1. Suppose we regress y on m with the following nonparametric model y = m(m) + E. To estimate m(:n), we approximate it by spline functions m) =15 0 4:8 is: +8 2x2 476 3x3 as m 0-301 as 5(22 0-5): as as: 0-7):- Based on dataTUA.dat and use package "hn" in R to (a) Estimate the model and write down the regression function m(a:) (b) Using t-test1 check whether the model can be simplified? if yes, write down your simplied model. (c) To answer whether m(m) indeed varies with 9:, we need to test whether H0 :m(a:) E a constant Base on the data, use Fstatistics to test Hg with signicant level 0.05. (d) For a sequence of x values 0,0.1,0.2, 0.3,0.4,0.5,0.6,0.7,0.8,U.9,1 predict the expected yvalues and its 95% condence intervals 2. We need to estimate the regression model y; :5 0 +5 12,; + g(x,,) + a; and g(m) is a spline function of the form J+4 9(3) = B ij(3') j=2 where 33- (at) is dened as above. (a) Write the expression for the estimator of g(m) (b) Find the 95% condence band for g(m) (c) For dataTOBdat, please fit the model by choosing two knots at 0.3 and 0.6 using package 'lm' in R. (d) Based on the data and the model test the following hypothesis with a = 0.05. Hi=0 HG :g(m) E a constant