w steps pls

The textbook explained a positive correlation between X,andui for 1>0 through an argument that started from "imagine that ui is negative." Repeat this exercise here and show that there is a positive correlation between X1 and ui for 1>0. ( 3 points) 9. Several authors have tried to measure the "persistence" in U.S state unemployment rates by running the following regression: uri,t=0+1uri,tt+zi,t where ur is the state unemployment rate, i is the index for the i-th state, t indicates a time period, and typically k10. (a) Explain why finding a slope estimate of one and an intercept of zero is typically interpreted as evidence of "persistence." ( 2 points) (b) You collect data on the 48 contiguous U.S. states' unemployment rates and find the following estimates: ( 2 points) ui.1995=2.25+0.60uri.1970;R2=0.40,SER=0.90(0.61)(0.13) Interpret the regression results. c) Analyzing the accompanying figure, and interpret the observation for Maryland and for Washington. Do you find evidence of persistence? How would you test for it? (2 points) XLS=0+1Xit1+(viswis1) It is not too hard to show that estimation of the observed unemployment rate in period t on the unemployment rate in period (tk) by OLS results in an estimator for the slope coefficient that is biased towards zero. The formula is ^11x2+r2r2. Using this insight, explain over which periods you would expect the slope to be closer to one, and over which period it should be closer to zero. (2 points) Estimating the same regression for a different time period results in uar.ses=3.19+0.27xar(0.56)(0.07) If your above analysis is correct, what are the implications for this time period? (I point) The textbook explained a positive correlation between X,andui for 1>0 through an argument that started from "imagine that ui is negative." Repeat this exercise here and show that there is a positive correlation between X1 and ui for 1>0. ( 3 points) 9. Several authors have tried to measure the "persistence" in U.S state unemployment rates by running the following regression: uri,t=0+1uri,tt+zi,t where ur is the state unemployment rate, i is the index for the i-th state, t indicates a time period, and typically k10. (a) Explain why finding a slope estimate of one and an intercept of zero is typically interpreted as evidence of "persistence." ( 2 points) (b) You collect data on the 48 contiguous U.S. states' unemployment rates and find the following estimates: ( 2 points) ui.1995=2.25+0.60uri.1970;R2=0.40,SER=0.90(0.61)(0.13) Interpret the regression results. c) Analyzing the accompanying figure, and interpret the observation for Maryland and for Washington. Do you find evidence of persistence? How would you test for it? (2 points) XLS=0+1Xit1+(viswis1) It is not too hard to show that estimation of the observed unemployment rate in period t on the unemployment rate in period (tk) by OLS results in an estimator for the slope coefficient that is biased towards zero. The formula is ^11x2+r2r2. Using this insight, explain over which periods you would expect the slope to be closer to one, and over which period it should be closer to zero. (2 points) Estimating the same regression for a different time period results in uar.ses=3.19+0.27xar(0.56)(0.07) If your above analysis is correct, what are the implications for this time period? (I point)