Lab 4 Objective
To achieve more experience with hypothesis testing and gain
Familiarity with regression.
Regression is amazingly popular. You will see it everywhere. Understand how to interpret the coefficients in regression is probably one of the most important things you’ll learn in this class.
Questions:
Read in the dataset useconstat from the website, then answer the following 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.
10) Does the scatter plot of GDP against Long Term Interest Rate 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.