STAT question:

Problem 5. Consider the set of five (x,y) data points: (1,0.84), (2,1.99), (3,3.25), (4,6.1), (5,9.27). Fit this data set using a simple linear model yi = 30 + lei + 61'. Answer the following questions and show all your work. a. Estimate [3'0 and B1. b. Estimate the variance 02 of 61. c. Construct 95% confidence intervals for [3'0 and 31. Using the following t quantiles: t(0.95,3) = 2.35,t(0.975,3) = 3.18,t(0.95,4) = 2.13,t(0.975,4) = 2.78. d. Is there a linear relation between x and y? Justify your