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Use the data in FERTIL3 for this exercise.(i) Regress $g f r_{t}$ on $t$ and $t^{2}$ and $t^{2}$ and save the residuals. This gives a detrended $g f r_{t},$ say, $g \ddot{f}_{r}$(ii) Regress $g f_{t}$ on all of the variables in equation $(10.35),$ including $t$ and $t^{2} .$ Compare the $R$ -squared with that from $(10.35) .$ What do you conclude?(iii) Reestimate equation $(10.35)$ but add $t^{3}$ to the equation. Is this additional term statistically significant?

(i) See video (ii) Still much variation in detrended gfr that can be explained by the equation (iii) Yes

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Chapter 10

Basic Regression Analysis with Time Series Data

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hard one. This'd is Theis. Estimated equation. Yeah. You may say that both T and T Square are individually insignificant. Their standard errors are much larger than there estimated coefficients. However, if you run an F test for their joint significance, you may find that they are jointly highly significant. From this equation, we will get a fitted value of G R f. We call that G r f with two dot and we use the fitted value as the dependent variable following the regression equation 10 point 35 we wouldn't get the are square of 0.602 and compared with the art square from the regression when we do not be train g r f, we get that are square of 0.7 to 7. Okay. It means that even after the train, there is still much variation in G r f that can be explained by there. Equation. Okay. In part three, we win at a cubic trend to the regression. In part one, you may find that the coefficient of the quadratic Now the cubic trend is okay minus zero 0.1 to 9 and the standard error is 90.0 Oh, one night. This result to a very significant T statistic. So the cubic trend is highly significant. However, we were not sure what to make of this result.

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