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Regression analysis Involving 30 observations, the following estimated regression equation was obtained y = 17.6 '811 2.332 7.623 + 2.724 For this estimated re...

Question

Regression analysis Involving 30 observations, the following estimated regression equation was obtained y = 17.6 '811 2.332 7.623 + 2.724 For this estimated regression equation SST 1805 and SSR = 1,760 _ a. At a = 0.05 _ test the significance of the relashlonship among the variables.SSEdecimal, If necessary)MSRdecimal, if necessary)MSEdecimals_ necessany )What Is the value of the test statistic (to declmal)? Use TableAppendixWhat the P-value?Eelcc vour .ueWeiUslng what Sticc Yur Mutwcvour c

regression analysis Involving 30 observations, the following estimated regression equation was obtained y = 17.6 '811 2.332 7.623 + 2.724 For this estimated regression equation SST 1805 and SSR = 1,760 _ a. At a = 0.05 _ test the significance of the relashlonship among the variables. SSE decimal, If necessary) MSR decimal, if necessary) MSE decimals_ necessany ) What Is the value of the test statistic (to declmal)? Use Table Appendix What the P-value? Eelcc vour .ueWei Uslng what Sticc Yur Mutwc vour conclusion? and the following estimated regression equation obtalned: Suppose varlables T, and T are dropped from the mode 11.1 3.612 8.lx3 For this model SST 1805 and SSR 1,705 Compute SSE(T,, Tz, I4 I4) declmal, necessany) Compute SSE(T2, *j) declmal; necessary) Use an F test and 05 to determlne whether and contrIbute signlficantly to the modol. What the value orthe tost statistic (to declmal:)? Usa Table Appendix What the p-value? Suled Yun 4scr Wnat your conclusion about the two variable: and I4? Sheclyout Cannat conclude that these vat lables contibute signiticantly madly Conclme tni these vanable * contributd eigulicantly to the modd



Answers

Use the data in MURDER for this exercise.
(i) Using the years 1990 and 1993 , estimate the equation
mrdrte$_{i t}=\delta_{0}+\delta_{1} d 93_{t}+\beta_{1}$ exec $_{i t}+\beta_{2}$ unem $_{i t}+a_{i}+u_{i n}, t=1,2$
by pooled OL.S and report the results in the usual form. Do not worry that the usual OLS
standard errors are inappropriate because of the presence of $a_{i}$ . Do you estimate a deterrent
effect of capital punishment?
(ii) Compute the FD estimates (use only the differences from 1990 to 1993 ; you should have 51 observations in the FD regression). Now what do you conclude about a deterrent effect?
(iii) In the FD regression from part (ii), obtain the residuals, say, $\hat{e}_{i} .$ Run the Breusch-Pagan regression $\hat{e}_{i}^{2}$ on $\Delta$ exec $_{i},$ \Deltaunem, and compute the $F$ test for heteroskedasticity. Do the same for the special case of the White test $\left[$ that is, regress $\hat{e}_{i}^{2}$ on $\hat{y}_{i}, \hat{y}_{i}^{2},$ where the fitted values are from \right. part (ii) $]$ . What do you conclude about heteroskedasticity in the FD equation?
(iv) Run the same regression from part (ii), but obtain the heteroskedasticity-robust $t$ statistics. What happens?
(v) Which $t$ statistic on $\Delta$exec$_{i}$ do you feel more comfortable relying on, the usual one or the heteroskedasticity-robust one? Why?

Part one. This is the result of the simple regression equation. The estimate on education is 0.1 oh one with a standard barrel of 10.7 This variable is highly significant, and you can calculate the 95% confidence interval of the return to education as a range of from 8.7% to 11.5%. Recall that the 95% confidence interval is calculated as the estimate plus or minus the margin of error and the margin of error is the standard error times a critical value. We need to look at the alpha level of 5% because we need the 95% confidence. Yeah, you should have the alpha level because this is a two sided interval. The degree of freedom is the number of observations minus two. We need to degree of freedom or two pieces of information to estimate the slope. And there, uh, the to intercept the intercept and the slope coefficient. So this is what you get. Part two. The simple regression of education on C two. It gives the variable see to it is not significant. The T statistic, which is the ratio of the estimate over the standard error is minus 0.59 And so we cannot use see to it as an instrument for education. Part three. The multiple regression equation estimated by L s is as follows. The coefficient on education is 1.137 experience 0.11 to experience square point oh three. And we have other factors which are not our main focus in this problem. Mhm, even the estimate on education. You can see that the estimated return to education is now higher 13.7%. We convert the estimate on education 2% because our dependent variable, the left hand side variable is in log and education is in level Part four in the multiple regression above. In part two. Mm hmm. No. The one with other explanatory variables. In part three, the coefficient on C two. It is minus point 165 Yeah, and the T statistic is minus 2.8. So an increase of $1000? Yeah. In institution reduces years of education by about Hong 165 Remember that the Tunisian variables are measured in thousands. Part five. Now we estimate the multiple regression model by Ivy using See to it as an I V for education. The I V estimate of beta education is point 25 with a standard error of 250.1 to 2. The point estimate seems large, but the 95% confidence interval is very white from 1.1% to 48.9%. We could reject the value zero for beta education, but this confidence interval is too white to be useful. Lastly, part six very large standard error of the Ivy Estimate in Part five shows that the ivy analysis is not very useful. Yeah, and see to it is not convincing as an I V, as we can see also from part two mhm.

First one. The test for a unit root in series you rate unemployment rate using the usual dickey fuller test with a constant yeah. And the augmented dickey fuller with two legs of change of unemployment rate. I find that seven both times we are unable to reject the now hypothesis that unemployment rate series is a unit fruit. The legs are not significant. However, the significance of the legs matters. So the outcome of the unit root test, we will repeat what we have done in part one two series vacancy rate and report the result in part two. I guess similar result. So the rate is a unit root. Well part one and two. I use package the R. Package A. T. S. A. And the function is a D. F. Dot test. R. Three. We assuming that unemployment rate and vacation re rate are both integrated of level one. We test for co integration using the angle grandeur test with no legs. So the step the steps are as follow. We first regress, you read on the rate then we yet the residual and we run the key fuller has on the residual to see whether the residuals our unit root. I find that you're right and we rate Arco integrated at the 5% level. Yeah Heart Forest. I get the leads and lacks estimator of the change in vacancy rate and I did note that uh CB rates up minus one. This is for the lack and plus one is for the lead. This is a regression result. So the usual centered errors are in green and in round brackets, the robots that Iran's are in blue and in square brackets you can see that the main estimate on vacancy rate is highly significant. This one is not correct. So the centered errol the usual one for the estimate of the first lack of change in vacancy rate is 164 In all cases except for the estimate of the lead of C. V. Right. The robust standard Iran's are larger than the usual standard errors. This is usually the case it happens but rare that the robot standard errors are smaller than the usual standard errors. The r square of this regression is 0.77 So for the rate, because the robot standard error is larger than the usual standard error. So we will get a wider confidence interval if we use a robot standard error and for confidence interval you will run this function in our count in and you impose the name of the regression. It was spits all the 95% confidence intervals for all explanatory variables. The default version is the 95% interval. But because the standard barrel of this estimate is are very close, two versions are very close to each other so the confidence intervals should be roughly equal. Yeah. Last part. What you could say about real business of the claim that you rate and the rate are co integrated. Yeah. When I run the test and good grandeur, the results are not consistent across alternative types of process. In one case I can reject the notion that the residuals are united and for all the cases I cannot reject. So I conclude that the claim that you rate and be rate our co integrated is not robust.


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