Statistics 101
  Data Analysis and Statistical Inference
 

Instructions for lab 4

Lab Objective

To gain more experience with histograms, box plots, correlations, and line fitting.

Lab Procedures

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.JMP.  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 JMP 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)  How did long-term interest rates change annually between 1980 - 1998?   Were they (i) generally going up; (ii) generally steady; (iii) generally going down; or (iv) all over the place?  Just write a short phrase as your answer.

4)  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.

5)  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.

6)  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.

7)  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.

8)  What is the correlation between government net borrowing and long-term interest rates?  Note that borrowing is the opposite of lending, so that net borrowing equals negative one times net lending.

9) 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 Analyze - Fit Y by X.  Select "Gross Domestic Product (Market Prices), Value" as the Y variable and "Interest rate, Long-term" as the X variable.  Once you see the scatter plot, go to the red arrow next to Bivariate Fit.   Select Fit Line.  The intercept and slope of the regression line are the values in the first column of the table labelled Parameter Estimates.  We'll talk about the values in the other columns, as well as the values in the other tables, later in the course.

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

11)  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.