Professor Paul Palley's
          Economics Seminars

Regression analysis is a valuable tool for modeling purposes, forecasting and analyzing trends, and estimating. Along with analysis of variance (ANOVA) it is one of the most often used statistical tools in business. The following is a brief description of other examples.

One example is the use of regression analysis in analyzing the pricing decisions of businesses and consumers. This is called hedonic pricing; a price determination model in which the price of a product reflects the value of the attributes of that product as determined by consumers. Regression analysis facilitates this analysis because it allows analysts to quantify the relationship between a dependent variable and the independent variables that determine or affect the value of that dependent variable. In other words a mathematical formula is produced by regression analysis that defines the relationship between the dependent variable and independent variables. An example like this which illustrates hedonic pricing is that of the value or price of a house.

The value of a home is dependent on many factors including; the size of the livable area of the home, size of the garage, size of the lot, number of bedrooms, number of bathrooms, whether or not there is a pool, the quality of the school district, etc. It is reasonable to assume that each of these should positively impact the value of a home. For example, the greater the size of the livable area of the home then it is logical to assume that the price of the home will be higher. It is also reasonable to assume that a pool adds value and so does better schools. The question is how much does each additional square foot of livable add to the price of a home? Multiple regression analysis will allow the analyst to use sample data to produce a regression equation in which the value of the home is the dependent variable and each of the factors listed above are the independent variables. Then a regression equation will be produced and the analyst will have a very good estimate regarding, for example, how much a pool adds to value.

Another example is found in finance. It is reasonable to assume that the price per share of stock issued by a particular firm is dependent on the firm’s earnings per share, interest rates, and the overall performance of the stock market as measured by the S&P 500. It is logical to assume that when a firm’s earnings per share increases than the stock price should increase. Higher interest rates will usually lead to lower stock prices because investors may think they will earn more by owning bonds and because the expected value of future earnings and dividends will be lower. Finally, the prices of the shares of stocks issued by firms will increase when the stock market performs better. The question for analysts to answer is related to how much each of these factors contributes to changes in share prices. The Beta or coefficient related to the affect of the overall stock market on the price per share is a key variable finance professionals focus on. A positive Beta or coefficient related to this independent variable means that a stronger stock market positively affect the price per share issued by a firm.

There are many other applications of regression analysis. I use it to create models that I use to forecast the amount of water the City of Phoenix sells through its water utility, and I also forecast water revenues as well. Social scientists use regression analysis to explain changes in the crime rate. It probably makes real sense that a better economy with a truly strong labor market leads to less crime. Regression analysis allows the analyst to quantify these relationships. We also see regression analysis used to create models that used to produce forecasts as well. Now, it is easy to poke fun at the quality of these forecasts, but it is true that no person can anticipate everything. Who could have predicted the events of September 11 or the excessively high stock prices of the late 1990s and 2000 that led to the stock market crash? The point is that these forecast models allow for sensitivity analysis in which the analyst can evaluate the impact of changes in the values of the independent variables and also allows for a detailed and analytical framework to evaluate deviations from forecasts.

There are two ways in which we define statistics. One definition we use is to say that statistics is the science of inference. This definition focuses us on the fact that we use sample data to arrive at inferences or conclusions about the population we are interested in. A second and more detailed definition is to say that statistics is the science of collecting, organizing, presenting, interpreting, and analyzing data. This post focuses on collecting data, and more specifically on proper random sampling.

A random sample is one where the sample is collected in a way that every possible sample of a given sample size has an equal chance of being selected. As we know there are four different types of random samples; simple, stratified, cluster, and systematic. The definitions for each of these are easy to identify, but I want to focus here on another key point. An important point is that a sample that is not collected using a true random sampling approach, and in which the sample is not collected from the population that the researcher is interested in, will not facilitate statistical inference. The data will not contribute to the efforts of an analyst to make smart decisions.

One way to look at this is to look at cases where samples have been collected poorly because this illustrates the point very well. An example based on a true story is related to a record store in a mall. Suppose the manager of a record store in a mall gives one of his employees, a sixteen year old boy, a survey to have customers in the mall fill out. The purpose of the survey is to assess interest in different types of music. Who will this employee ask to fill out the survey? He will likely ask other people in his age group, and will most likely ask girls in that age group. The problem is that this group does not necessarily represent the population they are interested in. The story further indicated that the record store chain hired a consultant to investigate their declining sales. One factor was music downloading, but the consultant also found that while teenagers shop in record stores more often than older people, in fact older people who shop less actually spend more money. The result is that now you see the music industry selling more box sets, DVDs of concerts, and best of CDs or essential collections. These more expensive products are more likely to be purchased by older customers.

The point here is that if a sample is not taken correctly from the population of interest then the data will not facilitate efforts to analyze and interpret the data in a way that leads to smart decisions. The point of statistical inference is to lead to accurate assessments of the population of interest. In terms of marketing efforts, which would be the focus of the record industry, poor research would not allow the industry to analyze the relationship between the characteristics of customers and their interest in products. If this is not assessed well then this will result in the industry having a more difficult time targeting their marketing efforts.

Given uncertainty related to the strength of the economy it is understandable that people look to experts for forecasts. One very good resource is the National Association for Business Economics (NABE). The May 2008 NABE Outlook (see: http://www.nabe.com/) anticipates gradual improvement in the credit and housing markets, and meager economic growth with gradual improvements in economic growth later this year. The forecast represents the consensus of macroeconomic forecasts that have been prepared by a panel of 52 forecasters.

The current forecast is for real GDP to grow at an annual rate of 2.1% during the second half of 2008, and steady economic growth equal to 2.9% in 2009. The housing market is the primary reason for the current weakness of the economy and is expected to continue to be weak through 2009 with below trend levels of housing starts and declining home prices into 2009. However, the housing market is expected to bottom out this year and credit conditions are expected to improve

The strength of the dollar is important to those who are interested in traveling and those who import and export goods and services. The economists expect the dollar to gradually strengthen through 2009. The reasons may include the expectation that exports from the U.S. will continue to increase while the economy strengthens, and interest rates in the U.S. are expected to increase.

The consensus of the economists who were surveyed by NABE is that the Federal Reserve will not raise the federal funds rate target this year, but that it will raise it to 3.00% by the end of 2009. The expectation is that long-term interest rates will also increase. The yield on the 10-year Treasury note is expected to end 2008 equal to 4.00% and increase to 4.50% by the end of 2009. This is good news because this combined with forecasts of lower rates of inflation indicates the expectation of steadier economic growth next year.

There are other very good resources on the internet for forecasts related to the economy and specific economic indicators. Among the good resources include websites for the Congressional Budget Office (http://www.cbo.gov/), Mortgage Bankers Association (http://www.mbaa.org/), National Association Home Builders (http://www.nahb.org/), Freddie Mac (http://www.freddiemac.com/), and RSQE Forecasts (http://www.umich.edu/~rsqe/).

There are a number of factors that have led to the weaker dollar, including the persistent trade deficits we run. One other important factor that contributed to the decline of the value of the dollar is lower interest rates. We also know that the weaker dollar has been an important factor that has contributed to higher oil prices. The dollar lost 10% of its value since the beginning of calendar year 2007 through March 2008. Oil prices rose 70% during the same period. At the same time the Federal Reserve’s target for the federal funds rate has dropped from 5.25% to 2.25% in order to stimulate economic growth. Then in April, the Federal Reserve dropped this rate to 2.00%, but signaled that it will proceed far more cautiously as it may be more focused on fighting inflation. This makes sense because the rate reductions have contributed to the weaker dollar and as a result to higher commodities prices including agricultural commodities and oil.

The weak dollar contributes to higher oil prices because oil is priced in the commodities market in dollars. A weaker dollar thus leads oil producers to restrain output in order to raise the market price. Furthermore, a weaker dollar will make oil more affordable to people in other countries, and the resulting increase in demand pushes prices up further. Supporting this point, OPEC President Chakib Khelil supported the link between the weaker dollar and higher oil prices by estimating that if the dollar strengthened by 10% the price of a barrel of oil may fall $40 from the current price in excess of $113 (as of April 30, 2008). In fact, oil prices had dropped from nearly $119 because of increases in supply and also perhaps in anticipation of this Federal Reserve policy. The quickest way to increase the value of the dollar would be higher interest rates in the U.S.

Factors related to supply and demand independent of the value of the dollar and interest rates also contribute to the high oil prices. The fact is that global demand for oil continues to increase despite the higher prices. Economic growth in Asia and the Middle East is triggering an increase in demand for oil as more people drive cars and their economies grow. On the other hand, for varying reasons supply from Russia, the United Kingdom, Norway, and Mexico is declining. At the same time, OPEC countries want to produce more but are having a difficult time doing so due to their available reserves, the time it takes to build the infrastructure necessary to increase output, and the war in Iraq restrains production in Iraq.

There are also demand side factors peculiar to the United States. An example is the relatively low price we pay for gasoline. While gas prices appear to be high to us (the average price of a gallon of gas was around $1.00 in 2001, and below $2.00 per gallon in February 2005), they are very low compared to other countries. The price of a gallon of gas is over as of the end of April 2008 was $8.00 per gallon in most of Europe compared to about $3.45 in the U.S. In fact price of a gallon of gas was about $8.45 in the United Kingdom. These relatively low prices in the U.S. led to bigger cars making us more greatly affected by higher gas prices. Gas prices are lower here because gas taxes are much lower in the U.S. than in Europe (the federal tax on gasoline in the U.S. is only about 18 cents per gallon). In exchange for the higher gas taxes in Europe which are meant to restrain the use of gasoline Europeans get infrastructure, including mass transit infrastructure, cheaper health care, and other social programs. Depending on the country you look at, Europeans have also seen their oil consumption either remain unchanged or drop over the last twenty years, but in the U.S., oil use is up over 20%.

Another important contributor to demand is the relatively low price elasticity of demand for gasoline in the U.S. The Congressional Budget Office (CBO) study, Effects of Gasoline Prices on Driving Behavior and Vehicle Markets (see: http://www.cbo.gov/doc.cfm?index=8893) raises very interesting points about how Americans actually respond to higher oil and gas prices. For this study, the CBO gathered data over the 2003 to 2006 period. Among the interesting points made in this CBO study is that as gas prices increase 50 cents a gallon freeway trips fall by only 0.7% where transit is an available substitute, and speeds only fell three-quarters of a mile per hour. Furthermore, we are less responsive to changes in the price of gasoline than we were in the 1970s and 1980s. The reasons include; our high real incomes, the small increases in gas mileage we have now, and the effect of urban sprawl. As such, the price elasticity of demand for gasoline demonstrates that a 10% increase in the price of gasoline leads to a reduction is gasoline consumption of only 0.6% in the short-run (demand is very price inelastic). In the long-run, assuming we are able to more easily shift to mass transit and cars that are more fuel efficient, an increase in price equal to 10% may lead to a decrease in gasoline consumption of approximately 4%.

There are other good resources available to you to learn more about the energy markets. A good resource for analysts is the U.S. Department of Energy. The link is: http://www.energy.gov/. The Energy Information Administration is an agency of the U.S. Department of Energy responsible for producing forecasts and analysis that is policy-neutral and promotes a better understanding of the energy markets. The link is: http://www.eia.doe.gov/. Another very good resources is the International Energy Agency is a very good resource for those interested in issues related to energy, and also related data and statistics: http://www.iea.org/.