A chemical Engineer wants to fit a straight line to the data found observing the tensile strength, Y, of 10 test pieces of plastic that have undergone baking (at a uniform temperature) for X minutes, where 10 values of X were preselected the data in coded units is given below. When the experiment is actually done, the results obtained are those given below. Find, Assuming n= E(Y|X) = beta0- Beta1X, the least squares estimates of beta0 and beta1 and hence the least squares estimate of n. Construct 95% confidence intervals for beta0, beta1, and n0 = beta0 +beta1x0
X (temperature): 23, 35, 45, 65, 75, 95, 105, 125, 155, 185
Y (response): 2, 9.8, 9.2, 26.2, 17.1, 24.8, 43, 55.3, 38.4, 63.3