Statistics W1111
Columbia University
 

Instructions for lab 2

Part 1:

Long-term interest rates drive much of the economic activity in the U.S.  When interest rates are low, people and establishments are more likely to borrow money for purchasing homes or growing their businesses.  When interest rates are high, people and establishments are less likely to do so.  In this lab, we'll work with economic data from the U.S. from 1980 to 1998 to explore relationships involving interest rates.

Open the data file USeconstat.  The data are culled from the 1997 Organization for Economic Cooperation and Development economic outlook report.  There are dozens of variables, but we'll only use a small number.  For convenience, all the relevant variables are among the first few columns in the Stata file.

IMPORTANT CAVEAT FOR ALL ANALYSES:   One can look at many relationships with economic (or any) data.  It is tempting to assign causal explanations to those relationships.  This is risky.  Just because there is (or is not) a relationship between two variables, it does not mean there is (or is not) a causal relationship between those variables.   There could be many other factors that affect both variables, and these could explain what is seen in the graphs.

Questions:
1)  Describe the distribution of long-term interest rates.  That is, say where most values are, note any outliers, and say whether the distribution is tightly packed around its mean or is spread out.  Also, report the mean and standard deviation. 

2)  Long-term interest rates right now are around 4.5%.  Describe how 4.5% compares to the historical record of long-term interest rates from 1980 -1998.

3)  Using the data, describe the relationship between long-term and short-term interest rates.   Include in your descriptions a one-number summary of the strength of the association between the two variables.

4)  Using the data, describe the relationship between long-term interest rates and unemployment rates.  Include in your descriptions a one-number summary of the strength of the association between the two variables.

5)  Using the data, describe the relationship between long-term interest rates and gross domestic product (market prices).  Include in your descriptions a one-number summary of the strength of the association between the two variables.

6)  Of the following two variables, which one has the weaker linear association with long-term interest rates:  (i) wage rate in business sector; or (ii) net lending, government?  Explain your choice in one sentence.

7) Suppose you had a model that gave reasonable predictions about long-term interest rates in the next year. (This is fantasy: interest rates are notoriously hard to predict.  You'd be a billionaire many times over if you come up with a good prediction model.  Believe me, there are many statisticians and economists trying to do so!)  Suppose you predict that interest rates next year will be 6.0%.  Predict gross domestic product (market prices) for next year using a regression line to make your prediction.

To fit a regression line, go to Statistics--Regression and Related--Linear Regression.  Select "Gross Domestic Product (Market Prices), Value" as the dependent variable and "Interest rate, Long-term" as the X (independent) variable.  The intercept and slope of the regression line are the values in the column of the table labeled Coef.  We'll talk about the values in the other columns, as well as the values in the other tables, later in the course.

8) What's the slope of the regression line?  Intercept?  Write down both the numerical values and their interpretations.

9)   Does the scatter plot suggest any clearly non-linear relationships in the data?   Justify your answer in at most two sentences.

10)  If interest rates were 1%, could you use the regression equation to predict the corresponding gross domestic product (market prices)?  If you think so, write down the predicted value of GDP.  If you think not, explain why not in at most one sentence.  ONLY WRITE ONE ANSWER: WRITING BOTH ANSWERS GETS NO CREDIT.

11)  Fit another model to predict long-term interest rates for the next year.  You can choose your dependant varaible from any of the other variables in the dataset.  Write down the regression equation, the slope, intercept, and the interpretation of each.

12) Most of the time, there is more than one reasonable regression model.  How could you compare your model to the model from questions (8) and (9)?  What criteria could you use to say that your model is "superior" to the model in the previous questions?  How could you test it?  (Note: We'll talk about some methods towards the end of the semester, so no need to actually do any comparison now--just think about it and write down your thoughts.)


Unit 2:  The Correlation Challenge.

Click here for the Guess the Correlations game.   Play it at least three times against a classmate. Don't forget to talk trash if you win.  You don't have to write anything down for this part of the lab.  If you're feeling really cocky, challenge the TA.  And, if you're feel like you need to be humbled, come challenge me.  If you beat me at the correlation game, I will buy you coffee.  If I win, I will do some serious gloating.