04 Jun Some parts of the following problems will require a lot of calculations in EXCEL (or Google Spreadsheets) and STATA. It will generate many p
Question
Some parts of the following problems will require a lot of calculations in EXCEL (or Google
Spreadsheets) and STATA. It will generate many pages of output. Here is how your should
organize it. The first pages should contain your answers to all the questions below, along
with showing any key algebraic equations or explanations you need to use to justify your
answers. After that, include a printout of the output from EXCEL/STATA to support of your
answers. Highlight any numbers in this output that you used in the first section. (To save paper,
you may print this section in a small font, double-sided and/or with 2-up format.) Be sure you
organize these in a way that will be clear to the reader.
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.)
b) (10) Whichever way youve chosen to model this problem, execute a linear regression.
For one time in your life, you are going to be calculating the slope and intercept
estimators in EXCEL (or Google Spreadsheet) using the by hand method that was
demonstrated in the lectures. DO NOT USE THE BUILT IN EXCEL
REGRESSION/VARIANCE/COVARIANCE FEATURES (except to check your work,
if you desire). Report your Betahats.
c) (10) What percentage of the variation of your dependent variable is explained by the
independent?
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d) (10) Also by hand, calculate the variance of ?1 . Next, calculate the test statistic and pvalue for a hypothesis test that the population slope is zero. (The p-value is going to be
extremely small and not be on any t-table. Figure out how you can use Excel to calculate
it. (Look up the t.dist functionality in the help menus.)
2) (20 points) The last lessons have spent a lot of time describing the slope and intercept terms
(and their variances) of the one-variable sample regression function. We also know that for
any particular value of the independent variable (call it X0), that the predicted value of Y0 is
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