Homework 2 100 points 1 40 points The file Corruption xls contains country level data on two variables One of these is a measure of perceptions of political corruption This data is assembled by the organization Transparency org NOTE I have modified the original corruption measure so that higher values mean higher corruption The least corruption possible has a measure of 0 the highest a measure of 10 The second variable is a measure of GDP per capita a 10 Before looking at any data propose a simple economic story model for how these two variables might be related Write a paragraph of no less than 50 words in which you explain your argument Which is the independent and which is the dependent variable in your model Plausible stories could be told in which either variable could be the independent or dependent variable Such a story might go like this When a country is poor low GDP per capita its people are poor When people are poor they are more likely to be desperate People with some power like the police or a local politician may be poor and desperate too and try to extort money from those they have power over Also the poor desperate populace may be more willing to pay bribes or protection money to preserve the little they have In sum low per capita GDP leads to more corruption Or a story might go like this Corruption may interfere with ordinary market function For instance if you have to say bribe a local official in order to open up a bakery this corruption is an impediment to free entry exit a cornerstone of the market system It can also artificially raise the costs of doing business and deter investment activity both domestically and from abroad These consequences of a corrupt political system can adversely effect productivity growth and GDP per capita In sum more corruption leads to lower GDP per capita Or it might be something else more clever b 20 Whichever way you ve chosen to model this problem execute a linear regression calculating the slope and intercept estimators in EXCEL or Google Spreadsheet using the by hand method that was demonstrated in the lectures Report your Betahats SEE BELOW YOUR BETAS AND OTHER KEY RESULTS SHOULD BE SEPARATED FROM THE DATA SO THEY RE EASY TO SEE c 10 What percentage of the variation of your dependent variable is explained by the independent To submit this problem include 1 the writeup of part a 2 a summary table that contains the important bits like your slope intercept R2 terms SST SSE etc 3 your excel spreadsheet containing your dataset and any variables or other calculations you used along the way Try to format 3 so it doesn t take up 20 pages It s OK if the spreadsheet part is small but not invisibly small See attached spreadsheet I ve hidden a lot of the data so I could fit it all on one page but basically a totally correct homework will have all of the information for one of the two versions of the regression NOT BOTH Some students may use different intermediate variables than I have chosen If the calculations are right and the supporting information is there that s all I care about d 10 Suppose the corruption measure was flipped That is the least corruption possible is rated a 10 and the highest corruption level is zero Argentina for instance was originally 8 is now 2 Australia was originally 1 3 and is now 8 7 Describe how this will change the R2 slope and intercept of your regression from above If you can do this without recalculating the whole regression that would be prefered To start write out a simple formula to describe this transformation Then apply the transformed variable to the slope intercept formulas for the regression The change I have described is equivalent to a transformation of the corruption variable C1 into C2 where C2 10 C1 This is a linear transformation This will not change the strength of the linear relationship at all between corruption and GDP so the R2 is unchanged How will the slope change This will depend on whether corruption is the dependent or independent variable Each student should work out one of these versions GRADERS TO GET FULL MARKS STUDENTS NEED TO HAVE AT LEAST SOME OF THE MATH BUT GIVE 8 POINTS FOR MORE INTUITIVE EXPLANATIONS ON THIS PROBLEM a If independent then C is the X variable in the regression Originally Now if we let denote the betahat value after the transformation Makes sense since all we did was turn the X variable on its head so the relationship should be the same but backwards For this problem that means the slope is 000177 The slope is equal but of opposite sign as the original The intercept will be which here is 9780 89 This change is a little tricky to decipher Essentially the intercept term is shifting to account for the flip in the sign of the regression line The direction of the shift will depend on whether beta1hat is positive or negative and its size b If instead corruption was the Y variable the effect on the slope is exactly the same as above The intercept also has to adjust transformation of C or 000177 or 3 153 The shift of the intercept is exactly the same as the I confirmed all these results by rerunning the regressions with the transformed values of corruption corrup Either version of the regression is fine Version a in which we regress corrup on gdp cap country Argentina Australia Austria Belarus Belgium Zimbabwe 8580 1 3 20930 21 2 5 26577 11 7 3 2112 4 6 25006 05 7 5 653 8 gdp cap corrup d 2 gdpcap d 2 corrup d gdpcap d Yhat Y Yhat 2 8 064 14 901 7 077 4 579 0 314 5 474 905 430 247 129 929 655 301 290 551 423 027 55 049 588 436 239 460 429 239 78 828 490 032 2702 15 5 328615 44001 61 3 143264 45345 32 2 144053 15876 03 6 473118 8669 45 2 42205 20773 65 6 731285 7 136299382 3 397620913 0 126698116 0 683734568 4 743466586 0 590922117 Avgs sums 5 160240964 9531 541 490 039 11 050 880 223 600 1955436 60 144 027 corrup Version b in which we regress gdp cap on corrup country Argentina Australia Austria Belarus Belgium Zimbabwe 8580 1 3 20930 21 2 5 26577 11 7 3 2112 4 6 25006 05 7 5 653 8 gdp cap corrup d 2 gdpcap d 2 corrup d gdpcap d Yhat Y Yhat 2 8 064 14 901 7 077 4 579 0 314 5 474 905 430 247 129 929 655 301 290 551 423 027 55 049 588 436 239 460 429 239 78 828 490 032 2702 15 1800 15 44001 61 24935 33 45345 32 20146 89 15876 03 993 1086 8669 45 11767 11 20773 65 195 0344 107747538 16041023 29 41347736 78 1251918 068 175269524 7 209732 5353 Avgs …