Conditional Expectation Function amp; OLS Regression ( Lectures 1 ) a ) Download necessary data from http : / / www . equality- of -opportunity ....

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Conditional Expectation Function & OLS Regression ( Lectures 1 )a ) Download necessary data from http : / / www . equality- of -opportunity . org / data / and replicatehe national intergenerational mobility plot for the US in my lecture. 1 . Make sure to include bothconditional expectation dots and OLS regression lines ( fitted values )b ) Let0 1 . . 100 be a parent income rank in the national income distribution and Y , be thI be theaverage child income rank among households where the parent income rank is a . For your plot in( 2 ) , what is the matimathematical expression of each conditional expectation dot indot in terms of V . and aI and a ?What is the mathematical definition of the slope of the OLS(the OLS regression line ? What about its intercept ?Your plot in a ) shows the line of fitted valuesVIOLS = DOES + BOLSAwhere ( dots , bots ) are OLS regression coefficients . Pick any other values a * * dots and 6 * * bossand form the associated linear approximation Y+ 6+ 6 * X . Compare the approximation perfor -mance of Y , OLs and Y . by computing mean- squared approximation errors , 2 ( X x - Ya OLS ) 2 INapproximatand IM ( V = - Y ) 2 / N . Which is a better approximation isin terms of the mean- squared approximtion errors ? Which approximation would you like to you ? Why1 ) Consider the following alternative approximation to Y0.5 X X 2 + 0 . 5 ( GOES + bots * )Compare the approximation performance of Yr , OLS and Y ." by computing mean-squared approxi -mation errors , I ( Y 2 - Y 2 ,OLS ) 2 N and If ( 1 2 - Y ) 2 / N. Which is a better approximation interms of the mean- squared approximation errors ? Which approximation would you like to you ? WhyPick the commuting zone where you live and another commuting zone of your choice ( eng . the placewhere you are born , a place where you lived or you'd like to live ) . Find out the two commutingzones ' " relative mobility " and " absolute mobility " measures . What does each measure say aboutintergenerational income mobility in the two commuting zones you pick