.69 19 11.54 10.19 20 10.64 11.26 21 7.19 8.47 22 10.8 10.76 23 11.6 9.75 24 10.93 7.51 25 11.87 8.79 26 6.34 8.47 27 9.78 8.42 28 11.31 9.74 29 10.15 9.1728 11.31 9.74 29 10.15 9.17 30 10.32 8.07 31 11.22 9.723. Consider the attached data set with file name "Assignment1_Q3". Fit regression of the dependent variable Y on the independent variable X. Assume that 6; ~ N(0, o?) a. Use the results from R and provide least square estimators and their corresponding 95% confidence intervals (CIs). Show the steps needed to construct the CIs. b. Use the results from R and a point estimate and 95% CI for the error variance o'. Show your steps. c. Use the pivotal quantity method to construct a test for Ho : 02 = 0? vs H1: 02# 0% d. Suppose o = 5. Use the results from your regression analy- sis in R to provide the observed test statistic and the critical values (the rejection region) for the test in Q3c. Calculate the p-value