1 w s the mean of x t is thus δ δ 1 t we might be

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=1Ws. Themean ofXtis thusδ0+δ1t. We might be interested in estimating this (linear) regression function.(a) Uselm()to regress the (untransformed) oil series on time. Print thesummary()of the resultsand plot the data with the regression line. Comment briefly on the statistical significance of thecoefficients.(b) Compute by hand the F-statistic for testingH0:δ1= 0 againstHA:δ16= 0 (i.e., for testingwhether there is a drift) and the correspondingp-value by comparing to the appropriate F-distribution (see?FDist). Check your result matches the F-statistic reported bysummary().(c) Compute also the regression with the quadratic time term, corresponding to the modelE(Xt) =δ0+δ1t+δ2t2(this does not correspond to the random walk with drift model, so is a slightdigression).Compute the F-statistic andp-value for testingH0:δ2= 0.Notice that thisshould match the result of thep-value for the quadratic term reported bysummary(). (For eachcoefficient,summary()reports results of testing that coefficient to be 0 in a model where all the

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