Consider the data set in DS 13.6.1.
(a) Plot the response variable y against the input variable x and confirm that the quadratic model
y = β0 + β1x + β2x2
appears to be appropriate.
(b) Write out the analysis of variance table using the fact that SSE = 39.0.
(c) The parameter estimates are β^0) = 18.18. β^0 = -44.90, and `β^2 = 44.08. The standard error of β^2 is s.e.( β^2) = 7.536. Verify that the quadratic term is needed in the model.
(d) What is the fitted value of the response variable when x = 1? If this fitted value has a standard error of s.e.(y^) = 1.005, construct a 95% two-sided confidence interval for the expected value of the response variable when x = 1.