# DMtutorial7 - g x 3 In the ﬁrst question if x i just...

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Tutorial 8 1. suppose we have sample ( x i ,y i ) ,i = 1 ,...,n . we estimate the regression model y i = g ( x i ) + ε i , where g ( x ) is a spline function of the form g ( x ) = J +4 X j =1 β j B j ( x ) (a) Estimate the derivative g 0 ( x ) of g ( x ) (b) ﬁnd the 95% conﬁdence band for g 0 ( x ). 2. suppose we have sample ( x i , z i ,y i ) ,i = 1 ,...,n . we estimate the regression model y i = β 0 + β 1 z i + g ( x i ) + ε i and g ( x ) is a spline function of the form g ( x ) = J +4 X j =1 β j B j ( x ) (a) write the expression for the estimator of g ( x ) (b) ﬁnd the 95% conﬁdence band for
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Unformatted text preview: g ( x ). 3. In the ﬁrst question, if x i just takes m ( < n ) values. what is the maximum number of knots you can use to estimate the regression function g . 4. Consider data A (the ﬁrst column is Y and the others X ). ﬁt a “best” generalized additive model to the data and plot the estimated functions with 2 times standard error conﬁdence bands. predict data B . 1...
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