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Use the data in BARIUM for this exercise.(i) Add a linear time trend to equation $(10.22) .$ Are any variables, other than the trend, statistically significant?(ii) In the equation estimated in part (i), test for joint significance of all variables except the time trend. What do you conclude?(iii) Add monthly dummy variables to this equation and test for seasonality. Does including the monthly dummies change any other estimates or their standard errors in important ways?
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(i) No (ii) Not significant (iii) No
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Basic Regression Analysis with Time Series Data
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April 25, 2021
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This is the estimation. Result of Equation 10.22. After we add a linear time trend. Peter, the list is a little bit long, so the estimate coefficients are in blue and it's standard error is in green. As you can see, almost all variables have standard, Errol larger than estimate coefficient. Except the time train. Tom train is the only variable that has. The beta had greater than standard error three times larger than the standard era. And so it would have a very high T statistic. We can easily conclude that Onley This variable is significant publications. Now, you may also notice that the variable above it has estimated coefficient larger than standard error. Yeah, this variable has 80 start slightly greater than one. It is the only variable beside the time trend to have t statistic larger than one. So this one could be significant, but very marginally, it would not be able to be significant at the 5% level. Okay, are two women test the joint significance off all variables except the time trend and the intercept? The F statistic is 0.54 The first degree of freedom is six, and the second degree of freedom is 123. The P value of this F statistic is 1230.78 Okay, Even this result, we can conclude that we are unable to reject Yeah, the non hypotheses meaning there is no God variable Other than the time train that can explain, I should stay no variable in their regression equation. So only the time trend can explain the dependent variable lark of C h N I m p hot three. Now we wonder if the monthly dummies can help improve the power of the model. We will add the monthly dummies and re estimate the equation. And we will do to tests the first test evaluate the joint significance of all variables except the time trend. The P value of the F statistic is Boeing 79 very high p value. And when we do the second test, we test the joint significance of the monthly dummies. The P value is also high 0.59 So again, we have a similar conclusion, as in part two, only time train and explain lack of c h n i m p the dependent variable
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