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 0 1x 2x2 appears to be appropriate (b) Write out the analysis of variance table using the fact that SSE 39 0 (c) The parameter estimates are 0) 18 18 0 44 90, and 2 44 08 The standard error of 2 is s e ( 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

Question: 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

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.

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